# List of all S-integral points on all rational elliptic curves (using Cremona's database) up to conductor 100, # where S is the set of the first 10000 primes. # It contains 1724 points in total. # Format: "(x,y)". # Computing this list took 121892 seconds. # Authors: Rafael von Känel and Benjamin Matschke, 2015. # License: Creative commons 3.0 by-nc. # # a-invariants: (0, -1, 1, -10, -20) # Cremona label: 11a1 # (16,-61) (5,-6) (16,60) (5,5) # # a-invariants: (0, -1, 1, -7820, -263580) # Cremona label: 11a2 # # # a-invariants: (0, -1, 1, 0, 0) # Cremona label: 11a3 # (0,-1) (0,0) (1,0) (1,-1) # # a-invariants: (1, 0, 1, 4, -6) # Cremona label: 14a1 # (2,2) (9,23) (1,-1) (2,-5) (9,-33) # # a-invariants: (1, 0, 1, -36, -70) # Cremona label: 14a2 # (-4,5) (10,19) (-4,-2) (10,-30) (-9/4,5/8) # # a-invariants: (1, 0, 1, -171, -874) # Cremona label: 14a3 # (15,-8) # # a-invariants: (1, 0, 1, -1, 0) # Cremona label: 14a4 # (0,-1) (0,0) (1,0) (1,-2) (-1,0) # # a-invariants: (1, 0, 1, -2731, -55146) # Cremona label: 14a5 # (-121/4,117/8) # # a-invariants: (1, 0, 1, -11, 12) # Cremona label: 14a6 # (2,-1) (0,-4) (0,3) (7/4,-11/8) (2,-2) # # a-invariants: (1, 1, 1, -10, -10) # Cremona label: 15a1 # (-2,3) (3,-2) (8,18) (-2,-2) (-1,0) (-13/4,9/8) (8,-27) # # a-invariants: (1, 1, 1, -135, -660) # Cremona label: 15a2 # (-7,3) (-29/4,25/8) (13,-7) # # a-invariants: (1, 1, 1, -5, 2) # Cremona label: 15a3 # (-3,1) (1,-1) (0,-2) (0,1) (2,1) (2,-4) (3/4,-7/8) # # a-invariants: (1, 1, 1, 35, -28) # Cremona label: 15a4 # (7,-29) (32,171) (32,-204) (7,21) (2,-9) (3/4,-7/8) (2,6) # # a-invariants: (1, 1, 1, -2160, -39540) # Cremona label: 15a5 # (-109/4,105/8) # # a-invariants: (1, 1, 1, -110, -880) # Cremona label: 15a6 # (51/4,-55/8) # # a-invariants: (1, 1, 1, -80, 242) # Cremona label: 15a7 # (5,-2) (19/4,-23/8) (5,-4) # # a-invariants: (1, 1, 1, 0, 0) # Cremona label: 15a8 # (0,-1) (0,0) (-1,0) # # a-invariants: (1, -1, 1, -1, -14) # Cremona label: 17a1 # (7,-21) (7,13) (11/4,-15/8) # # a-invariants: (1, -1, 1, -6, -4) # Cremona label: 17a2 # (-1,0) (3,-2) (-5/4,1/8) # # a-invariants: (1, -1, 1, -91, -310) # Cremona label: 17a3 # (-21/4,17/8) # # a-invariants: (1, -1, 1, -1, 0) # Cremona label: 17a4 # (0,-1) (0,0) (1,-1) # # a-invariants: (0, 1, 1, -9, -15) # Cremona label: 19a1 # (5,9) (5,-10) # # a-invariants: (0, 1, 1, -769, -8470) # Cremona label: 19a2 # # # a-invariants: (0, 1, 1, 1, 0) # Cremona label: 19a3 # (0,-1) (0,0) # # a-invariants: (0, 1, 0, 4, 4) # Cremona label: 20a1 # (-1,0) (0,-2) (0,2) (4,-10) (4,10) # # a-invariants: (0, 1, 0, -1, 0) # Cremona label: 20a2 # (0,0) (-1,1) (1,-1) (-1,-1) (1,1) # # a-invariants: (0, 1, 0, -36, -140) # Cremona label: 20a3 # (7,0) # # a-invariants: (0, 1, 0, -41, -116) # Cremona label: 20a4 # (-4,0) # # a-invariants: (1, 0, 0, -4, -1) # Cremona label: 21a1 # (2,-1) (-1/4,1/8) (-1,-1) (-1,2) (5,-13) (-2,1) (5,8) # # a-invariants: (1, 0, 0, -49, -136) # Cremona label: 21a2 # (-17/4,17/8) (8,-4) (-4,2) # # a-invariants: (1, 0, 0, -39, 90) # Cremona label: 21a3 # (3,-3) (-3,15) (6,-12) (3,0) (6,6) (15/4,-15/8) (-3,-12) # # a-invariants: (1, 0, 0, 1, 0) # Cremona label: 21a4 # (0,0) (1,-2) (1,1) # # a-invariants: (1, 0, 0, -784, -8515) # Cremona label: 21a5 # (-65/4,65/8) # # a-invariants: (1, 0, 0, -34, -217) # Cremona label: 21a6 # (31/4,-31/8) # # a-invariants: (0, -1, 0, -4, 4) # Cremona label: 24a1 # (4,-6) (2,0) (-2,0) (0,-2) (1,0) (0,2) (4,6) # # a-invariants: (0, -1, 0, -24, -36) # Cremona label: 24a2 # (-2,0) (-3,0) (6,0) # # a-invariants: (0, -1, 0, -64, 220) # Cremona label: 24a3 # (6,-4) (6,4) (5,0) # # a-invariants: (0, -1, 0, 1, 0) # Cremona label: 24a4 # (0,0) (1,-1) (1,1) # # a-invariants: (0, -1, 0, -384, -2772) # Cremona label: 24a5 # (-11,0) # # a-invariants: (0, -1, 0, 16, -180) # Cremona label: 24a6 # (5,0) # # a-invariants: (1, 0, 1, -5, -8) # Cremona label: 26a1 # (4,4) (4,-9) # # a-invariants: (1, 0, 1, -460, -3830) # Cremona label: 26a2 # # # a-invariants: (1, 0, 1, 0, 0) # Cremona label: 26a3 # (0,-1) (0,0) # # a-invariants: (1, -1, 1, -3, 3) # Cremona label: 26b1 # (-1,-2) (-1,2) (1,0) (1,-2) (3,2) (3,-6) # # a-invariants: (1, -1, 1, -213, -1257) # Cremona label: 26b2 # # # a-invariants: (0, 0, 1, 0, -7) # Cremona label: 27a1 # (3,4) (3,-5) # # a-invariants: (0, 0, 1, -270, -1708) # Cremona label: 27a2 # # # a-invariants: (0, 0, 1, 0, 0) # Cremona label: 27a3 # (0,-1) (0,0) # # a-invariants: (0, 0, 1, -30, 63) # Cremona label: 27a4 # (3,0) (3,-1) # # a-invariants: (1, 0, 1, 1, 2) # Cremona label: 30a1 # (3,-8) (0,-2) (0,1) (3,4) (-1,0) # # a-invariants: (1, 0, 1, -19, 26) # Cremona label: 30a2 # (4,-7) (13,-52) (-2,8) (1,-4) (3,-2) (4,2) (-2,-7) (7/4,-11/8) (13,38) (1,2) (-5,2) # # a-invariants: (1, 0, 1, -14, -64) # Cremona label: 30a3 # (5,-3) # # a-invariants: (1, 0, 1, -69, -194) # Cremona label: 30a4 # (-4,-3) (-4,6) (14,-48) (14,33) (-25/4,21/8) # # a-invariants: (1, 0, 1, -289, 1862) # Cremona label: 30a5 # (39/4,-43/8) (16,29) (10,-7) (10,-4) (16,-46) # # a-invariants: (1, 0, 1, -334, -2368) # Cremona label: 30a6 # (-11,5) (-41/4,37/8) (21,-11) # # a-invariants: (1, 0, 1, -5334, -150368) # Cremona label: 30a7 # (-169/4,165/8) # # a-invariants: (1, 0, 1, -454, -544) # Cremona label: 30a8 # (87/4,-91/8) # # a-invariants: (0, 0, 0, 4, 0) # Cremona label: 32a1 # (0,0) (2,-4) (2,4) # # a-invariants: (0, 0, 0, -1, 0) # Cremona label: 32a2 # (-1,0) (0,0) (1,0) # # a-invariants: (0, 0, 0, -11, -14) # Cremona label: 32a3 # (-2,0) # # a-invariants: (0, 0, 0, -11, 14) # Cremona label: 32a4 # (1,-2) (2,0) (1,2) # # a-invariants: (1, 1, 0, -11, 0) # Cremona label: 33a1 # (0,0) (11/4,-11/8) (-4,2) # # a-invariants: (1, 1, 0, -6, -9) # Cremona label: 33a2 # (-2,1) # # a-invariants: (1, 1, 0, -146, 621) # Cremona label: 33a3 # (27/4,-27/8) (4,-13) (4,9) # # a-invariants: (1, 1, 0, 44, 55) # Cremona label: 33a4 # (-5/4,5/8) # # a-invariants: (1, 0, 0, -3, 1) # Cremona label: 34a1 # (0,-1) (2,-3) (0,1) (2,1) (-2,1) # # a-invariants: (1, 0, 0, -43, 105) # Cremona label: 34a2 # (8,-21) (15/4,-15/8) (4,-1) (4,-3) (8,13) # # a-invariants: (1, 0, 0, -103, -411) # Cremona label: 34a3 # (-6,3) # # a-invariants: (1, 0, 0, -113, -329) # Cremona label: 34a4 # (47/4,-47/8) # # a-invariants: (0, 1, 1, 9, 1) # Cremona label: 35a1 # (1,-4) (1,3) # # a-invariants: (0, 1, 1, -131, -650) # Cremona label: 35a2 # # # a-invariants: (0, 1, 1, -1, 0) # Cremona label: 35a3 # (0,-1) (0,0) # # a-invariants: (0, 0, 0, 0, 1) # Cremona label: 36a1 # (0,-1) (2,-3) (0,1) (2,3) (-1,0) # # a-invariants: (0, 0, 0, -15, 22) # Cremona label: 36a2 # (3,-2) (2,0) (3,2) (-1,6) (-1,-6) # # a-invariants: (0, 0, 0, 0, -27) # Cremona label: 36a3 # (3,0) # # a-invariants: (0, 0, 0, -135, -594) # Cremona label: 36a4 # (-6,0) # # a-invariants: (0, 0, 1, -1, 0) # Cremona label: 37a1 # (0,-1) (0,0) (1,-1) (1,0) (-1,0) (-1,-1) (2,-3) (2,2) (1/4,-3/8) (1/4,-5/8) (6,-15) (6,14) (-5/9,8/27) (-5/9,-35/27) (21/25,-56/125) (21/25,-69/125) (-20/49,92/343) (-20/49,-435/343) (161/16,-2065/64) (161/16,2001/64) (116/529,-3612/12167) (116/529,-8555/12167) (1357/841,28888/24389) (1357/841,-53277/24389) (-3741/3481,-162024/205379) (-3741/3481,-43355/205379) (18526/16641,-2616119/2146689) (18526/16641,469430/2146689) (8385/98596,-2882165/30959144) (8385/98596,-28076979/30959144) (480106/4225,-332788379/274625) (480106/4225,332513754/274625) (-239785/2337841,-3906507129/3574558889) (-239785/2337841,331948240/3574558889) (12551561/13608721,-41922509264/50202571769) (12551561/13608721,-8280062505/50202571769) (-59997896/67387681,-641260644409/553185473329) (-59997896/67387681,88075171080/553185473329) (683916417/264517696,14482338863553/4302115807744) (683916417/264517696,-18784454671297/4302115807744) (1849037896/6941055969,-318128427505160/578280195945297) (1849037896/6941055969,-260151768440137/578280195945297) (51678803961/12925188721,-12133184284073305/1469451780501769) (51678803961/12925188721,10663732503571536/1469451780501769) (4881674119706/5677664356225,-8938035295591025771/13528653463047586625) (4881674119706/5677664356225,-4590618167456560854/13528653463047586625) (-16683000076735/61935294530404,100886180199254542253/487424450554237378792) (-16683000076735/61935294530404,-588310630753491921045/487424450554237378792) (2786836257692691/16063784753682169,-1600059682932627475385835/2035972062206737347698803) (2786836257692691/16063784753682169,-435912379274109872312968/2035972062206737347698803) (213822353304561757/158432514799144041,41974401721854929811774227/63061816101171948456692661) (213822353304561757/158432514799144041,-105036217823026878268466888/63061816101171948456692661) (-280251129922563291422645/1262082793174195430038441,-1671718055004040020388958925246733656/1417854835344178787714550500916300011) (-280251129922563291422645/1262082793174195430038441,253863219659861232674408424330433645/1417854835344178787714550500916300011) (-804287518035141565236193151/1063198259901027900600665796,8921582208740800454475419505849438719515/34667409118422632032070193604742966179656) (-804287518035141565236193151/1063198259901027900600665796,-43588991327163432486545613110592404899171/34667409118422632032070193604742966179656) # # a-invariants: (0, 1, 1, -23, -50) # Cremona label: 37b1 # (8,18) (8,-19) # # a-invariants: (0, 1, 1, -1873, -31833) # Cremona label: 37b2 # # # a-invariants: (0, 1, 1, -3, 1) # Cremona label: 37b3 # (1,0) (1,-1) # # a-invariants: (1, 0, 1, 9, 90) # Cremona label: 38a1 # (0,-10) (0,9) # # a-invariants: (1, 0, 1, -86, -2456) # Cremona label: 38a2 # # # a-invariants: (1, 0, 1, -16, 22) # Cremona label: 38a3 # (2,-1) (2,-2) # # a-invariants: (1, 1, 1, 0, 1) # Cremona label: 38b1 # (1,1) (1,-3) (-1,-1) (-1,1) # # a-invariants: (1, 1, 1, -70, -279) # Cremona label: 38b2 # # # a-invariants: (1, 1, 0, -4, -5) # Cremona label: 39a1 # (2,-1) (-5/4,5/8) (-2,1) # # a-invariants: (1, 1, 0, -69, -252) # Cremona label: 39a2 # (-21/4,21/8) # # a-invariants: (1, 1, 0, -19, 22) # Cremona label: 39a3 # (6,10) (11/4,-11/8) (6,-16) # # a-invariants: (1, 1, 0, 1, 0) # Cremona label: 39a4 # (0,0) # # a-invariants: (0, 0, 0, -7, -6) # Cremona label: 40a1 # (-1,0) (-2,0) (3,0) # # a-invariants: (0, 0, 0, -107, -426) # Cremona label: 40a2 # (-6,0) # # a-invariants: (0, 0, 0, -2, 1) # Cremona label: 40a3 # (0,-1) (0,1) (1,0) # # a-invariants: (0, 0, 0, 13, -34) # Cremona label: 40a4 # (7,-20) (2,0) (7,20) # # a-invariants: (1, 1, 1, -4, 5) # Cremona label: 42a1 # (-1,3) (1,-3) (-3,1) (1,1) (5,9) (-1,-3) (5,-15) # # a-invariants: (1, 1, 1, -84, 261) # Cremona label: 42a2 # (7,5) (3,-9) (-11,5) (19/4,-23/8) (5,-3) (7,-13) (3,5) # # a-invariants: (1, 1, 1, -104, 101) # Cremona label: 42a3 # (9,-5) (1,-1) (-45/4,41/8) # # a-invariants: (1, 1, 1, -1344, 18405) # Cremona label: 42a4 # (21,-9) (21,-13) (83/4,-87/8) # # a-invariants: (1, 1, 1, -914, -10915) # Cremona label: 42a5 # (-77/4,73/8) # # a-invariants: (1, 1, 1, 386, 1277) # Cremona label: 42a6 # (-13/4,9/8) # # a-invariants: (0, 1, 1, 0, 0) # Cremona label: 43a1 # (0,-1) (0,0) (-1,-1) (-1,0) (1,1) (1,-2) (2,3) (2,-4) (-3/4,1/8) (-3/4,-9/8) (-2/9,1/27) (-2/9,-28/27) (21,98) (21,-99) (11/49,-363/343) (11/49,20/343) (-140/121,-400/1331) (-140/121,-931/1331) (209/400,2527/8000) (209/400,-10527/8000) (1740/361,76400/6859) (1740/361,-83259/6859) (-3629/7569,-729620/658503) (-3629/7569,71117/658503) (-17139/36481,737371/6967871) (-17139/36481,-7705242/6967871) (194438/38809,90160188/7645373) (194438/38809,-97805561/7645373) (528157/1036324,-1372862351/1054977832) (528157/1036324,317884519/1054977832) (-8338438/7187761,-13217218757/19270387241) (-8338438/7187761,-6053168484/19270387241) (15659721/67092481,34731392058/549554511871) (15659721/67092481,-584285903929/549554511871) (665838199/34117281,-17715783977801/199279038321) (665838199/34117281,17516504939480/199279038321) (-1524968280/6607901521,-558321219582400/537149706740569) (-1524968280/6607901521,21171512841831/537149706740569) (-50443970239/68162766400,2249272978173441/17795935051712000) (-50443970239/68162766400,-20045208029885441/17795935051712000) (791991662680/385083543601,748041672403721449/238963978065144151) (791991662680/385083543601,-987005650468865600/238963978065144151) (8985658531079/9202249657441,-54741723389451832280/27915217583090079761) (8985658531079/9202249657441,26826505806361752519/27915217583090079761) (-211327567932999/209674135856641,-24519007717765931978/3036108535167687186689) (-211327567932999/209674135856641,-3011589527449921254711/3036108535167687186689) (38581695555082/4853089476046161,21535986157888203044/338086202776927409397159) (38581695555082/4853089476046161,-338107738763085297600203/338086202776927409397159) (112336114570262877/7099336433764,-37652423056467875392754681/18915883755633959912) (112336114570262877/7099336433764,37652404140584119758794769/18915883755633959912) (-20672037869235082/2600282294202480889,262883121764561512399492/4193056826234404749073084787) (-20672037869235082/2600282294202480889,-4193319709356169310585484279/4193056826234404749073084787) (63734020523767895773980/32762274577834729768201,-22984081517683542981673948618832400/5930087051247884911766587129132699) (63734020523767895773980/32762274577834729768201,17053994466435658069907361489699701/5930087051247884911766587129132699) (-2251247528715575677121711/2962461672130735982595600,-5728189780743455129766048960597244513/5098930710043708239050543108935896000) (-2251247528715575677121711/2962461672130735982595600,629259070699746890715505851661348513/5098930710043708239050543108935896000) # # a-invariants: (0, 1, 0, 3, -1) # Cremona label: 44a1 # (1,-2) (1,2) # # a-invariants: (0, 1, 0, -77, -289) # Cremona label: 44a2 # # # a-invariants: (1, -1, 0, 0, -5) # Cremona label: 45a1 # (2,-1) # # a-invariants: (1, -1, 0, -45, -104) # Cremona label: 45a2 # (8,-4) (-4,2) (-13/4,13/8) # # a-invariants: (1, -1, 0, -720, -7259) # Cremona label: 45a3 # (-61/4,61/8) # # a-invariants: (1, -1, 0, -90, 175) # Cremona label: 45a4 # (2,-1) (35/4,-35/8) (-10,5) # # a-invariants: (1, -1, 0, -1215, 16600) # Cremona label: 45a5 # (20,-10) (83/4,-83/8) (-40,20) # # a-invariants: (1, -1, 0, 315, 1066) # Cremona label: 45a6 # (-13/4,13/8) # # a-invariants: (1, -1, 0, -19440, 1048135) # Cremona label: 45a7 # (323/4,-323/8) # # a-invariants: (1, -1, 0, -990, 22765) # Cremona label: 45a8 # (-157/4,157/8) # # a-invariants: (1, -1, 0, -10, -12) # Cremona label: 46a1 # (4,-2) # # a-invariants: (1, -1, 0, -170, -812) # Cremona label: 46a2 # (-29/4,29/8) # # a-invariants: (0, 1, 0, -4, -4) # Cremona label: 48a1 # (-1,0) (-2,0) (2,0) # # a-invariants: (0, 1, 0, -64, -220) # Cremona label: 48a2 # (-5,0) # # a-invariants: (0, 1, 0, -24, 36) # Cremona label: 48a3 # (6,-12) (2,0) (0,-6) (6,12) (3,0) (-6,0) (0,6) # # a-invariants: (0, 1, 0, 1, 0) # Cremona label: 48a4 # (0,0) # # a-invariants: (0, 1, 0, -384, 2772) # Cremona label: 48a5 # (12,-6) (11,0) (12,6) # # a-invariants: (0, 1, 0, 16, 180) # Cremona label: 48a6 # (22,108) (-5,0) (-2,12) (4,18) (-2,-12) (4,-18) (22,-108) # # a-invariants: (1, -1, 0, -2, -1) # Cremona label: 49a1 # (2,-1) # # a-invariants: (1, -1, 0, -37, -78) # Cremona label: 49a2 # (-13/4,13/8) # # a-invariants: (1, -1, 0, -107, 552) # Cremona label: 49a3 # (-12,6) # # a-invariants: (1, -1, 0, -1822, 30393) # Cremona label: 49a4 # (99/4,-99/8) # # a-invariants: (1, 0, 1, -1, -2) # Cremona label: 50a1 # (2,1) (2,-4) # # a-invariants: (1, 0, 1, -126, -552) # Cremona label: 50a2 # # # a-invariants: (1, 0, 1, -76, 298) # Cremona label: 50a3 # (2,-14) (2,11) # # a-invariants: (1, 0, 1, 549, -2202) # Cremona label: 50a4 # # # a-invariants: (1, 1, 1, -3, 1) # Cremona label: 50b1 # (-1,2) (1,0) (1,-2) (-1,-2) # # a-invariants: (1, 1, 1, 22, -9) # Cremona label: 50b2 # (9,27) (1,-5) (1,3) (9,-37) # # a-invariants: (1, 1, 1, -13, -219) # Cremona label: 50b3 # # # a-invariants: (1, 1, 1, -3138, -68969) # Cremona label: 50b4 # # # a-invariants: (0, 1, 1, 1, -1) # Cremona label: 51a1 # (1,1) (1,-2) # # a-invariants: (0, 1, 1, -59, -196) # Cremona label: 51a2 # # # a-invariants: (0, 0, 0, 1, -10) # Cremona label: 52a1 # (2,0) # # a-invariants: (0, 0, 0, -4, -3) # Cremona label: 52a2 # (-1,0) # # a-invariants: (1, -1, 1, 0, 0) # Cremona label: 53a1 # (0,-1) (0,0) (1,-2) (1,0) (2,-4) (2,1) (-1/4,-1/8) (-1/4,-5/8) (10,25) (10,-36) (9/25,-162/125) (9/25,-8/125) (40/81,-1025/729) (40/81,-64/729) (369/64,4941/512) (369/64,-8405/512) (-488/1681,-33489/68921) (-488/1681,-15424/68921) (9881/3721,-1294370/226981) (9881/3721,464648/226981) (46970/58081,-24308900/13997521) (46970/58081,-1008391/13997521) (65311/592900,-502342569/456533000) (65311/592900,-4479901/456533000) (6659730/73441,-18028053441/19902511) (6659730/73441,16203364100/19902511) (-7406159/74805201,-7841148688/646990183449) (-7406159/74805201,-575093165570/646990183449) (923436432/746874241,-48737159360721/20411326132289) (923436432/746874241,3089238978304/20411326132289) (17805417409/11399405824,-3671324176651209/1217091761016832) (17805417409/11399405824,553183609710265/1217091761016832) (-79079320720/424479613441,-210043274426511616/276557382228693761) (-79079320720/424479613441,-14992269687367025/276557382228693761) (12004801505489/548584642225,-45546704121221417218/406317444033579625) (12004801505489/548584642225,36248850370124827408/406317444033579625) (79473427085170/339510437304481,-7501163916104104007684/6255754471278841750129) (79473427085170/339510437304481,-218952743221506894975/6255754471278841750129) (7354163999674719/11513311030809604,-1906494606001685862679789/1235379401910351528541192) (7354163999674719/11513311030809604,-117987313781834982683865/1235379401910351528541192) (602535402695121562/159299161944786081,276954824609623317112105636/63579957979196397503888271) (602535402695121562/159299161944786081,-581020514695886093550025849/63579957979196397503888271) (1966855766819785991074981801/86057425487806652104339321,76306640116537686756954186493213419910818/798330137046059985476921676270861438131) (1966855766819785991074981801/86057425487806652104339321,-95350928983752272119794412767585224782360/798330137046059985476921676270861438131) (-206800685993748397460418150533854751/2006085961301030988004495735042350625,-2510749323938238441000424257387809999916319657953497632/2841347214716916933677217043529395165633881026937640625) (-206800685993748397460418150533854751/2006085961301030988004495735042350625,-37692918367223951327925249504634192121101680493110018/2841347214716916933677217043529395165633881026937640625) # # a-invariants: (1, -1, 0, 12, 8) # Cremona label: 54a1 # (1,-5) (1,4) # # a-invariants: (1, -1, 0, -123, -667) # Cremona label: 54a2 # # # a-invariants: (1, -1, 0, -3, 3) # Cremona label: 54a3 # (1,0) (1,-1) # # a-invariants: (1, -1, 1, 1, -1) # Cremona label: 54b1 # (1,0) (1,-2) # # a-invariants: (1, -1, 1, -29, -53) # Cremona label: 54b2 # # # a-invariants: (1, -1, 1, -14, 29) # Cremona label: 54b3 # (9,19) (9,-29) (1,3) (3,1) (-3,7) (-3,-5) (1,-5) (3,-5) # # a-invariants: (1, -1, 0, -4, 3) # Cremona label: 55a1 # (2,-1) (3/4,-3/8) (-2,1) # # a-invariants: (1, -1, 0, -29, -52) # Cremona label: 55a2 # (-13/4,13/8) # # a-invariants: (1, -1, 0, -59, 190) # Cremona label: 55a3 # (19/4,-19/8) (6,-8) (6,2) # # a-invariants: (1, -1, 0, 1, 0) # Cremona label: 55a4 # (0,0) # # a-invariants: (0, 0, 0, 1, 2) # Cremona label: 56a1 # (-1,0) (1,-2) (1,2) # # a-invariants: (0, 0, 0, -19, 30) # Cremona label: 56a2 # (-5,0) (2,0) (3,0) # # a-invariants: (0, 0, 0, -59, -138) # Cremona label: 56a3 # (-6,0) # # a-invariants: (0, 0, 0, -299, 1990) # Cremona label: 56a4 # (10,0) # # a-invariants: (0, -1, 0, 0, -4) # Cremona label: 56b1 # (2,0) # # a-invariants: (0, -1, 0, -40, -84) # Cremona label: 56b2 # (-3,0) # # a-invariants: (0, -1, 1, -2, 2) # Cremona label: 57a1 # (2,-2) (2,1) (1,-1) (1,0) (-1,-2) (-1,1) (0,1) (0,-2) (5/4,-7/8) (5/4,-1/8) (4,6) (4,-7) (11,34) (11,-35) (13/9,-28/27) (13/9,1/27) (14/25,62/125) (14/25,-187/125) (-23/16,-51/64) (-23/16,-13/64) (86/121,-1765/1331) (86/121,434/1331) (261/169,-2588/2197) (261/169,391/2197) (995/49,30358/343) (995/49,-30701/343) (1660/529,44122/12167) (1660/529,-56289/12167) (8789/7396,-80647/636056) (8789/7396,-555409/636056) (-1976/7569,750007/658503) (-1976/7569,-1408510/658503) (-29113/39601,9205279/7880599) (-29113/39601,-17085878/7880599) (185449/172225,-66516807/71473375) (185449/172225,-4956568/71473375) (1466042/638401,-1336363406/510082399) (1466042/638401,826281007/510082399) (3369249/23104,6161143535/3511808) (3369249/23104,-6164655343/3511808) (30917834/17297281,42537929839/71939391679) (30917834/17297281,-114477321518/71939391679) (59125465/65011969,50754531736/524191506047) (59125465/65011969,-574946037783/524191506047) 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(59000748635295805/35265451793778441,-9189383072274976822025516/6622533717230959544483739) (1022898683763443579/20193751730487841,-1025317728797554957955893667/2869627455604241839197361) (1022898683763443579/20193751730487841,1022448101341950716116696306/2869627455604241839197361) (7839056405877618676/3041466522924766561,-17249702241230521558997352215/5304257033009122743958871441) (7839056405877618676/3041466522924766561,11945445208221398815038480774/5304257033009122743958871441) (-351830423415021677424/652674714607575664225,19964341487288039456051164835249/16674206739507146876614021156625) (-351830423415021677424/652674714607575664225,-36638548226795186332665185991874/16674206739507146876614021156625) # # a-invariants: (1, 0, 1, -7, 5) # Cremona label: 57b1 # (-3,1) (7/4,-11/8) (1,-1) # # a-invariants: (1, 0, 1, -2, -1) # Cremona label: 57b2 # (-1,0) # # a-invariants: (1, 0, 1, -102, 385) # Cremona label: 57b3 # (5,-6) (5,0) (23/4,-27/8) # # a-invariants: (1, 0, 1, 8, 29) # Cremona label: 57b4 # (-9/4,5/8) # # a-invariants: (0, 1, 1, 20, -32) # Cremona label: 57c1 # (11,40) (11,-41) (2,-5) (2,4) # # a-invariants: (0, 1, 1, -4390, -113432) # Cremona label: 57c2 # # # a-invariants: (1, -1, 0, -1, 1) # Cremona label: 58a1 # (0,1) (0,-1) (1,0) (1,-1) (2,-3) (2,1) (-1,0) (-1,1) (4,-9) (4,5) (3/4,1/8) (3/4,-7/8) (4/9,13/27) (4/9,-25/27) (15,49) (15,-64) (-14/25,169/125) (-14/25,-99/125) (65/49,-512/343) (65/49,57/343) (224/169,363/2197) (224/169,-3275/2197) (-143/256,5537/4096) (-143/256,-3249/4096) (1824/121,-85805/1331) (1824/121,65741/1331) (1441/3249,89383/185193) (1441/3249,-171520/185193) (12882/17161,279631/2248091) (12882/17161,-1967173/2248091) (50959/12769,-12940767/1442897) (50959/12769,7182400/1442897) (-151420/151321,58747931/58863869) (-151420/151321,154449/58863869) (898979/448900,-904264473/300763000) (898979/448900,301948543/300763000) (5337220/5340721,-12334326031/12342406231) (5337220/5340721,10611/12342406231) 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(4377139749257604/293252507396689,-319077541282305333270275/5021836873457966193113) (-12158771603059997/21657732071898244,-2520442360494645871568409/3187274477779536674897528) (-12158771603059997/21657732071898244,4309796032565771555791423/3187274477779536674897528) # # a-invariants: (1, 1, 1, 5, 9) # Cremona label: 58b1 # (3,-10) (-1,-2) (-1,2) (3,6) # # a-invariants: (1, 1, 1, -455, -3951) # Cremona label: 58b2 # # # a-invariants: (1, 0, 0, -2, 1) # Cremona label: 61a1 # (1,0) (1,-1) (0,-1) (0,1) (-1,-1) (-1,2) (3/4,-5/8) (3/4,-1/8) (7,-22) (7,15) (16/9,29/27) (16/9,-77/27) (25/49,-232/343) (25/49,57/343) (-111/64,475/512) (-111/64,413/512) (329/625,-10408/15625) (329/625,2183/15625) (2544/1369,61147/50653) (2544/1369,-155275/50653) (13975/2209,1318273/103823) (13975/2209,-1975098/103823) (74851/101124,-3886007/32157432) (74851/101124,-19916611/32157432) (-330833/312481,352199310/174676879) (-330833/312481,-167263663/174676879) (157728/4092529,7796009255/8279186167) (157728/4092529,-8115092999/8279186167) (50550929/49547521,7200511856/348765000319) (50550929/49547521,-363028501087/348765000319) (636789825/246016,15912046652039/122023936) (636789825/246016,-16227894405239/122023936) (8021637361/8177765761,-13838487752816/739523535532991) (8021637361/8177765761,-711566200439775/739523535532991) (-3971776544/99083300625,33045229680632279/31188945954234375) (-3971776544/99083300625,-31795013718994679/31188945954234375) (-1221910816049/1298685880801,2926136433566438126/1479981131074938799) (-1221910816049/1298685880801,-1533648089507813775/1479981131074938799) (40820670707996208/23959460228902969,-9859213184715650978697691/3708647400195552796169453) (40820670707996208/23959460228902969,3540645368533234540450795/3708647400195552796169453) (768089693699034217/1557159673368685681,377317173653917904709070663/1943120448172741459380134921) (768089693699034217/1557159673368685681,-1335787146504259582463527560/1943120448172741459380134921) # # a-invariants: (1, -1, 1, -1, 1) # Cremona label: 62a1 # (-1,0) (1,0) (1,-2) # # a-invariants: (1, -1, 1, -21, 41) # Cremona label: 62a2 # (3,-2) (-5,2) (11/4,-15/8) # # a-invariants: (1, -1, 1, -31, 5) # Cremona label: 62a3 # (-21/4,17/8) # # a-invariants: (1, -1, 1, -331, 2397) # Cremona label: 62a4 # (43/4,-47/8) # # a-invariants: (1, -1, 0, 9, 0) # Cremona label: 63a1 # (0,0) # # a-invariants: (1, -1, 0, -36, 27) # Cremona label: 63a2 # (6,-3) (3/4,-3/8) (-6,3) # # a-invariants: (1, -1, 0, -351, -2430) # Cremona label: 63a3 # (-45/4,45/8) # # a-invariants: (1, -1, 0, -441, 3672) # Cremona label: 63a4 # (12,-6) (51/4,-51/8) (-24,12) # # a-invariants: (1, -1, 0, -7056, 229905) # Cremona label: 63a5 # (195/4,-195/8) (48,-33) (48,-15) # # a-invariants: (1, -1, 0, -306, 5859) # Cremona label: 63a6 # (-93/4,93/8) # # a-invariants: (0, 0, 0, -4, 0) # Cremona label: 64a1 # (0,0) (2,0) (-2,0) # # a-invariants: (0, 0, 0, -44, -112) # Cremona label: 64a2 # (-4,0) # # a-invariants: (0, 0, 0, -44, 112) # 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(12003349222225/9039445125489,-50819983814052831680/27177697412606086263) (12003349222225/9039445125489,14731110153035480105/27177697412606086263) (19929760024531204/813698958617281,2541276247103056153830294/23211095597432014992929) (19929760024531204/813698958617281,-3109780803074658781192730/23211095597432014992929) (-40425467006303895961/35847585754553486281,97989489980808744039301421941/214629724698478512410675906821) (35847585754553486281/40425467006303895961,-92274548860241491731002571149/257029261583258839473953227709) (35847585754553486281/40425467006303895961,-135648074633474257384781156640/257029261583258839473953227709) (-40425467006303895961/35847585754553486281,144049316029113726839182985760/214629724698478512410675906821) (291904095699083933751841/25755221305358595590400,-182254919068328046281953649646488249/4133309525850578617928554910208000) (291904095699083933751841/25755221305358595590400,135408884818302262699249613688477929/4133309525850578617928554910208000) # # 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(15080960313/7723070161,2152966759750682/678711128818841) (15080960313/7723070161,-3478296633017435/678711128818841) (8345243251/5234377801,1013536555647753/378701999524549) (8345243251/5234377801,-1617306559614352/378701999524549) (-43404604529/269267588100,-72285427858876861/139725644140971000) (4351686014129/95649169984,8438690504082706531/29581610099291648) (4351686014129/95649169984,-9784545141044410619/29581610099291648) (-43404604529/269267588100,94808511195020251/139725644140971000) (37246927016913/93816833156281,-1670781338884562173495/908701308619920544429) (37246927016913/93816833156281,1310010993269101394578/908701308619920544429) (8036680130364480/1310488580850241,627640249399433858187839/47440565964616474711711) (8036680130364480/1310488580850241,-918573462730995508753919/47440565964616474711711) (7827513324879232531/179634982368670929,20326648671097063702696589656/76135354376604039966392217) (7827513324879232531/179634982368670929,-23644212394037071107731406019/76135354376604039966392217) (1431421349946195726179473564899615961/1141437756253177890812361776671846449,-4295184974217992404785223990612142728046192961728463866/1219490302003729239191077821411365139377748175458867543) (1431421349946195726179473564899615961/1141437756253177890812361776671846449,2765881738209312265452525025029291234008122801269078539/1219490302003729239191077821411365139377748175458867543) (-349168978247698833965490249475856902560/1449155395176351510437249086525264811041,-3927942661773834535351107371977094911806567330274983678271/55166119653068064013544009838942377657109301407133479303089) (-349168978247698833965490249475856902560/1449155395176351510437249086525264811041,17220028311986657023747598246514013542993146919329637516511/55166119653068064013544009838942377657109301407133479303089) # # a-invariants: (1, 0, 1, -6, 4) # Cremona label: 66a1 # (2,-3) (-1,3) (2,0) (1,-1) (-1,-3) # # a-invariants: (1, 0, 1, 4, 20) # Cremona label: 66a2 # (6,13) (6,-20) (0,-5) (0,4) (-9/4,5/8) # # a-invariants: (1, 0, 1, -81, -284) # Cremona label: 66a3 # (-5,2) # # a-invariants: (1, 0, 1, -41, -556) # Cremona label: 66a4 # (39/4,-43/8) # # a-invariants: (1, 1, 1, -2, -1) # Cremona label: 66b1 # (-1,-1) (1,-1) (-1,1) # # a-invariants: (1, 1, 1, -22, -49) # Cremona label: 66b2 # (-3,1) (-13/4,9/8) (5,-3) # # a-invariants: (1, 1, 1, -352, -2689) # Cremona label: 66b3 # (-45/4,41/8) # # a-invariants: (1, 1, 1, -12, -81) # Cremona label: 66b4 # (19/4,-23/8) # # a-invariants: (1, 0, 0, -45, 81) # Cremona label: 66c1 # (0,9) (18,-81) (6,3) (0,-9) (-6,15) (18,63) (-6,-9) (2,-1) (6,-9) # # a-invariants: (1, 0, 0, 115, 561) # Cremona label: 66c2 # (70,-629) (-17/4,17/8) (-2,19) (70,559) (16,-89) (-2,-17) (16,73) (4,31) (4,-35) # # a-invariants: (1, 0, 0, -10065, -389499) # Cremona label: 66c3 # (-58,29) # # a-invariants: (1, 0, 0, -10055, -390309) # Cremona label: 66c4 # (463/4,-463/8) # # a-invariants: (0, 1, 1, -12, -21) # Cremona label: 67a1 # # # a-invariants: (1, 0, 1, -1, -1) # Cremona label: 69a1 # (1,-1) # # a-invariants: (1, 0, 1, -16, -25) # Cremona label: 69a2 # (-9/4,5/8) # # a-invariants: (1, -1, 1, 2, -3) # Cremona label: 70a1 # (3,3) (1,-1) (3,-7) # # a-invariants: (1, -1, 1, -18, -19) # Cremona label: 70a2 # (-3,1) (5,-3) (-5/4,1/8) # # a-invariants: (1, -1, 1, -268, -1619) # Cremona label: 70a3 # (-37/4,33/8) # # a-invariants: (1, -1, 1, -88, 317) # Cremona label: 70a4 # (27/4,-31/8) # # a-invariants: (0, 0, 0, 6, -7) # Cremona label: 72a1 # (1,0) (4,-9) (4,9) # # a-invariants: (0, 0, 0, -39, -70) # Cremona label: 72a2 # (7,0) (-2,0) (-5,0) # # a-invariants: (0, 0, 0, -579, -5362) # Cremona label: 72a3 # (-14,0) # # a-invariants: (0, 0, 0, -219, 1190) # Cremona label: 72a4 # (7,0) (-17,0) (10,0) # # a-invariants: (0, 0, 0, -3459, 78302) # Cremona label: 72a5 # (34,0) # # a-invariants: (0, 0, 0, 141, 4718) # Cremona label: 72a6 # (-14,0) # # a-invariants: (1, -1, 0, 4, -3) # Cremona label: 73a1 # (3/4,-3/8) # # a-invariants: (1, -1, 0, -1, 0) # Cremona label: 73a2 # (0,0) # # a-invariants: (0, -1, 1, -8, -7) # Cremona label: 75a1 # # # a-invariants: (0, -1, 1, 42, 443) # Cremona label: 75a2 # # # a-invariants: (1, 0, 1, -1, 23) # Cremona label: 75b1 # (-3,1) # # a-invariants: (1, 0, 1, -126, 523) # Cremona label: 75b2 # (7,-4) (-13,6) (23/4,-27/8) # # a-invariants: (1, 0, 1, -251, -727) # Cremona label: 75b3 # (-3,1) (17,-9) (-57/4,53/8) # # a-invariants: (1, 0, 1, -2001, 34273) # Cremona label: 75b4 # (103/4,-107/8) # # a-invariants: (1, 0, 1, -3376, -75727) # Cremona label: 75b5 # (-137/4,133/8) (-33,16) (67,-34) # # a-invariants: (1, 0, 1, 874, -5227) # Cremona label: 75b6 # (23/4,-27/8) # # a-invariants: (1, 0, 1, -54001, -4834477) # Cremona label: 75b7 # (-537/4,533/8) # # a-invariants: (1, 0, 1, -2751, -104477) # Cremona label: 75b8 # (167,-2109) (167,1941) (263/4,-267/8) # # a-invariants: (0, 1, 1, 2, 4) # Cremona label: 75c1 # (-1,-2) (-1,1) (2,-5) (2,4) # # a-invariants: (0, 1, 1, -208, -1256) # Cremona label: 75c2 # # # a-invariants: (0, -1, 0, -21, -31) # Cremona label: 76a1 # # # a-invariants: (0, 0, 1, 2, 0) # Cremona label: 77a1 # (2,3) (2,-4) (0,-1) (0,0) (1/4,-11/8) (1/4,3/8) (4,-9) (4,8) (30,164) (30,-165) (17/16,-153/64) (17/16,89/64) (-26/225,-2132/3375) (-26/225,-1243/3375) (188/289,-9096/4913) (188/289,4183/4913) (6945/676,575509/17576) (6945/676,-593085/17576) (16456/2209,2097409/103823) (16456/2209,-2201232/103823) (110266/214369,68432052/99252847) (110266/214369,-167684899/99252847) (-89535/937024,-235033185/907039232) (-89535/937024,-672006047/907039232) (23063882/17986081,131110547628/76278969521) (23063882/17986081,-207389517149/76278969521) (218519224/3629025,-3234586932368/6913292625) (218519224/3629025,3227673639743/6913292625) (7973152097/2481434596,718497415008747/123610182965144) (7973152097/2481434596,-842107597973891/123610182965144) (8268637260/50959902049,2999979806182185/11503841168247407) (8268637260/50959902049,-14503820974429592/11503841168247407) (45608241417361/18839870802064,-399939295961570492967/81774308497392375488) (45608241417361/18839870802064,318164987464178117479/81774308497392375488) (6174123728937390/17785189128001,-485176959169774178704380/75004571064873089249) (6174123728937390/17785189128001,485101954598709305615131/75004571064873089249) # # a-invariants: (0, 1, 1, -49, 600) # Cremona label: 77b1 # (0,24) (0,-25) # # a-invariants: (0, 1, 1, 441, -15815) # Cremona label: 77b2 # # # a-invariants: (0, 1, 1, -89, 295) # Cremona label: 77b3 # (5,-1) (5,0) # # a-invariants: (1, 1, 0, 4, 11) # Cremona label: 77c1 # (-2,1) # # a-invariants: (1, 1, 0, -51, 110) # Cremona label: 77c2 # (11/4,-11/8) # # a-invariants: (1, 1, 0, -19, 685) # Cremona label: 78a1 # (-10,5) # # a-invariants: (1, 1, 0, -1299, 17325) # Cremona label: 78a2 # (22,-11) (75/4,-75/8) (-42,21) # # a-invariants: (1, 1, 0, -2339, -15747) # Cremona label: 78a3 # (-181/4,181/8) # # a-invariants: 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(42489382401/72546190336,-16158766011097743/19539881089859584) (-1004045749280/1000018000081,1417678909930559815/1000027000243000729) (-1004045749280/1000018000081,-1413651124481817024/1000027000243000729) (47167073499841/13896082785025,-475181882285587184224/51801053121463018625) (47167073499841/13896082785025,247554006760459377054/51801053121463018625) (83211563428572931/15258676134728196,-32159870119648042354024013/1884843441839901025290744) (83211563428572931/15258676134728196,19996233928768353454006235/1884843441839901025290744) (200639136161400650593/332294716648211006209,-3997632947072959747217695538574/6057384673237025121747900332927) (200639136161400650593/332294716648211006209,-5717193049621014808423430697232/6057384673237025121747900332927) # # a-invariants: (0, 0, 0, -7, 6) # Cremona label: 80a1 # (1,0) (2,0) (-3,0) # # a-invariants: (0, 0, 0, -2, -1) # Cremona label: 80a2 # (-1,0) # # a-invariants: (0, 0, 0, -107, 426) # Cremona label: 80a3 # (5,4) (5,-4) (6,0) # # 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(1693226/133225,-2548164644/48627125) (-32972351/76370121,430637145769/667398487419) (-21698885/54671236,244647369955/404239118984) (-32972351/76370121,-809890257799/667398487419) (-21698885/54671236,-488444933249/404239118984) (4231090802/3534183601,-78089035103236/210103680895849) (7765274403/696907201,576180829146727/18397653199199) (7765274403/696907201,-799573961310723/18397653199199) (4231090802/3534183601,-383548762880711/210103680895849) (134667872351/789569084929,-354517418023872767/701592928778956033) (134667872351/789569084929,-466738284765117793/701592928778956033) (86447867049601/60425125689600,-1154489259680647508281/469706255030509056000) (86447867049601/60425125689600,12792612841452022921/469706255030509056000) (-18324131242014049/27320821455552769,-5407793964070674058802303/4515861665641141665472897) (-18324131242014049/27320821455552769,3920730022048864900126943/4515861665641141665472897) (13237969509795411602/334879050207397201,-52221384108416344725445686409/193790270469914686851504551) (13237969509795411602/334879050207397201,44366948329704154746678135556/193790270469914686851504551) (935639796343208846395/7678563625792283559556,-195943478280787846703407075178801/672852671198001258463984559292296) (935639796343208846395/7678563625792283559556,-558896888393751767453462801947565/672852671198001258463984559292296) (8365052429052422656566026/2614143309230587344366025,14571778593441310534651647150651799516/4226628609099266054832166217227461125) (8365052429052422656566026/2614143309230587344366025,-32323285424941662390828707789306977411/4226628609099266054832166217227461125) (29402820233799672638199287945377/29381652105142129716548497421376,-165369201908377563637664021879277062171144909899/159262789523277829143745125777326689976919077376) (29402820233799672638199287945377/29381652105142129716548497421376,-153271118651246310043207670421719664766780159229/159262789523277829143745125777326689976919077376) # # a-invariants: (1, 0, 1, -12, -16) # Cremona label: 82a2 # (-9/4,5/8) (-2,1) (-2,0) (8,16) (8,-25) (4,0) (-46/25,32/125) (-46/25,73/125) (4,-5) (333/16,5329/64) (333/16,-6725/64) (-77/36,221/216) (-77/36,25/216) (1276/25,42336/125) (-11734/5329,361805/389017) (1276/25,-48841/125) (-11734/5329,105760/389017) (-91802/48841,8297856/10793861) (-91802/48841,1196525/10793861) (337808/72361,64432939/19465109) (337808/72361,-174768400/19465109) (-84131721/43692100,10672036513/288804781000) (7811329/1382976,-22265879285/1626379776) (-84131721/43692100,256633858297/288804781000) (7811329/1382976,11453376605/1626379776) (-5117471402/2290675321,45930680442725/109634011538381) (-5117471402/2290675321,89362606790016/109634011538381) (23150489408/146192281,-3665218242455600/1767610869571) (23150489408/146192281,3383538064153901/1767610869571) (-26170699822534/12578208416929,46515243682303574560/44609584672686802033) (2676932054476/207831133225,3594972450617447471/94747096170279125) (-26170699822534/12578208416929,1691573709512789525/44609584672686802033) (2676932054476/207831133225,-4910092716442517856/94747096170279125) (-7635034564550477/4175248908539556,117881547335098689946661/269788576565510768062296) (-7635034564550477/4175248908539556,105676536938121879202225/269788576565510768062296) (26962821995558733/7037101918654096,-1233359008131124791434569/590324436826572684337856) (26962821995558733/7037101918654096,-1618807433227273391681875/590324436826572684337856) (27929585099153319604/2462998001193010801,117866730597885493050437710685/3865414656997002173169224951) (27929585099153319604/2462998001193010801,-165564672749350470062358171840/3865414656997002173169224951) # # a-invariants: (1, 1, 1, 1, 0) # Cremona label: 83a1 # (0,-1) (0,0) (1,-3) (1,1) (4,-12) (4,7) (-3/16,-21/64) (-3/16,-31/64) (76/9,-844/27) (76/9,589/27) (201/361,-14137/6859) (201/361,3459/6859) (760/4489,46120/300763) (760/4489,-397803/300763) (83281/1600,22629451/64000) (83281/1600,-26024691/64000) (-171960/1545049,-254749480/1920495907) (-171960/1545049,-1452000147/1920495907) (31854361/18481401,-379605063937/79451542899) (31854361/18481401,163211623099/79451542899) (1437258876/656743129,-102100630245916/16830356166883) (1437258876/656743129,48437640863781/16830356166883) (-16091936483/111772536976,-7074994042789751/37368241651964224) (-16091936483/111772536976,-24913327036431981/37368241651964224) (9943745574484/394294829041,28914548126023241823/247589157704886089) (9943745574484/394294829041,-35406103498568291548/247589157704886089) (233986695950961/884636590751281,-39463100584985913456843/26311605461497421329321) (233986695950961/884636590751281,6192066029703715307321/26311605461497421329321) # # a-invariants: (0, 1, 0, 7, 0) # Cremona label: 84a1 # (7,-21) (0,0) (1,-3) (7,21) (1,3) # # a-invariants: (0, 1, 0, -28, -28) # Cremona label: 84a2 # (-1,0) (8,-18) (-4,-6) (8,18) (-4,6) # # a-invariants: (0, 1, 0, -113, -516) # Cremona label: 84a3 # (12,0) # # a-invariants: (0, 1, 0, -1828, -30700) # Cremona label: 84a4 # (-25,0) # # a-invariants: (0, -1, 0, -1, -2) # Cremona label: 84b1 # (2,0) # # a-invariants: (0, -1, 0, -36, -72) # Cremona label: 84b2 # (-3,0) # # a-invariants: (1, 1, 0, -8, -13) # Cremona label: 85a1 # (-2,1) # # a-invariants: (1, 1, 0, -3, -22) # Cremona label: 85a2 # (11/4,-11/8) # # a-invariants: (0, 0, 0, -4, 4) # Cremona label: 88a1 # (2,-2) (2,2) (0,2) (0,-2) (-2,-2) (-2,2) (1,1) (1,-1) (6,-14) (6,14) (8,22) (8,-22) (10/9,-26/27) (10/9,26/27) (-7/4,19/8) (-7/4,-19/8) (-6/25,-278/125) (-6/25,278/125) (88/49,554/343) (88/49,-554/343) (310,5458) (310,-5458) (273/121,-3383/1331) (273/121,3383/1331) (206/961,52894/29791) (206/961,-52894/29791) (-3344/1521,87326/59319) (-3344/1521,-87326/59319) (9362/10609,-1175566/1092727) (9362/10609,1175566/1092727) (27105/5776,-4131247/438976) (27105/5776,4131247/438976) (256882/22801,128313838/3442951) (256882/22801,-128313838/3442951) (589456/483025,324783646/335702375) (589456/483025,-324783646/335702375) (-2280402/1555009,-5023772066/1939096223) (-2280402/1555009,5023772066/1939096223) (-1896655/3759721,-17691806567/7290099019) (-1896655/3759721,17691806567/7290099019) (92869078/57017601,578576841362/430539905151) (92869078/57017601,-578576841362/430539905151) (577248056/7447441,-13864396131434/20324066489) (577248056/7447441,13864396131434/20324066489) (3585622554/1386594169,170843334241718/51632607071053) (3585622554/1386594169,-170843334241718/51632607071053) (2237389753/5539229476,-645323489165837/412262692980776) (2237389753/5539229476,645323489165837/412262692980776) (-131331547670/56371580329,10986125818040506/13384135202773483) (-131331547670/56371580329,-10986125818040506/13384135202773483) (506947340328/672165500449,-654881490861845206/551079590701615793) (506947340328/672165500449,654881490861845206/551079590701615793) (49635494724193/2899721962449,347439493543546259441/4937811841810016793) (49635494724193/2899721962449,-347439493543546259441/4937811841810016793) (-4277233106588832/3665291263639201,590389814613616226511742/221902777166010969582449) (-4277233106588832/3665291263639201,-590389814613616226511742/221902777166010969582449) (586509016323934081/394320629809807936,-286744414433978270106575681/247613459678861700138781184) (586509016323934081/394320629809807936,286744414433978270106575681/247613459678861700138781184) # # a-invariants: (1, 1, 1, -1, 0) # Cremona label: 89a1 # (0,-1) (0,0) (-1,1) (-1,-1) (2,2) (2,-5) (3/4,1/8) (3/4,-15/8) (-14/9,-7/27) (-14/9,22/27) (15/49,-393/343) (15/49,-55/343) (224/25,2947/125) (224/25,-4192/125) (-415/1024,15455/32768) (-415/1024,-34943/32768) (-2784/6889,268917/571787) (-2784/6889,-609632/571787) (68143/7569,15640871/658503) (68143/7569,-22227815/658503) (205842/674041,-633626630/553387661) (205842/674041,-88757313/553387661) (-8703421/5597956,10815129599/13244763896) (-8703421/5597956,-3467599409/13244763896) (84454370/112381201,-2237416325326/1191353111801) (84454370/112381201,150762437155/1191353111801) (2541600351/1274133025,-226721386903311/45480178327375) (2541600351/1274133025,90518784046991/45480178327375) (-57566611520/57480542001,13791307992501545/13781017425281751) (-57566611520/57480542001,-13770672739251776/13781017425281751) (1946538369/2600917405696,-3136899554310689/4194593133192544256) (1946538369/2600917405696,-4194595486141301151/4194593133192544256) (117600010805312/65918161,-1275773976290310283367/535189549159) (117600010805312/65918161,1274819181267392406080/535189549159) (21765443137366566595/10854228924425765124,-179337038416517153987529782143/35760078661274141591774114568) (21765443137366566595/10854228924425765124,71869060086921336572035124785/35760078661274141591774114568) (-311444414036426949148945/200111026123300263492049,-22979688242225030520444912816028793/89517208023064825103317707093197593) (-311444414036426949148945/200111026123300263492049,72783310955104093802637487721115065/89517208023064825103317707093197593) # # a-invariants: (1, 1, 0, 4, 5) # Cremona label: 89b1 # (-5/4,5/8) # # a-invariants: (1, 1, 0, -1, 0) # Cremona label: 89b2 # (0,0) # # a-invariants: (1, -1, 0, 6, 0) # Cremona label: 90a1 # (0,0) (1,-3) (1,2) (6,12) (6,-18) # # a-invariants: (1, -1, 0, -24, 18) # Cremona label: 90a2 # (-3,-6) (-3,9) (3/4,-3/8) (7,-16) (7,9) # # a-invariants: (1, -1, 0, -69, -235) # Cremona label: 90a3 # (10,-5) # # a-invariants: (1, -1, 0, -1149, -14707) # Cremona label: 90a4 # (-77/4,77/8) # # a-invariants: (1, -1, 1, -8, 11) # Cremona label: 90b1 # (1,1) (1,-3) (3,1) (3,-5) (-3,1) # # a-invariants: (1, -1, 1, -128, 587) # Cremona label: 90b2 # (27/4,-31/8) (3,-17) (3,13) (7,-3) (7,-5) # # a-invariants: (1, -1, 1, 52, -53) # Cremona label: 90b3 # (1,-1) # # a-invariants: (1, -1, 1, -218, -269) # Cremona label: 90b4 # (-5/4,1/8) # # a-invariants: (1, -1, 1, 13, -61) # Cremona label: 90c1 # (9,-32) (9,22) (3,-2) # # a-invariants: (1, -1, 1, -167, -709) # Cremona label: 90c2 # (-21/4,17/8) (15,-8) (-9,4) # # a-invariants: (1, -1, 1, -122, 1721) # Cremona label: 90c3 # (9,31) (21,-101) (-9,-41) (9,-41) (-15,7) (81,679) (1,39) (1,-41) (81,-761) (21,79) (-9,49) # # a-invariants: (1, -1, 1, -2597, -50281) # Cremona label: 90c4 # (-117/4,113/8) # # a-invariants: (1, -1, 1, -617, 5231) # Cremona label: 90c5 # (75/4,-79/8) # # a-invariants: (1, -1, 1, -3002, 63929) # Cremona label: 90c6 # (37,-69) (-3,271) (123/4,-127/8) (-63,31) (27,31) (-3,-269) (87,-719) (37,31) (87,631) (33,-17) (27,-59) # # a-invariants: (1, -1, 1, -4082, 14681) # Cremona label: 90c7 # (91,579) (-261/4,257/8) (91,-671) (-9,-221) (-9,229) # # a-invariants: (1, -1, 1, -48002, 4059929) # Cremona label: 90c8 # (147,-479) (147,331) (127,-69) (127,-59) (507/4,-511/8) # # a-invariants: (0, 0, 1, 1, 0) # Cremona label: 91a1 # (0,-1) (0,0) (1,-2) (1,1) (3,5) (3,-6) (-2/9,-10/27) (-2/9,-17/27) (33/4,-195/8) (33/4,187/8) (58/121,-1885/1331) (58/121,554/1331) (231/841,5817/24389) (231/841,-30206/24389) (8845/441,828269/9261) (8845/441,-837530/9261) (-16044/93025,-6552021/28372625) (-16044/93025,-21820604/28372625) (1147105/583696,1173435761/445943744) (1147105/583696,-1619379505/445943744) (20497356/14145121,-142446992589/53199800081) (20497356/14145121,89247192508/53199800081) (-78330347/719795241,-16878465999370/19311386520789) (-78330347/719795241,-2432920521419/19311386520789) (28027370943/433763929,4688214953513390/9034001349283) (28027370943/433763929,-4697248954862673/9034001349283) (152802992098/1091329140889,-1284529949068680638/1140075539625088963) (152802992098/1091329140889,144454409443591675/1140075539625088963) (6088653225047446/1223724862004841,463665670601289577745374/42808072679458844792139) (6088653225047446/1223724862004841,-506473743280748422537513/42808072679458844792139) # # a-invariants: (0, 1, 1, -7, 5) # Cremona label: 91b1 # (1,-1) (1,0) (3,4) (5/4,-5/8) (5/4,-3/8) (-1,3) (-1,-4) (3,-5) (85/49,225/343) (-47/16,-225/64) (109/81,-568/729) (-47/16,161/64) (85/49,-568/343) (109/81,-161/729) (20901/17956,-759469/2406104) (13691/961,1616844/29791) (4871/9025,-1616844/857375) (4871/9025,759469/857375) (20901/17956,-1646635/2406104) (13691/961,-1646635/29791) (36469273/30813601,-111937825791/171046299151) (4846825/13417569,59108473360/49148555247) (22717249/2383936,-111937825791/3680797184) (4846825/13417569,-108257028607/49148555247) (36469273/30813601,-59108473360/171046299151) (22717249/2383936,108257028607/3680797184) (407788778123/252115456321,-174776984587105611/126589943888793631) (-226016952585/69813793729,-48187040698311980/18446410020457567) (407788778123/252115456321,48187040698311980/126589943888793631) (479795277029/347126002276,-29740630677854413/204517615264960024) (-226016952585/69813793729,29740630677854413/18446410020457567) (479795277029/347126002276,-174776984587105611/204517615264960024) (-8706102688770479/14132512413499536,-6074750571827983688473055/1680076524049853733566784) (62989801426645381/50962942852570225,-7110196796009742407734104/11504870843787872362640375) (37072117251022141/10234933671286801,6074750571827983688473055/1035446224181758719261049) (62989801426645381/50962942852570225,-4394674047778129954906271/11504870843787872362640375) (-8706102688770479/14132512413499536,4394674047778129954906271/1680076524049853733566784) (37072117251022141/10234933671286801,-7110196796009742407734104/1035446224181758719261049) (29965857377871914025413/32056087306372877829316,-6486606660575048668222152668238885/5739390418595515978229534469185864) (29965857377871914025413/32056087306372877829316,747216241979532689992618199053021/5739390418595515978229534469185864) (-122429680233587827681547852591/85998926312432282815737159361,-108168085979628682638912941284150945057012737/25219678374588164869889855451870137728836641) (-122429680233587827681547852591/85998926312432282815737159361,82948407605040517769023085832280807328176096/25219678374588164869889855451870137728836641) # # a-invariants: (0, 1, 1, 13, 42) # Cremona label: 91b2 # (0,-7) (0,6) (13/4,-95/8) (26,-137) (13/4,87/8) (-2,-4) (26,136) (-2,3) (-39/16,-123/64) (52/9,487/27) (52/9,-514/27) (-39/16,59/64) (12,45) (12,-46) (130,-1489) (5/4,59/8) (5/4,-67/8) (130,1488) (-26/25,607/125) (-26/25,-732/125) (5577/64,-419493/512) (264/169,-19323/2197) (-1352/1089,-200287/35937) (264/169,17126/2197) (5577/64,418981/512) (-1352/1089,164350/35937) (91117/13924,-35689713/1643032) (19234/1849,-3026643/79507) (-65962/26569,1795993/4330747) (91117/13924,34046681/1643032) (-65962/26569,-6126740/4330747) (19234/1849,2947136/79507) (-117935/63504,-70292447/16003008) (1687140/52441,-2246099358/12008989) 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