# Lists of S-integral points (x,y) on the Mordell curves
# y^2 = x^3 + a, with the following constraints:
# we consider only curves of rank r = 1,
# a is bounded by |a| <= 10,
# S is the set of the first 100000 primes.
# It contains 9 curves in total.
# It contains 107 points in total.
# For each point P, only one of +P, -P is listed.
# Format of the points: "(P(x),P(y))".
# Computing this list took 137302 seconds.
# Authors: Rafael von Känel and Benjamin Matschke, 2015.
# License: Creative commons 3.0 by-nc.
#
# a = -7:
#
(2,1)
(32,181)
(631/225,13096/3375)
(262592/32761,133644239/5929741)
(228526082/43151761,3372257766151/283463918009)
(561031306921/154354694400,388387867640090219/60642872335872000)
(21958037024628002/1475405612398081,3250339065359504018865089/56671818256473200873729)
(1317947790778206465152/585137099344665493081,29780202482245925777232666757439/14154236625817924554358971874979)
#
# a = -4:
#
(2,2)
(5,11)
(106/9,1090/27)
(785/484,5497/10648)
(151322/3721,58862702/226981)
(8045029/2673225,21077984917/4370722875)
(5495994962/1957089121,368819269296622/86579665623919)
(3227836439105/58500129424,5799120182710629023/14149309303524032)
(8152570498330546/4944742493612769,241351355149002573947470/347708669978634678361647)
(32786487748262370725/3223146653090632921,187376684827540113816418141909/5786555188766724790916482531)
(775591358322596517307322/140311824962137940692681,674908317729768049643355850347699278/52558312156241243832650598792940421)
(9106951205882530770279227281/4750657097043745532284388100,571343831586698159826130934072937894196679/327439091144059530733072053389243920779000)
(139421383226822591551922450733390799685/66554560158273542805057086258862648241,1237296057881637800073948377696431849457500695604198666571/542958612617904356291482054241183458703817640478849101289)
#
# a = -2:
#
(3,5)
(129/100,383/1000)
(164323/29241,66234835/5000211)
(2340922881/58675600,113259286337279/449455096000)
(307326105747363/160280942564521,4559771683571581358275/2029190552145716973931)
(794845361623184880769/513127310073606144900,15230044576037327107200537568897/11623520729117946174953656293000)
(30037088724630450803382035538503505921/3010683982898763071786842993779918400,164455721751979625643914376686667695661898155872010593281/5223934923525719974563641453744978655831227509874752000)
#
# a = 2:
#
(-1,1)
(17/4,71/8)
(127/441,13175/9261)
(66113/80656,36583777/22906304)
(108305279/48846121,1226178094681/341385539669)
(-174016613231/306196222500,228355009922164103/169433679720375000)
(11140700095100159/357683450575441,1175934405978496374576911/6764695770360489996761)
(-535925530724803712767/431791166736106232896,2661377178406628694765981631103/8972441396523924058823922413056)
(325834850451854833442478847/30317214134131077328593201,5886346872409528149568212334188213358225/166929824520321193945622172391945198551)
(-64363752249455070879137307239023/293763056960316465372944069236324,7101756495124011219835271161698654764912754876409/5034957028437368992912415633092962882910696377832)
#
# a = 3:
#
(1,2)
(-23/16,11/64)
(1873/1521,130870/59319)
(2540833/7744,4050085583/681472)
(3320340721/4218632401,511703877377158/274004393077351)
(-145867600463831/104200405779600,538944270136094954197/1063663154141347656000)
(22099605479196054241/14823289114202355361,143403774211367540349170651858/57071182195170780711429750641)
(41677742803929195922238593/508105313480846959761664,269065159484683478575364835230449703617/362185120840307392031376980918259712)
#
# a = 5:
#
(-1,2)
(41/16,299/64)
(6319/3249,650998/185193)
(-3891679/5721664,29624702641/13686220288)
(176488611599/1030731025,74143869240845882/33091619557625)
(-7074384193140119/5507683954467984,693768972019321282636981/408746001244945345875648)
(8136547711004626087199/2381367765518967252769,778581937566486548253491056248238/116208984476084560395716851377103)
#
# a = 8:
#
(-2,0)
(1,3)
(2,4)
(-7/4,13/8)
(46,312)
(433/121,9765/1331)
(34/225,9548/3375)
(31073/2704,5491823/140608)
(-40514/36481,17941872/6967871)
(-4519919/6651241,47556428853/17153550539)
(20749922/2927521,95576099756/5008988431)
(-1549041479/5127992100,1036851436174931/367215514281000)
(44122019758/8706942721,9548576010693720/812453532239231)
(-68394192210238/47602948461121,736905526791161954404/328436019275071267169)
(129402993027361/6702926178001,1472847512264815811667/17353882577770767001)
(892933489418780033/326211856441766464,994822284545339876177687617/186315768712277487672882688)
(189231302456678460252994/1215154827148543193025,82317074576916570468069669003991972/42359168328730279219055304158625)
(-92185341574042143740447/47915403027743886659761,9831718303952050895782458506386995/10488483955253302585843822915996009)
(13374331097609148804915017515455796368481/22051615223193262916034847731979421552400,9390275466685011476921783529988027183542763096970141655632879/3274617729483833474933109530005465059622804745547908703768000)
#
# a = 9:
#
(0,3)
(6,15)
(-2,1)
(3,6)
(24/25,393/125)
(-15/16,183/64)
(40,253)
(4662/289,318657/4913)
(-629/441,22870/9261)
(2142/1369,181437/50653)
(639280/64009,513439919/16194277)
(497145/238144,494391309/116214272)
(-740784/429025,551537139/281011375)
(1441917363/11895601,54753470848434/41027927849)
(-181479482/333756361,18128073165931/6097394959109)
(378058686/692163481,55122722199075/18210129021629)
(4040707888729/922637091600,8546494108076860067/886229831965464000)
(-10406815022520/5007404224729,1711276861163052201/11205183603973252067)
(12896534702520/3260635552729,49567687787298108201/5887804612180468067)
(41943625953091798/103802620711907881,100697737447433265898973381/33443558187614849111115221)
(-54928226011163037/136185739621657441,150220714680825282075797706/50257103002569453308079761)
(713380487781542766/3229537400502361,602534641703950361848515555/183531442294359282813859)
(125360522428103195662176/14500721596011932260225,44693567751508804428095897134543299/1746161553045819126092142165853375)
(-46927369902193698259815/25870140126697906710784,7244528443524108073316654410465731/4161004367553855150531026969341952)
(17712591252741962842340733211/12654009844270166724136500681,4877803567355428492994311983166753463586290/1423450115448743112962893498889083773773829)
(121718706505022206745564313301055800/109681363898325266141990093298246721,116955202775183728481587575846782002407577728230665693/36324468085809037890186889114233321124528706519663519)
#
# a = 10:
#
(-1,3)
(9/4,37/8)
(719/169,20493/2197)
(-39519/21904,6585841/3241792)
(77021039/1836025,675994981587/2487813875)
(-1154375351/31543891236,17716251448859003/5602384346861016)
(535679026291679/503001144169969,37767156800862666634077/11281152222085939531703)
(35664161894143913601/3800195199756652096,214269011180479331956684653119/7408134480949922621385529856)
(-6667498841987843978554081/3096286159358371640073361,658266729411156585323428700148708963/5448307828525549302791376223929256391)