# List of all rational elliptic curves with good reduction outside S, up to Q-isomorphisms,
# for all sets S = {2, 3, p},
# where p ranges over all other primes less or equal to 100.
# It contains 105088 pairs (c4,c6), some of which may appear for more than one S.
# Format: "(c4,c6)".
# Computing this list took 3557 seconds.
# Authors: Rafael von Känel and Benjamin Matschke, 2015.
# License: Creative commons 3.0 by-nc.
#
#
# S = {2, 3, 5}:
#
(-10791921600,-1316232618048000)
(-10791921600,1316232618048000)
(-2697980400,164529077256000)
(-2697980400,-164529077256000)
(-1199102400,48749356224000)
(-1199102400,-48749356224000)
(3611304000,-224950737600000)
(3611304000,224950737600000)
(-387633600,-16444980288000)
(-387633600,16444980288000)
(399297600,19419580224000)
(399297600,-19419580224000)
(78926400,15348750912000)
(78926400,-15348750912000)
(-431676864,10529860944384)
(-431676864,-10529860944384)
(-299775600,6093669528000)
(-299775600,-6093669528000)
(902826000,-28118842200000)
(-96908400,2055622536000)
(99824400,2427447528000)
(401256000,-8331508800000)
(401256000,8331508800000)
(19731600,1918593864000)
(-107919216,1316232618048)
(-107919216,-1316232618048)
(-138801600,-383372352000)
(-138801600,383372352000)
(3032769600,-167021528256000)
(3032769600,167021528256000)
(1708776000,70645348800000)
(1708776000,-70645348800000)
(243777600,-3955075776000)
(243777600,3955075776000)
(76046400,-1245125952000)
(76046400,1245125952000)
(65448000,-1075560768000)
(65448000,1075560768000)
(-43070400,-609073344000)
(-43070400,609073344000)
(44366400,719243712000)
(44366400,-719243712000)
(8769600,568472256000)
(8769600,-568472256000)
(138627158400,51614589975552000)
(138627158400,-51614589975552000)
(-47964096,-389994849792)
(-47964096,389994849792)
(144452160,1799605900800)
(144452160,-1799605900800)
(222782400,3357039168000)
(222782400,-3357039168000)
(22550400,441739008000)
(22550400,-441739008000)
(19368000,-409579200000)
(19368000,409579200000)
(13608000,-361817280000)
(13608000,361817280000)
(18792000,-337089600000)
(18792000,337089600000)
(100314000,1041438600000)
(-24753600,-192549312000)
(-24753600,192549312000)
(-17366400,213964416000)
(-17366400,-213964416000)
(26049600,-256561344000)
(26049600,256561344000)
(-17496000,-199454400000)
(-17496000,199454400000)
(-34700400,47921544000)
(155649600,-1950267456000)
(155649600,1950267456000)
(89481600,-863028864000)
(89481600,863028864000)
(758192400,-20877691032000)
(-5054400,-150652224000)
(-5054400,150652224000)
(-15505344,-131559842304)
(-15505344,131559842304)
(15971904,-155356641792)
(427194000,-8830668600000)
(34344000,246110400000)
(15971904,155356641792)
(34344000,-246110400000)
(-24177600,-63298368000)
(-24177600,63298368000)
(60944400,-494384472000)
(19011600,155640744000)
(3157056,122790007296)
(3157056,-122790007296)
(16362000,134445096000)
(56426625,439356909375)
(-3369600,110481408000)
(216950400,-3197428992000)
(-3369600,-110481408000)
(216950400,3197428992000)
(1166400,106235712000)
(1166400,-106235712000)
(-1022400,92563776000)
(-1022400,-92563776000)
(-15422400,-69937344000)
(-15422400,69937344000)
(9345600,-93496896000)
(9345600,93496896000)
(278121600,4639052736000)
(12830400,-98817408000)
(12830400,98817408000)
(278121600,-4639052736000)
(16718400,110434752000)
(16718400,-110434752000)
(29160000,-178459200000)
(29160000,178459200000)
(-10767600,-76134168000)
(11091600,-89905464000)
(-12312000,59019840000)
(-12312000,-59019840000)
(2192400,-71059032000)
(34656789600,-6451823746944000)
(34656789600,6451823746944000)
(30326400,-179718912000)
(30326400,179718912000)
(-15192000,-26844480000)
(-15192000,26844480000)
(-11991024,48749356224)
(-11991024,-48749356224)
(-15422400,14198976000)
(-15422400,-14198976000)
(36113040,-224950737600)
(55695600,419629896000)
(55695600,-419629896000)
(-14385600,-15256512000)
(-14385600,15256512000)
(3470400,55363392000)
(3470400,-55363392000)
(5637600,55217376000)
(5637600,-55217376000)
(4842000,-51197400000)
(-201600,48788352000)
(-201600,-48788352000)
(336974400,6185982528000)
(336974400,-6185982528000)
(49896000,-355285440000)
(49896000,355285440000)
(3402000,-45227160000)
(189864000,-2616494400000)
(189864000,2616494400000)
(4698000,42136200000)
(27086400,-146484288000)
(27086400,146484288000)
(8449600,46115776000)
(8449600,-46115776000)
(26049600,-137588544000)
(-9201600,-21788352000)
(-9201600,21788352000)
(26049600,137588544000)
(-6056775,-32119102125)
(-7257600,-29020032000)
(-7257600,29020032000)
(7272000,39835584000)
(7272000,-39835584000)
(6239025,-37928867625)
(-1166400,33172416000)
(-1166400,-33172416000)
(1233225,-29978029125)
(-6188400,-24068664000)
(486518400,-10731253248000)
(486518400,10731253248000)
(-4341600,-26745552000)
(-4341600,26745552000)
(44712000,300231360000)
(44712000,-300231360000)
(-1944000,27293760000)
(-1944000,-27293760000)
(6512400,-32070168000)
(-4374000,-24931800000)
(9460800,-38584512000)
(9460800,38584512000)
(110030400,1154409408000)
(110030400,-1154409408000)
(38912400,243783432000)
(277992000,-4635040320000)
(277992000,4635040320000)
(744552000,20316215232000)
(744552000,-20316215232000)
(22370400,107878608000)
(22370400,-107878608000)
(0,20995200000)
(10080000,-38275200000)
(0,-20995200000)
(24494400,123031872000)
(24494400,-123031872000)
(10080000,38275200000)
(15403017600,1911651480576000)
(15403017600,-1911651480576000)
(-1065600,-20172672000)
(-1065600,20172672000)
(6609600,-25614144000)
(6609600,25614144000)
(1872000,-19068480000)
(1872000,19068480000)
(-1263600,18831528000)
(-3876336,16444980288)
(-5054400,13576896000)
(-1944000,17496000000)
(-1944000,-17496000000)
(-5054400,-13576896000)
(3992976,19419580224)
(8586000,-30763800000)
(16050240,-66652070400)
(16050240,66652070400)
(3110400,-18335808000)
(24753600,-124334784000)
(24753600,124334784000)
(-6044400,7912296000)
(489600,16498944000)
(489600,-16498944000)
(2505600,-16360704000)
(2505600,16360704000)
(13608000,52488000000)
(13608000,-52488000000)
(789264,15348750912)
(2152000,-15169600000)
(2152000,15169600000)
(5313600,-19175616000)
(5313600,19175616000)
(34344000,-201787200000)
(34344000,201787200000)
(3240000,15163200000)
(3240000,-15163200000)
(-842400,13810176000)
(-842400,-13810176000)
(54237600,399678624000)
(54237600,-399678624000)
(2721600,14276736000)
(2721600,-14276736000)
(-5552064,3066978816)
(-5552064,-3066978816)
(291600,13279464000)
(11664000,41990400000)
(11664000,-41990400000)
(1512000,13400640000)
(1512000,-13400640000)
(439862400,9225197568000)
(439862400,-9225197568000)
(-5054400,4618944000)
(-5054400,-4618944000)
(2088000,12484800000)
(2088000,-12484800000)
(-255600,11570472000)
(-255600,-11570472000)
(-3855600,-8742168000)
(3240000,-12830400000)
(3240000,12830400000)
(2336400,11687112000)
(69530400,-579881592000)
(3207600,-12352176000)
(3207600,12352176000)
(69530400,579881592000)
(-1944000,10497600000)
(-1944000,-10497600000)
(4179600,-13804344000)
(103809600,1057738176000)
(103809600,-1057738176000)
(7290000,22307400000)
(-4665600,2939328000)
(0,-10497600000)
(121310784,1336172226048)
(121310784,-1336172226048)
(6350400,18988992000)
(6350400,-18988992000)
(-3078000,7377480000)
(68351040,565162790400)
(68351040,-565162790400)
(-1944000,8538048000)
(-1944000,-8538048000)
(9751104,-31640606208)
(9751104,31640606208)
(-2750400,-7131456000)
(-2750400,7131456000)
(3041856,9961007616)
(3041856,-9961007616)
(-1929600,-7924608000)
(-1929600,7924608000)
(-4017600,-2192832000)
(-4017600,2192832000)
(7581600,-22464864000)
(7581600,22464864000)
(5544000,15379200000)
(5544000,-15379200000)
(2894400,9502272000)
(2894400,-9502272000)
(-3798000,3355560000)
(-1944000,-7387200000)
(-1944000,7387200000)
(-3855600,-1774872000)
(2617920,-8604486144)
(2617920,8604486144)
(16718400,-68724288000)
(-3596400,-1907064000)
(16718400,68724288000)
(0,6998400000)
(0,-6998400000)
(867600,-6920424000)
(867600,6920424000)
(17294400,72232128000)
(17294400,-72232128000)
(5313600,-13950144000)
(5313600,13950144000)
(17496000,-73483200000)
(17496000,73483200000)
(7905600,-23164704000)
(7905600,23164704000)
(-3441600,1245888000)
(-3441600,-1245888000)
(9942400,-31964032000)
(9942400,31964032000)
(6883200,-19084032000)
(6883200,19084032000)
(-50400,-6098544000)
(-50400,6098544000)
(84243600,773247816000)
(3240000,-8164800000)
(3240000,8164800000)
(12474000,-44410680000)
(-1944000,-4898880000)
(1166400,5738688000)
(-1944000,4898880000)
(1166400,-5738688000)
(-561600,5579712000)
(-561600,-5579712000)
(-1722816,4872586752)
(-1722816,-4872586752)
(1166400,-5458752000)
(1166400,5458752000)
(0,5248800000)
(0,-5248800000)
(3816000,9115200000)
(47466000,327061800000)
(1774656,5753949696)
(3816000,-9115200000)
(1774656,-5753949696)
(-2980800,513216000)
(-2980800,-513216000)
(86760000,808142400000)
(86760000,-808142400000)
(-2686400,2344384000)
(-2686400,-2344384000)
(6771600,18310536000)
(2112400,-5764472000)
(34344000,201320640000)
(34344000,-201320640000)
(350784,-4547778048)
(350784,4547778048)
(5545086336,412916719804416)
(309096000,5434257600000)
(309096000,-5434257600000)
(1296000,-4665600000)
(777600,4478976000)
(5545086336,-412916719804416)
(-2300400,-2723544000)
(6998400,-19035648000)
(777600,-4478976000)
(1296000,4665600000)
(6998400,19035648000)
(-1944000,3499200000)
(-1944000,-3499200000)
(6512400,17198568000)
(-1814400,-3627504000)
(-1814400,3627504000)
(1818000,-4979448000)
(6269625,-16272478125)
(5832000,14696640000)
(0,-4199040000)
(4665600,-10917504000)
(5832000,-14696640000)
(0,4199040000)
(4665600,10917504000)
(-291600,-4146552000)
(-291600,4146552000)
(-676800,-4076352000)
(-676800,4076352000)
(-374400,-4091904000)
(24105600,-118423296000)
(24105600,118423296000)
(-374400,4091904000)
(129600,-3934656000)
(129600,3934656000)
(-1425600,3522528000)
(-1425600,-3522528000)
(4276800,9657792000)
(4276800,-9657792000)
(-1944000,2566080000)
(-1944000,-2566080000)
(8911296,26856313344)
(8911296,-26856313344)
(121629600,-1341406656000)
(121629600,1341406656000)
(0,3499200000)
(3888000,-8398080000)
(-1944000,-2099520000)
(-1944000,2099520000)
(16718400,-68444352000)
(-2102400,1569024000)
(540432000,-12563527680000)
(-777600,-3359232000)
(-113600,3428288000)
(-777600,3359232000)
(11178000,-37528920000)
(3888000,8398080000)
(-486000,3411720000)
(902016,-3533912064)
(16718400,68444352000)
(540432000,12563527680000)
(902016,3533912064)
(-113600,-3428288000)
(-2102400,-1569024000)
(-1713600,2590272000)
(-1713600,-2590272000)
(-1022400,-3174336000)
(-1022400,3174336000)
(1814400,-4105728000)
(1814400,4105728000)
(1038400,-3462848000)
(1038400,3462848000)
(-2168775,-748774125)
(30902400,-171816768000)
(1425600,3659904000)
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(30902400,171816768000)
(1857600,-4090176000)
(1857600,4090176000)
(774720,-3276633600)
(774720,3276633600)
(2365200,-4823064000)
(3240000,-6609600000)
(3240000,6609600000)
(-1944000,1166400000)
(-1944000,-1166400000)
(27507600,-144301176000)
(544320,-2894538240)
(544320,2894538240)
(2462400,-4805568000)
(2462400,4805568000)
(-1944000,699840000)
(-1944000,-699840000)
(69498000,579380040000)
(2088000,-4104000000)
(2088000,4104000000)
(-1944000,-419904000)
(186138000,-2539526904000)
(-1944000,419904000)
(-1368000,2185920000)
(-1368000,-2185920000)
(1166400,-2939328000)
(1166400,2939328000)
(0,2624400000)
(6123600,-15378984000)
(0,-2624400000)
(6123600,15378984000)
(2520000,-4784400000)
(2520000,4784400000)
(751680,2696716800)
(751680,-2696716800)
(3850754400,-238956435072000)
(3850754400,238956435072000)
(-1814400,746496000)
(47387025,326213922375)
(-1814400,-746496000)
(360000,2548800000)
(360000,-2548800000)
(-266400,2521584000)
(-266400,-2521584000)
(3369600,-6656256000)
(3369600,6656256000)
(-1688000,-994240000)
(-1688000,994240000)
(1652400,-3201768000)
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(468000,2383560000)
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(0,2332800000)
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(129600,2286144000)
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(1569600,2984256000)
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(13608000,-50248512000)
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(4017600,8351424000)
(-1166400,1819584000)
(1944000,-3499200000)
(1944000,3499200000)
(1311422400,-47491282368000)
(26699625,137979196875)
(-486000,-2187000000)
(-1263600,-1697112000)
(4017600,-8351424000)
(1311422400,47491282368000)
(-1166400,-1819584000)
(4012560,8331508800)
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(6188400,-15541848000)
(6188400,15541848000)
(11664000,-39890880000)
(-1166400,1679616000)
(3809025,7724757375)
(-1166400,-1679616000)
(0,-2099520000)
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(-1598400,565056000)
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(-1368000,-1339200000)
(-1368000,1339200000)
(122400,-2062368000)
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(1188225,-2431886625)
(385600,-2050496000)
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(3402000,-6561000000)
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(538000,1896200000)
(1328400,2396952000)
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(-990144,1540394496)
(-990144,-1540394496)
(1022625,-2100704625)
(3240000,-6111936000)
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(8586000,25223400000)
(-694656,-1711715328)
(-1425600,-606528000)
(-1425600,606528000)
(4406400,9424512000)
(-504000,1771200000)
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(-22400,-1806976000)
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(-694656,1711715328)
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(4406400,-9424512000)
(1041984,2052490752)
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(19440000,85730400000)
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(-777600,1609632000)
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(-699840,1595635200)
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(680400,1784592000)
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(1166400,2099520000)
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(-1388016,383372352)
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(378000,1675080000)
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(109965600,1153149696000)
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(-1263600,-577368000)
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(522000,-1560600000)
(8424000,24494400000)
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(-1296000,0)
(-777600,1306368000)
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(6225984,-15602139648)
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(129600,1446336000)
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(810000,-1603800000)
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(0,1399680000)
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(-486000,1312200000)
(-486000,-1312200000)
(3579264,6904230912)
(3579264,-6904230912)
(-1166400,419904000)
(-1166400,-419904000)
(25952400,-132217272000)
(0,-1312200000)
(0,1312200000)
(-1166400,367416000)
(-1166400,-367416000)
(-672975,1189596375)
(2894400,5095872000)
(-1022400,806976000)
(2894400,-5095872000)
(-1022400,-806976000)
(30327696,-167021528256)
(-806400,-1074816000)
(-806400,1074816000)
(693225,1404772875)
(-648000,-1166400000)
(-648000,1166400000)
(1587600,-2373624000)
(-129600,-1228608000)
(-129600,1228608000)
(-202176,1205217792)
(-202176,-1205217792)
(1166400,1726272000)
(1166400,-1726272000)
(777600,-1353024000)
(9720000,-30326400000)
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(-720000,-993600000)
(-720000,993600000)
(0,-1166400000)
(777600,1353024000)
(1296000,1866240000)
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(1373760,1968883200)
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(17087760,-70645348800)
(-486000,-1067256000)
(137025,1110297375)
(-1022400,-374976000)
(-1022400,374976000)
(489600,1137024000)
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(2721600,4618944000)
(-777600,839808000)
(-777600,-839808000)
(2721600,-4618944000)
(-967104,506386944)
(-967104,-506386944)
(2437776,-3955075776)
(54057600,-397453824000)
(-687600,891432000)
(54057600,397453824000)
(-907200,606528000)
(-907200,-606528000)
(760464,1245125952)
(0,1049760000)
(0,-1049760000)
(-482400,-990576000)
(-482400,990576000)
(-1004400,-274104000)
(648000,1166400000)
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#
# S = {2, 3, 7}:
#
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#
# S = {2, 3, 11}:
#
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#
# S = {2, 3, 13}:
#
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#
# S = {2, 3, 17}:
#
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#
# S = {2, 3, 19}:
#
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#
# S = {2, 3, 23}:
#
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#
# S = {2, 3, 29}:
#
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#
# S = {2, 3, 31}:
#
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#
# S = {2, 3, 37}:
#
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#
# S = {2, 3, 41}:
#
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#
# S = {2, 3, 43}:
#
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#
# S = {2, 3, 47}:
#
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#
# S = {2, 3, 53}:
#
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#
# S = {2, 3, 59}:
#
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#
# S = {2, 3, 61}:
#
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#
# S = {2, 3, 67}:
#
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#
# S = {2, 3, 71}:
#
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#
# S = {2, 3, 73}:
#
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#
# S = {2, 3, 79}:
#
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#
# S = {2, 3, 83}:
#
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#
# S = {2, 3, 89}:
#
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#
# S = {2, 3, 97}:
#
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