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Label Class Conductor Discriminant Rank* Torsion $\textrm{End}^0(J_{\overline\Q})$ Igusa-Clebsch invariants Igusa invariants G2-invariants Equation
196.a.21952.1 196.a \( 2^{2} \cdot 7^{2} \) \( - 2^{6} \cdot 7^{3} \) $0$ $\Z/6\Z\oplus\Z/6\Z$ \(\mathrm{M}_2(\Q)\) $[1340,1345,149855,2809856]$ $[335,4620,90160,2214800,21952]$ $[4219140959375/21952,6203236875/784,12905875/28]$ $y^2 + (x^2 + x)y = x^6 + 3x^5 + 6x^4 + 7x^3 + 6x^2 + 3x + 1$
363.a.11979.1 363.a \( 3 \cdot 11^{2} \) \( - 3^{2} \cdot 11^{3} \) $0$ $\Z/2\Z\oplus\Z/10\Z$ \(\Q \times \Q\) $[344,-3068,-526433,-47916]$ $[172,1744,45841,1210779,-11979]$ $[-150536645632/11979,-8874253312/11979,-1356160144/11979]$ $y^2 + (x^2 + 1)y = x^5 + 2x^3 + 4x^2 + 2x$
363.a.43923.1 363.a \( 3 \cdot 11^{2} \) \( - 3 \cdot 11^{4} \) $0$ $\Z/10\Z$ \(\Q \times \Q\) $[11096,25612,88274095,-175692]$ $[5548,1278244,392069161,135322995423,-43923]$ $[-5256325630316243968/43923,-1804005053317888/363,-99735603013264/363]$ $y^2 + x^2y = 11x^5 - 13x^4 - 7x^3 + 10x^2 + x - 2$
450.a.36450.1 450.a \( 2 \cdot 3^{2} \cdot 5^{2} \) \( 2 \cdot 3^{6} \cdot 5^{2} \) $0$ $\Z/2\Z\oplus\Z/12\Z$ \(\Q \times \Q\) $[23444,212089,1627179821,4665600]$ $[5861,1422468,457836300,164990835819,36450]$ $[6916057684302385301/36450,5303516319500302/675,1294426477922/3]$ $y^2 + (x^3 + 1)y = x^5 - 4x^4 - 9x^3 + 28x^2 - 6x - 16$
464.a.29696.1 464.a \( 2^{4} \cdot 29 \) \( - 2^{10} \cdot 29 \) $0$ $\Z/2\Z\oplus\Z/8\Z$ \(\Q\) $[680,-5255,-1253953,-3712]$ $[680,22770,1180736,71106895,-29696]$ $[-141985700000/29,-6991813125/29,-533176100/29]$ $y^2 + (x + 1)y = 8x^5 + 3x^4 - 4x^3 - 2x^2$
464.a.29696.2 464.a \( 2^{4} \cdot 29 \) \( - 2^{10} \cdot 29 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ \(\Q\) $[45368,202225,3012190355,-3712]$ $[45368,85625826,215176422416,607585463496703,-29696]$ $[-187693059992988715232/29,-7808250185554819143/29,-432507850151022641/29]$ $y^2 + xy = 4x^5 + 33x^4 + 72x^3 + 16x^2 + x$
472.a.60416.1 472.a \( 2^{3} \cdot 59 \) \( 2^{10} \cdot 59 \) $0$ $\Z/8\Z$ \(\Q\) $[152,17065,1592025,7552]$ $[152,-10414,-926656,-62325777,60416]$ $[79235168/59,-35714813/59,-20907676/59]$ $y^2 + (x + 1)y = 8x^5 + 5x^4 + 4x^3 + 2x^2$
504.a.27216.1 504.a \( 2^{3} \cdot 3^{2} \cdot 7 \) \( - 2^{4} \cdot 3^{5} \cdot 7 \) $0$ $\Z/4\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[8456,9496,26675348,108864]$ $[4228,743250,173847744,45651924783,27216]$ $[12063042849801664/243,167186257609000/81,3083035208512/27]$ $y^2 + (x^3 + x)y = 3x^4 + 15x^2 + 21$
588.a.18816.1 588.a \( 2^{2} \cdot 3 \cdot 7^{2} \) \( - 2^{7} \cdot 3 \cdot 7^{2} \) $0$ $\Z/24\Z$ \(\Q \times \Q\) $[748,11545,2902787,2408448]$ $[187,976,-192,-247120,18816]$ $[228669389707/18816,398891383/1176,-34969/98]$ $y^2 + (x^3 + 1)y = x^5 + x^4 + 5x^2 + 12x + 8$
600.a.18000.1 600.a \( 2^{3} \cdot 3 \cdot 5^{2} \) \( 2^{4} \cdot 3^{2} \cdot 5^{3} \) $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/6\Z$ \(\Q \times \Q\) $[1376,23824,11410044,72000]$ $[688,15752,244900,-19908576,18000]$ $[9634345320448/1125,320612931584/1125,289804864/45]$ $y^2 + xy = 10x^5 - 18x^4 + 8x^3 + x^2 - x$
600.a.96000.1 600.a \( 2^{3} \cdot 3 \cdot 5^{2} \) \( 2^{8} \cdot 3 \cdot 5^{3} \) $0$ $\Z/2\Z\oplus\Z/6\Z$ \(\Q \times \Q\) $[92,4981,43947,-12000]$ $[92,-2968,47600,-1107456,-96000]$ $[-25745372/375,9027914/375,-62951/15]$ $y^2 + (x + 1)y = 4x^5 + 5x^4 + 3x^3 + 2x^2$
600.b.30000.1 600.b \( 2^{3} \cdot 3 \cdot 5^{2} \) \( 2^{4} \cdot 3 \cdot 5^{4} \) $0$ $\Z/2\Z\oplus\Z/8\Z$ \(\Q \times \Q\) $[600,18744,4690524,120000]$ $[300,626,-198336,-14973169,30000]$ $[81000000,563400,-595008]$ $y^2 + (x^3 + x)y = x^4 + x^2 - 3$
630.a.34020.1 630.a \( 2 \cdot 3^{2} \cdot 5 \cdot 7 \) \( 2^{2} \cdot 3^{5} \cdot 5 \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[24100,969793,7474503265,4354560]$ $[6025,1472118,470090880,166291536519,34020]$ $[1587871127345703125/6804,10732293030978125/1134,13543327580000/27]$ $y^2 + (x^2 + x)y = 3x^5 + 10x^4 - 23x^2 - 6x + 15$
640.a.81920.1 640.a \( 2^{7} \cdot 5 \) \( - 2^{14} \cdot 5 \) $0$ $\Z/12\Z$ \(\mathsf{CM} \times \Q\) $[912,147,44562,10]$ $[3648,552928,111431680,25193348864,81920]$ $[39432490647552/5,1638374321664/5,18102076416]$ $y^2 + x^3y = 3x^4 + 13x^2 + 20$
640.a.81920.2 640.a \( 2^{7} \cdot 5 \) \( 2^{14} \cdot 5 \) $0$ $\Z/12\Z$ \(\mathsf{CM} \times \Q\) $[912,147,44562,10]$ $[3648,552928,111431680,25193348864,81920]$ $[39432490647552/5,1638374321664/5,18102076416]$ $y^2 + x^3y = -3x^4 + 13x^2 - 20$
644.b.14812.1 644.b \( 2^{2} \cdot 7 \cdot 23 \) \( - 2^{2} \cdot 7 \cdot 23^{2} \) $0$ $\Z/10\Z$ \(\Q\) $[1268,-40511,-17688719,-1895936]$ $[317,5875,170781,4905488,-14812]$ $[-3201078401357/14812,-187148201375/14812,-17161611909/14812]$ $y^2 + (x^3 + 1)y = x^5 - x^4 - 4x^3 + 5x^2 - x - 1$
676.b.17576.1 676.b \( 2^{2} \cdot 13^{2} \) \( - 2^{3} \cdot 13^{3} \) $0$ $\Z/3\Z\oplus\Z/3\Z$ \(\mathrm{M}_2(\Q)\) $[1244,1249,129167,2249728]$ $[311,3978,72332,1667692,17576]$ $[2909390022551/17576,4602275343/676,10349147/26]$ $y^2 + (x^2 + x)y = -x^6 + 3x^5 - 6x^4 + 6x^3 - 6x^2 + 3x - 1$
704.a.45056.1 704.a \( 2^{6} \cdot 11 \) \( - 2^{12} \cdot 11 \) $0$ $\Z/2\Z\oplus\Z/6\Z$ \(\Q\) $[134,-464,-15328,-176]$ $[268,4230,61444,-356477,-45056]$ $[-1350125107/44,-636113745/352,-68955529/704]$ $y^2 + y = 4x^5 + 4x^4 - x^3 - 2x^2$
708.a.19116.1 708.a \( 2^{2} \cdot 3 \cdot 59 \) \( - 2^{2} \cdot 3^{4} \cdot 59 \) $0$ $\Z/10\Z$ \(\Q\) $[908,-132815,8426215,2446848]$ $[227,7681,-438901,-39657072,19116]$ $[602738989907/19116,89845294523/19116,-383324231/324]$ $y^2 + (x^3 + 1)y = -x^5 + 4x^2 + 4x - 1$
731.a.12427.1 731.a \( 17 \cdot 43 \) \( - 17^{2} \cdot 43 \) $0$ $\Z/10\Z$ \(\Q\) $[480,-21564,-3373785,-49708]$ $[240,5994,167265,1053891,-12427]$ $[-796262400000/12427,-82861056000/12427,-9634464000/12427]$ $y^2 + (x^3 + x^2)y = x^5 + 2x^4 - x - 3$
741.a.28899.1 741.a \( 3 \cdot 13 \cdot 19 \) \( - 3^{2} \cdot 13^{2} \cdot 19 \) $0$ $\Z/2\Z\oplus\Z/8\Z$ \(\Q\) $[576,-840,740385,115596]$ $[288,3596,-38169,-5980972,28899]$ $[220150628352/3211,9544531968/3211,-351765504/3211]$ $y^2 + (x + 1)y = -3x^5 - x^4 + 2x^2 + x$
762.a.82296.1 762.a \( 2 \cdot 3 \cdot 127 \) \( 2^{3} \cdot 3^{4} \cdot 127 \) $0$ $\Z/2\Z\oplus\Z/12\Z$ \(\Q\) $[12004,205249,810020577,10533888]$ $[3001,366698,58441312,10228738527,82296]$ $[243405270090015001/82296,4955375073324349/41148,65790314289164/10287]$ $y^2 + (x^2 + x)y = x^5 - 8x^4 + 14x^3 + 2x^2 - x$
784.a.43904.1 784.a \( 2^{4} \cdot 7^{2} \) \( - 2^{7} \cdot 7^{3} \) $0$ $\Z/12\Z$ \(\Q \times \Q\) $[21288,3000,20891172,175616]$ $[10644,4720114,2790613504,1855953490895,43904]$ $[1067368445729034408/343,6352710665144931/49,50408453477952/7]$ $y^2 + (x^3 + x)y = 4x^4 + 27x^2 + 56$
784.b.12544.1 784.b \( 2^{4} \cdot 7^{2} \) \( 2^{8} \cdot 7^{2} \) $0$ $\Z/2\Z\oplus\Z/6\Z$ \(\Q \times \Q\) $[116,445,16259,1568]$ $[116,264,-1280,-54544,12544]$ $[82044596/49,1609674/49,-67280/49]$ $y^2 + (x^3 + x)y = -1$
784.b.25088.1 784.b \( 2^{4} \cdot 7^{2} \) \( - 2^{9} \cdot 7^{2} \) $0$ $\Z/2\Z$ \(\Q \times \Q\) $[2740,15382525,36170522453,3136]$ $[2740,-9942200,-24298750736,-41356479464160,25088]$ $[301635777856250/49,-399451653071875/49,-712598832131225/98]$ $y^2 + (x^2 + 1)y = -x^6 - 3x^5 + 7x^4 + 2x^3 - 49x^2 + 41x - 9$
784.b.76832.1 784.b \( 2^{4} \cdot 7^{2} \) \( - 2^{5} \cdot 7^{4} \) $0$ $\Z/6\Z$ \(\Q \times \Q\) $[1520,132280,50979316,307328]$ $[760,2020,6076,134340,76832]$ $[7923516800000/2401,27710360000/2401,2238200/49]$ $y^2 + (x + 1)y = -x^6 + 4x^5 - 4x^4 - 2x^3 + 10x - 9$
816.a.13872.1 816.a \( 2^{4} \cdot 3 \cdot 17 \) \( - 2^{4} \cdot 3 \cdot 17^{2} \) $0$ $\Z/2\Z\oplus\Z/6\Z$ \(\Q\) $[688,9592,2944404,55488]$ $[344,3332,-80164,-9669660,13872]$ $[301073291264/867,498667904/51,-592892944/867]$ $y^2 + (x^3 + x^2)y = -2x^4 + 6x^2 - 8x + 3$
816.a.39168.1 816.a \( 2^{4} \cdot 3 \cdot 17 \) \( 2^{8} \cdot 3^{2} \cdot 17 \) $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/6\Z$ \(\Q\) $[436,3373,434667,4896]$ $[436,5672,77824,439920,39168]$ $[61544958196/153,1836351122/153,57789184/153]$ $y^2 + (x^2 + 1)y = 3x^5 - 4x^3 - x^2 + x$
816.b.52224.1 816.b \( 2^{4} \cdot 3 \cdot 17 \) \( - 2^{10} \cdot 3 \cdot 17 \) $0$ $\Z/6\Z$ \(\Q \times \Q\) $[15964,2380825,11444690699,6528]$ $[15964,9031504,6282991104,4683401370560,52224]$ $[1012531723491160951/51,35882713644370099/51,30660536527816]$ $y^2 + (x^3 + x)y = -x^6 - 12x^4 - 27x^2 - 17$
826.a.11564.1 826.a \( 2 \cdot 7 \cdot 59 \) \( - 2^{2} \cdot 7^{2} \cdot 59 \) $0$ $\Z/2\Z\oplus\Z/6\Z$ \(\Q\) $[92,-554591,-3126961,1480192]$ $[23,23130,-104176,-134348237,11564]$ $[6436343/11564,140711355/5782,-13777276/2891]$ $y^2 + (x^2 + x)y = x^5 + x^4 + 3x^3 - 4x^2 - 4x + 3$
882.a.63504.1 882.a \( 2 \cdot 3^{2} \cdot 7^{2} \) \( 2^{4} \cdot 3^{4} \cdot 7^{2} \) $0$ $\Z/2\Z\oplus\Z/8\Z$ \(\Q \times \Q\) $[548,6049,662961,8128512]$ $[137,530,6336,146783,63504]$ $[48261724457/63504,681408545/31752,825836/441]$ $y^2 + (x^2 + x)y = x^5 + x^4 + x^3 + 3x^2 + 3x + 1$
925.a.23125.1 925.a \( 5^{2} \cdot 37 \) \( 5^{4} \cdot 37 \) $0$ $\Z/2\Z\oplus\Z/8\Z$ \(\Q\) $[3496,50536,55764955,92500]$ $[1748,118890,10257041,948618892,23125]$ $[16319511005139968/23125,126998797147776/4625,31340429803664/23125]$ $y^2 + xy = 5x^5 + x^4 - 19x^3 + 18x^2 - 5x$
975.a.63375.1 975.a \( 3 \cdot 5^{2} \cdot 13 \) \( - 3 \cdot 5^{3} \cdot 13^{2} \) $0$ $\Z/2\Z\oplus\Z/6\Z$ \(\Q\) $[148,-48575,-4076175,-8112000]$ $[37,2081,35929,-750297,-63375]$ $[-69343957/63375,-105408893/63375,-49186801/63375]$ $y^2 + (x^3 + 1)y = -x^5 + x^3 + 2x^2 + x - 1$
1008.a.27216.1 1008.a \( 2^{4} \cdot 3^{2} \cdot 7 \) \( 2^{4} \cdot 3^{5} \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/8\Z$ \(\Q \times \Q\) $[8456,9496,26675348,108864]$ $[4228,743250,173847744,45651924783,27216]$ $[12063042849801664/243,167186257609000/81,3083035208512/27]$ $y^2 + (x^3 + x)y = -4x^4 + 15x^2 - 21$
1083.a.20577.1 1083.a \( 3 \cdot 19^{2} \) \( 3 \cdot 19^{3} \) $1$ $\Z/3\Z$ \(\Q \times \Q\) $[904,13684,4578992,82308]$ $[452,6232,-8664,-10688488,20577]$ $[18866536236032/20577,30289293824/1083,-1634432/19]$ $y^2 + x^3y = x^5 - 5x^4 + 11x^3 - 13x^2 + 9x - 3$
1083.b.87723.1 1083.b \( 3 \cdot 19^{2} \) \( - 3^{5} \cdot 19^{2} \) $0$ $\Z/15\Z$ \(\Q \times \Q\) $[5464,8692,15768656,350892]$ $[2732,309544,46549080,7838649656,87723]$ $[152196082896530432/87723,6311963449851392/87723,1429770125440/361]$ $y^2 + y = -x^6 - 3x^5 - 8x^4 - 11x^3 - 14x^2 - 9x - 6$
1104.a.17664.1 1104.a \( 2^{4} \cdot 3 \cdot 23 \) \( 2^{8} \cdot 3 \cdot 23 \) $0$ $\Z/10\Z$ \(\Q\) $[88,160,4888,69]$ $[176,864,-1280,-242944,17664]$ $[659664896/69,6133248/23,-154880/69]$ $y^2 = x^5 - 2x^4 + 4x^3 - 4x^2 + 3x - 1$
1147.a.35557.1 1147.a \( 31 \cdot 37 \) \( 31^{2} \cdot 37 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q\) $[3712,11944,14677639,142228]$ $[1856,141540,14195057,1578113548,35557]$ $[22023678539595776/35557,904926084464640/35557,48898223869952/35557]$ $y^2 + xy = x^5 + 8x^4 + 18x^3 + 8x^2 + x$
1147.a.35557.2 1147.a \( 31 \cdot 37 \) \( 31^{2} \cdot 37 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ \(\Q\) $[12352,2309104,8338761079,142228]$ $[6176,1204440,279006977,68117844088,35557]$ $[8985379753611493376/35557,283731159059005440/35557,10642156427543552/35557]$ $y^2 + xy = x^5 + 6x^4 - 32x^2 + x$
1148.a.47068.1 1148.a \( 2^{2} \cdot 7 \cdot 41 \) \( - 2^{2} \cdot 7 \cdot 41^{2} \) $0$ $\Z/10\Z$ \(\Q\) $[1236,129537,36025137,-6024704]$ $[309,-1419,31221,1908432,-47068]$ $[-2817036000549/47068,41865649551/47068,-2981012301/47068]$ $y^2 + (x^2 + x + 1)y = x^5 + 2x^4 - 5x^3 + x$
1170.a.10530.1 1170.a \( 2 \cdot 3^{2} \cdot 5 \cdot 13 \) \( - 2 \cdot 3^{4} \cdot 5 \cdot 13 \) $0$ $\Z/2\Z\oplus\Z/6\Z$ \(\Q \times \Q\) $[507196,192673,32552199279,1347840]$ $[126799,669908072,4718980180980,37396285759331459,10530]$ $[32777750301275239538233999/10530,682861614668954802420364/5265,7205289570406928666]$ $y^2 + (x^2 + x)y = 15x^6 + 28x^5 + 62x^4 + 59x^3 + 62x^2 + 28x + 15$
1176.b.16464.1 1176.b \( 2^{3} \cdot 3 \cdot 7^{2} \) \( 2^{4} \cdot 3 \cdot 7^{3} \) $0$ $\Z/2\Z\oplus\Z/6\Z$ \(\Q \times \Q\) $[160,4720,130020,-65856]$ $[80,-520,4220,16800,-16464]$ $[-204800000/1029,16640000/1029,-1688000/1029]$ $y^2 + (x + 1)y = -2x^5 + x^2$
1180.a.18880.1 1180.a \( 2^{2} \cdot 5 \cdot 59 \) \( - 2^{6} \cdot 5 \cdot 59 \) $0$ $\Z/18\Z$ \(\Q\) $[916,23257,5960477,-2416640]$ $[229,1216,6656,11392,-18880]$ $[-629763392149/18880,-228170791/295,-5453864/295]$ $y^2 + (x^3 + 1)y = -2x^4 + 4x^2 + 2x$
1192.a.19072.1 1192.a \( 2^{3} \cdot 149 \) \( - 2^{7} \cdot 149 \) $0$ $\Z/22\Z$ \(\Q\) $[160,3184,271780,76288]$ $[80,-264,-17220,-361824,19072]$ $[25600000/149,-1056000/149,-861000/149]$ $y^2 + (x^3 + x)y = x^3 - 2x^2 - x + 1$
1197.a.10773.1 1197.a \( 3^{2} \cdot 7 \cdot 19 \) \( 3^{4} \cdot 7 \cdot 19 \) $0$ $\Z/10\Z$ \(\Q\) $[520,10900,1557089,-43092]$ $[260,1000,-1121,-322865,-10773]$ $[-1188137600000/10773,-17576000000/10773,3988400/567]$ $y^2 + (x^3 + x^2)y = -x^3 - x^2 - x + 2$
1200.a.30000.1 1200.a \( 2^{4} \cdot 3 \cdot 5^{2} \) \( - 2^{4} \cdot 3 \cdot 5^{4} \) $0$ $\Z/2\Z\oplus\Z/8\Z$ \(\Q \times \Q\) $[600,18744,4690524,120000]$ $[300,626,-198336,-14973169,30000]$ $[81000000,563400,-595008]$ $y^2 + (x^3 + x)y = -2x^4 + x^2 + 3$
1216.a.19456.1 1216.a \( 2^{6} \cdot 19 \) \( - 2^{10} \cdot 19 \) $0$ $\Z/2\Z$ \(\Q\) $[3996,347595,394636194,-2432]$ $[3996,433604,54136720,7079476076,-19456]$ $[-995009990004999/19,-108076122094599/76,-3376781293545/76]$ $y^2 + x^2y = 4x^5 + 3x^4 - 11x^3 - 6x^2 + 6x - 1$
1258.a.21386.1 1258.a \( 2 \cdot 17 \cdot 37 \) \( 2 \cdot 17^{2} \cdot 37 \) $0$ $\Z/10\Z$ \(\Q\) $[2360,51148,37529695,85544]$ $[1180,49492,2427545,103761259,21386]$ $[1143878878400000/10693,40658469872000/10693,1690056829000/10693]$ $y^2 + xy = x^5 + 4x^4 - 5x^3 - 4x^2 + 5x - 1$
1280.a.12800.1 1280.a \( 2^{8} \cdot 5 \) \( - 2^{9} \cdot 5^{2} \) $0$ $\Z/2\Z\oplus\Z/6\Z$ \(\Q\) $[22,-170,-1832,-50]$ $[44,534,7684,13235,-12800]$ $[-322102/25,-355377/100,-232441/200]$ $y^2 + y = 2x^5 + x^4 - x^3 - x^2$
1296.a.20736.1 1296.a \( 2^{4} \cdot 3^{4} \) \( 2^{8} \cdot 3^{4} \) $0$ $\Z/2\Z\oplus\Z/6\Z$ \(\mathrm{M}_2(\Q)\) $[78,216,4806,81]$ $[156,438,-428,-64653,20736]$ $[4455516,160381/2,-18083/36]$ $y^2 = x^5 - x^4 - 3x^3 + 4x^2 - x$
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