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Label Class Conductor Rank* Torsion $\textrm{End}^0(J_{\overline\Q})$ Igusa-Clebsch invariants Igusa invariants G2-invariants Equation
504.a.27216.1 504.a \( 2^{3} \cdot 3^{2} \cdot 7 \) $0$ $\Z/4\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[8456,9496,26675348,108864]$ $[4228,743250,173847744,45651924783,27216]$ $[12063042849801664/243,167186257609000/81,3083035208512/27]$ $y^2 + (x^3 + x)y = 3x^4 + 15x^2 + 21$
523.a.523.1 523.a \( 523 \) $0$ $\Z/10\Z$ \(\Q\) $[120,-540,-29169,-2092]$ $[60,240,2241,19215,-523]$ $[-777600000/523,-51840000/523,-8067600/523]$ $y^2 + (x + 1)y = x^5 - x^4 - x^3$
523.a.523.2 523.a \( 523 \) $0$ $\Z/2\Z$ \(\Q\) $[332400,10084860,1107044456391,-2092]$ $[166200,1149254190,10581558955401,109467476288772525,-523]$ $[-126810465636208320000000000/523,-5276053055713522320000000/523,-292288477352026798440000/523]$ $y^2 + xy = x^5 - 31x^4 - 110x^3 + 21x^2 - x$
529.a.529.1 529.a \( 23^{2} \) $0$ $\Z/11\Z$ \(\mathsf{RM}\) $[284,2401,246639,-67712]$ $[71,110,-624,-14101,-529]$ $[-1804229351/529,-39370210/529,3145584/529]$ $y^2 + (x^3 + x + 1)y = -x^5$
555.a.8325.1 555.a \( 3 \cdot 5 \cdot 37 \) $0$ $\Z/2\Z\oplus\Z/10\Z$ \(\Q\) $[1264,18124,6869487,33300]$ $[632,13622,351361,9125317,8325]$ $[100828984082432/8325,3438682756096/8325,140342016064/8325]$ $y^2 + (x + 1)y = 3x^5 - 2x^4 - 4x^3 + x^2 + x$
574.a.293888.1 574.a \( 2 \cdot 7 \cdot 41 \) $0$ $\Z/2\Z\oplus\Z/10\Z$ \(\Q\) $[68,-55823,-955895,-37617664]$ $[17,2338,2304,-1356769,-293888]$ $[-1419857/293888,-820471/20992,-2601/1148]$ $y^2 + (x^2 + x)y = x^5 - x^4 - 3x^2 + x + 1$
576.a.576.1 576.a \( 2^{6} \cdot 3^{2} \) $0$ $\Z/10\Z$ \(\mathrm{M}_2(\Q)\) $[68,124,2616,72]$ $[68,110,-36,-3637,576]$ $[22717712/9,540430/9,-289]$ $y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x$
576.b.147456.1 576.b \( 2^{6} \cdot 3^{2} \) $0$ $\Z/4\Z\oplus\Z/4\Z$ \(\mathrm{M}_2(\Q)\) $[152,109,5469,18]$ $[608,14240,405504,10942208,147456]$ $[5071050752/9,195344320/9,1016576]$ $y^2 = x^6 + 2x^4 + 2x^2 + 1$
578.a.2312.1 578.a \( 2 \cdot 17^{2} \) $0$ $\Z/12\Z$ \(\Q \times \Q\) $[228,705,135777,295936]$ $[57,106,-992,-16945,2312]$ $[601692057/2312,9815229/1156,-402876/289]$ $y^2 + (x^2 + x)y = x^5 - 2x^4 + 2x^3 - 2x^2 + x$
587.a.587.1 587.a \( 587 \) $1$ $\mathsf{trivial}$ \(\Q\) $[60,1401,54147,-75136]$ $[15,-49,-501,-2479,-587]$ $[-759375/587,165375/587,112725/587]$ $y^2 + (x^3 + x + 1)y = -x^2 - x$
588.a.18816.1 588.a \( 2^{2} \cdot 3 \cdot 7^{2} \) $0$ $\Z/24\Z$ \(\Q \times \Q\) $[748,11545,2902787,2408448]$ $[187,976,-192,-247120,18816]$ $[228669389707/18816,398891383/1176,-34969/98]$ $y^2 + (x^3 + 1)y = x^5 + x^4 + 5x^2 + 12x + 8$
597.a.597.1 597.a \( 3 \cdot 199 \) $0$ $\Z/7\Z$ \(\Q\) $[120,192,9912,2388]$ $[60,118,-68,-4501,597]$ $[259200000/199,8496000/199,-81600/199]$ $y^2 + y = x^5 + 2x^4 + 3x^3 + 2x^2 + x$
600.a.18000.1 600.a \( 2^{3} \cdot 3 \cdot 5^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/6\Z$ \(\Q \times \Q\) $[1376,23824,11410044,72000]$ $[688,15752,244900,-19908576,18000]$ $[9634345320448/1125,320612931584/1125,289804864/45]$ $y^2 + xy = 10x^5 - 18x^4 + 8x^3 + x^2 - x$
600.a.96000.1 600.a \( 2^{3} \cdot 3 \cdot 5^{2} \) $0$ $\Z/2\Z\oplus\Z/6\Z$ \(\Q \times \Q\) $[92,4981,43947,-12000]$ $[92,-2968,47600,-1107456,-96000]$ $[-25745372/375,9027914/375,-62951/15]$ $y^2 + (x + 1)y = 4x^5 + 5x^4 + 3x^3 + 2x^2$
600.b.30000.1 600.b \( 2^{3} \cdot 3 \cdot 5^{2} \) $0$ $\Z/2\Z\oplus\Z/8\Z$ \(\Q \times \Q\) $[600,18744,4690524,120000]$ $[300,626,-198336,-14973169,30000]$ $[81000000,563400,-595008]$ $y^2 + (x^3 + x)y = x^4 + x^2 - 3$
600.b.450000.1 600.b \( 2^{3} \cdot 3 \cdot 5^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/8\Z$ \(\Q \times \Q\) $[18072,38904,233095932,1800000]$ $[9036,3395570,1698206400,953774351375,450000]$ $[418329622965299904/3125,3479436045234936/625,38515932506304/125]$ $y^2 + (x^3 + x)y = -5x^4 + 25x^2 - 45$
603.a.603.1 603.a \( 3^{2} \cdot 67 \) $0$ $\Z/10\Z$ \(\Q\) $[1672,75628,49887881,2412]$ $[836,16516,-1263521,-332270453,603]$ $[408348897330176/603,9649919856896/603,-883069772816/603]$ $y^2 + (x^2 + 1)y = x^5 + 8x^4 + 4x^3 + 4x^2 + 2x$
603.a.603.2 603.a \( 3^{2} \cdot 67 \) $0$ $\Z/10\Z$ \(\Q\) $[176,148,7375,-2412]$ $[88,298,1361,7741,-603]$ $[-5277319168/603,-203078656/603,-10539584/603]$ $y^2 + (x^2 + 1)y = x^5 - x^3 + x$
604.a.9664.1 604.a \( 2^{2} \cdot 151 \) $0$ $\mathsf{trivial}$ \(\Q\) $[49556,-797087975,-23996873337603,1236992]$ $[12389,39607304,223396249616,299729401586052,9664]$ $[291864493641401980949/9664,9414430497536890397/1208,2143030742187944921/604]$ $y^2 + (x^2 + x + 1)y = 4x^5 + 9x^4 + 48x^3 - 4x^2 - 53x - 21$
604.a.9664.2 604.a \( 2^{2} \cdot 151 \) $0$ $\Z/27\Z$ \(\Q\) $[116,6265,95277,1236992]$ $[29,-226,836,-6708,9664]$ $[20511149/9664,-2755957/4832,175769/2416]$ $y^2 + (x^3 + 1)y = -x^4 + x^3 + x^2 - x$
630.a.34020.1 630.a \( 2 \cdot 3^{2} \cdot 5 \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[24100,969793,7474503265,4354560]$ $[6025,1472118,470090880,166291536519,34020]$ $[1587871127345703125/6804,10732293030978125/1134,13543327580000/27]$ $y^2 + (x^2 + x)y = 3x^5 + 10x^4 - 23x^2 - 6x + 15$
640.a.81920.1 640.a \( 2^{7} \cdot 5 \) $0$ $\Z/12\Z$ \(\mathsf{CM} \times \Q\) $[912,147,44562,10]$ $[3648,552928,111431680,25193348864,81920]$ $[39432490647552/5,1638374321664/5,18102076416]$ $y^2 + x^3y = 3x^4 + 13x^2 + 20$
640.a.81920.2 640.a \( 2^{7} \cdot 5 \) $0$ $\Z/12\Z$ \(\mathsf{CM} \times \Q\) $[912,147,44562,10]$ $[3648,552928,111431680,25193348864,81920]$ $[39432490647552/5,1638374321664/5,18102076416]$ $y^2 + x^3y = -3x^4 + 13x^2 - 20$
644.a.2576.1 644.a \( 2^{2} \cdot 7 \cdot 23 \) $0$ $\Z/6\Z$ \(\Q \times \Q\) $[39036,4124865,50880984159,329728]$ $[9759,3796384,1910683600,1058457444236,2576]$ $[88516980336138032799/2576,220529201888022246/161,70640465629725]$ $y^2 + (x^2 + x)y = -5x^6 + 11x^5 - 20x^4 + 20x^3 - 20x^2 + 11x - 5$
644.a.659456.1 644.a \( 2^{2} \cdot 7 \cdot 23 \) $0$ $\Z/2\Z$ \(\Q \times \Q\) $[161796,1070662305,46065265919409,84410368]$ $[40449,23560804,14638854160,9253881697856,659456]$ $[108277681088425330677249/659456,389810454818831018649/164864,9297727292338785/256]$ $y^2 + (x^2 + x)y = -3x^6 - 13x^5 + 4x^4 + 51x^3 + 4x^2 - 13x - 3$
644.b.14812.1 644.b \( 2^{2} \cdot 7 \cdot 23 \) $0$ $\Z/10\Z$ \(\Q\) $[1268,-40511,-17688719,-1895936]$ $[317,5875,170781,4905488,-14812]$ $[-3201078401357/14812,-187148201375/14812,-17161611909/14812]$ $y^2 + (x^3 + 1)y = x^5 - x^4 - 4x^3 + 5x^2 - x - 1$
672.a.172032.1 672.a \( 2^{5} \cdot 3 \cdot 7 \) $0$ $\Z/4\Z$ \(\Q \times \Q\) $[16916,151117825,232872423961,-21504]$ $[16916,-88822256,277597802496,-798387183476800,-172032]$ $[-1352659309173012149/168,419870026410625699/168,-461744933079368]$ $y^2 + (x^3 + x)y = -x^6 - 16x^4 - 75x^2 + 56$
676.a.5408.1 676.a \( 2^{2} \cdot 13^{2} \) $0$ $\Z/21\Z$ \(\Q \times \Q\) $[204,3273,161211,692224]$ $[51,-28,0,-196,5408]$ $[345025251/5408,-928557/1352,0]$ $y^2 + (x^3 + x^2 + x)y = x^3 + 3x^2 + 3x + 1$
676.a.562432.1 676.a \( 2^{2} \cdot 13^{2} \) $0$ $\Z/21\Z$ \(\Q \times \Q\) $[1620,52953,29527389,71991296]$ $[405,4628,-8112,-6175936,562432]$ $[10896201253125/562432,5912281125/10816,-492075/208]$ $y^2 + (x^3 + 1)y = 2x^5 + 2x^4 + 4x^3 + 2x^2 + 2x$
676.b.17576.1 676.b \( 2^{2} \cdot 13^{2} \) $0$ $\Z/3\Z\oplus\Z/3\Z$ \(\mathrm{M}_2(\Q)\) $[1244,1249,129167,2249728]$ $[311,3978,72332,1667692,17576]$ $[2909390022551/17576,4602275343/676,10349147/26]$ $y^2 + (x^2 + x)y = -x^6 + 3x^5 - 6x^4 + 6x^3 - 6x^2 + 3x - 1$
686.a.686.1 686.a \( 2 \cdot 7^{3} \) $0$ $\Z/6\Z$ \(\mathsf{CM} \times \Q\) $[420,4305,640185,87808]$ $[105,280,-980,-45325,686]$ $[37209375/2,472500,-15750]$ $y^2 + (x^2 + x)y = x^5 + x^4 + 2x^3 + x^2 + x$
688.a.2752.1 688.a \( 2^{4} \cdot 43 \) $0$ $\Z/20\Z$ \(\Q\) $[32,112,-680,-344]$ $[32,-32,1344,10496,-2752]$ $[-524288/43,16384/43,-21504/43]$ $y^2 + y = 2x^5 - 5x^4 + 4x^3 - x$
688.a.704512.2 688.a \( 2^{4} \cdot 43 \) $0$ $\Z/10\Z$ \(\Q\) $[464,-248,-39602,-86]$ $[1856,146176,15688704,1937702912,-704512]$ $[-1344218660864/43,-57041383424/43,-3298550016/43]$ $y^2 = 2x^5 - 7x^4 - 8x^3 + 2x^2 + 4x + 1$
688.a.704512.1 688.a \( 2^{4} \cdot 43 \) $0$ $\Z/10\Z$ \(\Q\) $[128,532,26830,86]$ $[512,5248,-408576,-59183104,704512]$ $[2147483648/43,42991616/43,-6537216/43]$ $y^2 = 2x^5 + 4x^3 + x^2 + 2x + 1$
691.a.691.1 691.a \( 691 \) $0$ $\Z/8\Z$ \(\Q\) $[104,-824,-20333,-2764]$ $[52,250,601,-7812,-691]$ $[-380204032/691,-35152000/691,-1625104/691]$ $y^2 + (x + 1)y = x^5 - x^3 - x^2$
704.a.45056.1 704.a \( 2^{6} \cdot 11 \) $0$ $\Z/2\Z\oplus\Z/6\Z$ \(\Q\) $[134,-464,-15328,-176]$ $[268,4230,61444,-356477,-45056]$ $[-1350125107/44,-636113745/352,-68955529/704]$ $y^2 + y = 4x^5 + 4x^4 - x^3 - 2x^2$
708.a.2832.1 708.a \( 2^{2} \cdot 3 \cdot 59 \) $0$ $\Z/10\Z$ \(\Q\) $[148,2065,76361,362496]$ $[37,-29,-59,-756,2832]$ $[69343957/2832,-1468937/2832,-1369/48]$ $y^2 + (x^2 + x + 1)y = x^5$
708.a.19116.1 708.a \( 2^{2} \cdot 3 \cdot 59 \) $0$ $\Z/10\Z$ \(\Q\) $[908,-132815,8426215,2446848]$ $[227,7681,-438901,-39657072,19116]$ $[602738989907/19116,89845294523/19116,-383324231/324]$ $y^2 + (x^3 + 1)y = -x^5 + 4x^2 + 4x - 1$
708.a.181248.1 708.a \( 2^{2} \cdot 3 \cdot 59 \) $0$ $\Z/2\Z$ \(\Q\) $[234100,3468879025,202585466081177,-23199744]$ $[58525,-1820975,60952909,62829762150,-181248]$ $[-686605237334059580078125/181248,365029741228054296875/181248,-208774418179643125/181248]$ $y^2 + (x^3 + 1)y = -x^6 - 4x^5 + 9x^4 + 48x^3 - 41x^2 - 98x - 36$
709.a.709.1 709.a \( 709 \) $0$ $\Z/8\Z$ \(\Q\) $[160,-1280,-42089,2836]$ $[80,480,1121,-35180,709]$ $[3276800000/709,245760000/709,7174400/709]$ $y^2 + xy = x^5 - 2x^2 + x$
713.a.713.1 713.a \( 23 \cdot 31 \) $1$ $\mathsf{trivial}$ \(\Q\) $[36,1305,-2547,91264]$ $[9,-51,173,-261,713]$ $[59049/713,-37179/713,14013/713]$ $y^2 + (x^3 + x + 1)y = -x^5 - x$
713.b.713.1 713.b \( 23 \cdot 31 \) $0$ $\Z/9\Z$ \(\Q\) $[92,73,6379,-91264]$ $[23,19,-41,-326,-713]$ $[-279841/31,-10051/31,943/31]$ $y^2 + (x^3 + x + 1)y = -x^4$
720.a.6480.1 720.a \( 2^{4} \cdot 3^{2} \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[2360,11992,9047820,25920]$ $[1180,56018,3453120,234166319,6480]$ $[28596971960000/81,1150492082200/81,6677950400/9]$ $y^2 + (x^3 + x)y = 2x^4 + 7x^2 + 5$
720.b.116640.1 720.b \( 2^{4} \cdot 3^{2} \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/12\Z$ \(\Q \times \Q\) $[35416,45688,537039964,466560]$ $[17708,13057938,12831384960,14177105014959,116640]$ $[54412363190235229024/3645,251762275020280012/405,310461362928064/9]$ $y^2 + (x^3 + x)y = -6x^4 + 39x^2 - 90$
726.a.1452.1 726.a \( 2 \cdot 3 \cdot 11^{2} \) $0$ $\Z/10\Z$ \(\Q \times \Q\) $[760,-69236,-16142609,-5808]$ $[380,17556,702601,-10306189,-1452]$ $[-1980879200000/363,-7297976000/11,-25363896100/363]$ $y^2 + (x^2 + 1)y = 2x^5 + 2x^4 + 6x^3 - 2x^2 - x$
731.a.12427.1 731.a \( 17 \cdot 43 \) $0$ $\Z/10\Z$ \(\Q\) $[480,-21564,-3373785,-49708]$ $[240,5994,167265,1053891,-12427]$ $[-796262400000/12427,-82861056000/12427,-9634464000/12427]$ $y^2 + (x^3 + x^2)y = x^5 + 2x^4 - x - 3$
741.a.28899.1 741.a \( 3 \cdot 13 \cdot 19 \) $0$ $\Z/2\Z\oplus\Z/8\Z$ \(\Q\) $[576,-840,740385,115596]$ $[288,3596,-38169,-5980972,28899]$ $[220150628352/3211,9544531968/3211,-351765504/3211]$ $y^2 + (x + 1)y = -3x^5 - x^4 + 2x^2 + x$
743.a.743.1 743.a \( 743 \) $1$ $\mathsf{trivial}$ \(\Q\) $[28,1945,15219,95104]$ $[7,-79,-53,-1653,743]$ $[16807/743,-27097/743,-2597/743]$ $y^2 + (x^3 + x + 1)y = -x^4 + x^2$
745.a.745.1 745.a \( 5 \cdot 149 \) $0$ $\Z/9\Z$ \(\Q\) $[124,1417,38763,95360]$ $[31,-19,39,212,745]$ $[28629151/745,-566029/745,37479/745]$ $y^2 + (x^3 + x + 1)y = -x$
762.a.3048.1 762.a \( 2 \cdot 3 \cdot 127 \) $0$ $\Z/12\Z$ \(\Q\) $[428,3169,355487,390144]$ $[107,345,1823,19009,3048]$ $[14025517307/3048,140879945/1016,20871527/3048]$ $y^2 + (x^3 + x^2 + x)y = x^2 + x + 1$
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