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Label Class Conductor Rank* Torsion $\textrm{End}^0(J_{\overline\Q})$ Igusa-Clebsch invariants Igusa invariants G2-invariants Equation
294.a.294.1 294.a \( 2 \cdot 3 \cdot 7^{2} \) $0$ $\Z/12\Z$ \(\Q \times \Q\) $[236,505,18451,37632]$ $[59,124,564,4475,294]$ $[714924299/294,12733498/147,327214/49]$ $y^2 + (x^3 + 1)y = x^4 + x^2$
294.a.8232.1 294.a \( 2 \cdot 3 \cdot 7^{2} \) $0$ $\Z/12\Z$ \(\Q \times \Q\) $[7636,11785,29745701,1053696]$ $[1909,151354,15951264,1885732415,8232]$ $[25353016669288549/8232,75211396489919/588,49431027484/7]$ $y^2 + (x^3 + 1)y = -2x^4 + 4x^2 - 9x - 14$
336.a.172032.1 336.a \( 2^{4} \cdot 3 \cdot 7 \) $0$ $\Z/2\Z$ \(\Q \times \Q\) $[16916,151117825,232872423961,-21504]$ $[16916,-88822256,277597802496,-798387183476800,-172032]$ $[-1352659309173012149/168,419870026410625699/168,-461744933079368]$ $y^2 + (x^3 + x)y = -x^6 + 15x^4 - 75x^2 - 56$
360.a.6480.1 360.a \( 2^{3} \cdot 3^{2} \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/8\Z$ \(\Q \times \Q\) $[2360,11992,9047820,25920]$ $[1180,56018,3453120,234166319,6480]$ $[28596971960000/81,1150492082200/81,6677950400/9]$ $y^2 + (x^3 + x)y = -3x^4 + 7x^2 - 5$
448.a.448.2 448.a \( 2^{6} \cdot 7 \) $0$ $\Z/12\Z$ \(\mathsf{CM} \times \Q\) $[828,16635,5308452,56]$ $[828,17476,-853888,-253107460,448]$ $[6080953884912/7,155007628668/7,-1306723104]$ $y^2 + (x^3 + x)y = -2x^4 + 7$
448.a.448.1 448.a \( 2^{6} \cdot 7 \) $0$ $\Z/6\Z$ \(\mathsf{CM} \times \Q\) $[828,16635,5308452,56]$ $[828,17476,-853888,-253107460,448]$ $[6080953884912/7,155007628668/7,-1306723104]$ $y^2 + (x^3 + x)y = x^4 - 7$
450.a.2700.1 450.a \( 2 \cdot 3^{2} \cdot 5^{2} \) $0$ $\Z/24\Z$ \(\Q \times \Q\) $[364,3529,393211,345600]$ $[91,198,0,-9801,2700]$ $[6240321451/2700,8289281/150,0]$ $y^2 + (x^3 + 1)y = x^5 + 3x^4 + 3x^3 + 3x^2 + x$
450.a.36450.1 450.a \( 2 \cdot 3^{2} \cdot 5^{2} \) $0$ $\Z/2\Z\oplus\Z/12\Z$ \(\Q \times \Q\) $[23444,212089,1627179821,4665600]$ $[5861,1422468,457836300,164990835819,36450]$ $[6916057684302385301/36450,5303516319500302/675,1294426477922/3]$ $y^2 + (x^3 + 1)y = x^5 - 4x^4 - 9x^3 + 28x^2 - 6x - 16$
476.a.952.1 476.a \( 2^{2} \cdot 7 \cdot 17 \) $0$ $\Z/3\Z\oplus\Z/6\Z$ \(\Q \times \Q\) $[7340,1042345,2905273355,121856]$ $[1835,96870,-3910340,-4139817700,952]$ $[20805604708146875/952,299272981175625/476,-27661753375/2]$ $y^2 + (x^3 + 1)y = -5x^4 + 7x^3 + 25x^2 - 75x + 54$
484.a.1936.1 484.a \( 2^{2} \cdot 11^{2} \) $0$ $\Z/15\Z$ \(\Q \times \Q\) $[184,37,721,242]$ $[184,1386,15040,211591,1936]$ $[13181630464/121,49057344/11,31824640/121]$ $y^2 + y = x^6 + 2x^4 + x^2$
504.a.27216.1 504.a \( 2^{3} \cdot 3^{2} \cdot 7 \) $0$ $\Z/4\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[8456,9496,26675348,108864]$ $[4228,743250,173847744,45651924783,27216]$ $[12063042849801664/243,167186257609000/81,3083035208512/27]$ $y^2 + (x^3 + x)y = 3x^4 + 15x^2 + 21$
578.a.2312.1 578.a \( 2 \cdot 17^{2} \) $0$ $\Z/12\Z$ \(\Q \times \Q\) $[228,705,135777,295936]$ $[57,106,-992,-16945,2312]$ $[601692057/2312,9815229/1156,-402876/289]$ $y^2 + (x^2 + x)y = x^5 - 2x^4 + 2x^3 - 2x^2 + x$
588.a.18816.1 588.a \( 2^{2} \cdot 3 \cdot 7^{2} \) $0$ $\Z/24\Z$ \(\Q \times \Q\) $[748,11545,2902787,2408448]$ $[187,976,-192,-247120,18816]$ $[228669389707/18816,398891383/1176,-34969/98]$ $y^2 + (x^3 + 1)y = x^5 + x^4 + 5x^2 + 12x + 8$
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 \( 2^{3} \cdot 3 \cdot 5^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/8\Z$ \(\Q \times \Q\) $[18072,38904,233095932,1800000]$ $[9036,3395570,1698206400,953774351375,450000]$ $[418329622965299904/3125,3479436045234936/625,38515932506304/125]$ $y^2 + (x^3 + x)y = -5x^4 + 25x^2 - 45$
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 \( 2^{2} \cdot 7 \cdot 23 \) $0$ $\Z/2\Z$ \(\Q \times \Q\) $[161796,1070662305,46065265919409,84410368]$ $[40449,23560804,14638854160,9253881697856,659456]$ $[108277681088425330677249/659456,389810454818831018649/164864,9297727292338785/256]$ $y^2 + (x^2 + x)y = -3x^6 - 13x^5 + 4x^4 + 51x^3 + 4x^2 - 13x - 3$
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 \( 2^{2} \cdot 13^{2} \) $0$ $\Z/21\Z$ \(\Q \times \Q\) $[1620,52953,29527389,71991296]$ $[405,4628,-8112,-6175936,562432]$ $[10896201253125/562432,5912281125/10816,-492075/208]$ $y^2 + (x^3 + 1)y = 2x^5 + 2x^4 + 4x^3 + 2x^2 + 2x$
686.a.686.1 686.a \( 2 \cdot 7^{3} \) $0$ $\Z/6\Z$ \(\mathsf{CM} \times \Q\) $[420,4305,640185,87808]$ $[105,280,-980,-45325,686]$ $[37209375/2,472500,-15750]$ $y^2 + (x^2 + x)y = x^5 + x^4 + 2x^3 + x^2 + x$
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 \( 2^{4} \cdot 3^{2} \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/12\Z$ \(\Q \times \Q\) $[35416,45688,537039964,466560]$ $[17708,13057938,12831384960,14177105014959,116640]$ $[54412363190235229024/3645,251762275020280012/405,310461362928064/9]$ $y^2 + (x^3 + x)y = -6x^4 + 39x^2 - 90$
784.a.1568.1 784.a \( 2^{4} \cdot 7^{2} \) $0$ $\Z/12\Z$ \(\Q \times \Q\) $[792,120,15228,6272]$ $[396,6514,144256,3673295,1568]$ $[304316815968/49,12641055372/49,14427072]$ $y^2 + (x^3 + x)y = -2x^4 + 3x^2 - 2$
784.a.43904.1 784.a \( 2^{4} \cdot 7^{2} \) $0$ $\Z/12\Z$ \(\Q \times \Q\) $[21288,3000,20891172,175616]$ $[10644,4720114,2790613504,1855953490895,43904]$ $[1067368445729034408/343,6352710665144931/49,50408453477952/7]$ $y^2 + (x^3 + x)y = 4x^4 + 27x^2 + 56$
784.b.12544.1 784.b \( 2^{4} \cdot 7^{2} \) $0$ $\Z/2\Z\oplus\Z/6\Z$ \(\Q \times \Q\) $[116,445,16259,1568]$ $[116,264,-1280,-54544,12544]$ $[82044596/49,1609674/49,-67280/49]$ $y^2 + (x^3 + x)y = -1$
800.a.1600.1 800.a \( 2^{5} \cdot 5^{2} \) $0$ $\Z/12\Z$ \(\Q \times \Q\) $[0,84,936,200]$ $[0,-56,832,-784,-1600]$ $[0,-134456/625,728/25]$ $y^2 + (x^3 + x^2 + x + 1)y = -x^4 - x^2$
800.a.8000.1 800.a \( 2^{5} \cdot 5^{2} \) $0$ $\Z/4\Z$ \(\Q \times \Q\) $[192,11604,322392,-1000]$ $[192,-6200,142400,-2774800,-8000]$ $[-4076863488/125,27426816/5,-3280896/5]$ $y^2 + (x^3 + x^2 + x + 1)y = -x^6 + 2x^4 + 4x^3 + 2x^2 - 1$
800.a.409600.1 800.a \( 2^{5} \cdot 5^{2} \) $0$ $\Z/24\Z$ \(\Q \times \Q\) $[120,309,14889,50]$ $[480,6304,-151552,-28121344,409600]$ $[62208000,1702080,-85248]$ $y^2 = x^6 - 2x^2 + 1$
816.b.52224.1 816.b \( 2^{4} \cdot 3 \cdot 17 \) $0$ $\Z/6\Z$ \(\Q \times \Q\) $[15964,2380825,11444690699,6528]$ $[15964,9031504,6282991104,4683401370560,52224]$ $[1012531723491160951/51,35882713644370099/51,30660536527816]$ $y^2 + (x^3 + x)y = -x^6 - 12x^4 - 27x^2 - 17$
847.a.847.1 847.a \( 7 \cdot 11^{2} \) $1$ $\Z/5\Z$ \(\Q \times \Q\) $[120,276,6864,3388]$ $[60,104,504,4856,847]$ $[777600000/847,22464000/847,259200/121]$ $y^2 + (x^3 + x^2 + x + 1)y = x^4 + x^3 + x^2$
847.d.847.1 847.d \( 7 \cdot 11^{2} \) $0$ $\Z/3\Z$ \(\Q \times \Q\) $[80408,402403732,8094753026048,3388]$ $[40204,281112,1967560,19956424,847]$ $[105037970421355597057024/847,18267839107785466368/847,454326923025280/121]$ $y^2 + (x^3 + x^2 + x + 1)y = -12x^6 - 15x^5 + 9x^4 + 31x^3 + 9x^2 - 15x - 12$
847.d.456533.1 847.d \( 7 \cdot 11^{2} \) $0$ $\Z/15\Z$ \(\Q \times \Q\) $[90952,10132,303847072,1826132]$ $[45476,86167752,217689875480,618695823148744,456533]$ $[194496275421254111077376/456533,736713878289412204032/41503,10847340081772160/11]$ $y^2 + y = -x^6 - 9x^5 - 22x^4 + 3x^3 + 37x^2 - 24x + 4$
864.a.1728.1 864.a \( 2^{5} \cdot 3^{3} \) $0$ $\Z/12\Z$ \(\mathsf{CM} \times \Q\) $[96,180,5256,216]$ $[96,264,576,-3600,1728]$ $[4718592,135168,3072]$ $y^2 + (x^3 + x^2 + x + 1)y = x^4 + x^2$
864.a.221184.1 864.a \( 2^{5} \cdot 3^{3} \) $0$ $\Z/12\Z$ \(\mathsf{CM} \times \Q\) $[168,34560,-211428,-864]$ $[336,-87456,10192896,-1055934720,-221184]$ $[-19361664,14998704,-5202624]$ $y^2 + x^3y = x^5 - 4x^4 - 6x^3 + 33x^2 - 36x + 12$
864.a.442368.1 864.a \( 2^{5} \cdot 3^{3} \) $0$ $\Z/12\Z$ \(\mathsf{CM} \times \Q\) $[552,45,7083,54]$ $[2208,202656,24809472,3427464960,442368]$ $[118634674176,4931431104,273421056]$ $y^2 = x^6 - 4x^4 + 6x^2 - 3$
882.a.63504.1 882.a \( 2 \cdot 3^{2} \cdot 7^{2} \) $0$ $\Z/2\Z\oplus\Z/8\Z$ \(\Q \times \Q\) $[548,6049,662961,8128512]$ $[137,530,6336,146783,63504]$ $[48261724457/63504,681408545/31752,825836/441]$ $y^2 + (x^2 + x)y = x^5 + x^4 + x^3 + 3x^2 + 3x + 1$
930.a.930.1 930.a \( 2 \cdot 3 \cdot 5 \cdot 31 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[46596,239073,3674852529,119040]$ $[11649,5644172,3640360380,2637470125259,930]$ $[71502622649365111083/310,1487013548016809538/155,531176338621566]$ $y^2 + (x^2 + x)y = -x^5 - 7x^4 + 37x^2 - 45x + 15$
936.a.1872.1 936.a \( 2^{3} \cdot 3^{2} \cdot 13 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[45352,11224,169415364,7488]$ $[22676,21423170,26983749312,38232821637503,1872]$ $[374724646811252438336/117,15612163699641478120/117,7411896491650496]$ $y^2 + (x^3 + x)y = -x^6 - 9x^4 - 32x^2 - 39$
960.a.245760.1 960.a \( 2^{6} \cdot 3 \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[120,213,10095,30]$ $[480,7328,-15360,-15268096,245760]$ $[103680000,3297600,-14400]$ $y^2 = 2x^5 + x^4 + 4x^3 + x^2 + 2x$
960.a.368640.1 960.a \( 2^{6} \cdot 3 \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[8952,6072,17987052,1440]$ $[17904,13340192,13237770240,14762078945024,368640]$ $[24952719973569408/5,1038436236963696/5,11510985848256]$ $y^2 = x^5 + 13x^4 + 44x^3 + 13x^2 + x$
960.a.983040.1 960.a \( 2^{6} \cdot 3 \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[9,33,666,120]$ $[36,-298,-34260,-330541,983040]$ $[19683/320,-36207/2560,-46251/1024]$ $y^2 = x^5 - 2x^4 - x^3 - 2x^2 + x$
968.a.1936.1 968.a \( 2^{3} \cdot 11^{2} \) $1$ $\Z/5\Z$ \(\Q \times \Q\) $[120,357,14937,242]$ $[120,362,-1344,-73081,1936]$ $[1555200000/121,39096000/121,-1209600/121]$ $y^2 + y = x^6 - x^4$
968.a.234256.1 968.a \( 2^{3} \cdot 11^{2} \) $1$ $\Z/5\Z$ \(\Q \times \Q\) $[23544,6117,47655081,29282]$ $[23544,23092586,30194746560,44409396210311,234256]$ $[452148675314325387264/14641,1712381980706754624/1331,785948064456960/11]$ $y^2 + x^3y = 6x^4 + 47x^2 + 121$
980.a.7840.1 980.a \( 2^{2} \cdot 5 \cdot 7^{2} \) $0$ $\Z/12\Z$ \(\Q \times \Q\) $[276,3945,280149,1003520]$ $[69,34,20,56,7840]$ $[1564031349/7840,5584653/3920,4761/392]$ $y^2 + (x^2 + x + 1)y = -x^6 + 3x^5 - 3x^4 - x$
980.a.878080.1 980.a \( 2^{2} \cdot 5 \cdot 7^{2} \) $0$ $\Z/12\Z$ \(\Q \times \Q\) $[2508,50745,41700723,112394240]$ $[627,14266,359660,5497016,878080]$ $[96903107471907/878080,251175228777/62720,144278343/896]$ $y^2 + (x^3 + 1)y = -x^6 + x^5 - 4x^4 + 2x^3 - 4x^2 + x - 1$
990.a.8910.1 990.a \( 2 \cdot 3^{2} \cdot 5 \cdot 11 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[3268,252577,318023313,1140480]$ $[817,17288,-766260,-231227341,8910]$ $[364007458703857/8910,4713906106372/4455,-57404054]$ $y^2 + (x^2 + x)y = 3x^5 + 4x^4 + 7x^3 + 4x^2 + 3x$
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