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Label Class Conductor Discriminant Rank* Torsion $\textrm{End}^0(J_{\overline\Q})$ Igusa-Clebsch invariants Igusa invariants G2-invariants Equation
336.a.172032.1 336.a \( 2^{4} \cdot 3 \cdot 7 \) \( - 2^{13} \cdot 3 \cdot 7 \) $0$ $\Z/2\Z$ \(\Q \times \Q\) $[16916,151117825,232872423961,-21504]$ $[16916,-88822256,277597802496,-798387183476800,-172032]$ $[-1352659309173012149/168,419870026410625699/168,-461744933079368]$ $y^2 + (x^3 + x)y = -x^6 + 15x^4 - 75x^2 - 56$
400.a.409600.1 400.a \( 2^{4} \cdot 5^{2} \) \( - 2^{14} \cdot 5^{2} \) $0$ $\Z/3\Z\oplus\Z/6\Z$ \(\mathrm{M}_2(\Q)\) $[248,181,14873,50]$ $[992,39072,1945600,100853504,409600]$ $[58632501248/25,2327987904/25,4674304]$ $y^2 = x^6 + 4x^4 + 4x^2 + 1$
574.a.293888.1 574.a \( 2 \cdot 7 \cdot 41 \) \( - 2^{10} \cdot 7 \cdot 41 \) $0$ $\Z/2\Z\oplus\Z/10\Z$ \(\Q\) $[68,-55823,-955895,-37617664]$ $[17,2338,2304,-1356769,-293888]$ $[-1419857/293888,-820471/20992,-2601/1148]$ $y^2 + (x^2 + x)y = x^5 - x^4 - 3x^2 + x + 1$
576.b.147456.1 576.b \( 2^{6} \cdot 3^{2} \) \( - 2^{14} \cdot 3^{2} \) $0$ $\Z/4\Z\oplus\Z/4\Z$ \(\mathrm{M}_2(\Q)\) $[152,109,5469,18]$ $[608,14240,405504,10942208,147456]$ $[5071050752/9,195344320/9,1016576]$ $y^2 = x^6 + 2x^4 + 2x^2 + 1$
600.b.450000.1 600.b \( 2^{3} \cdot 3 \cdot 5^{2} \) \( 2^{4} \cdot 3^{2} \cdot 5^{5} \) $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/8\Z$ \(\Q \times \Q\) $[18072,38904,233095932,1800000]$ $[9036,3395570,1698206400,953774351375,450000]$ $[418329622965299904/3125,3479436045234936/625,38515932506304/125]$ $y^2 + (x^3 + x)y = -5x^4 + 25x^2 - 45$
644.a.659456.1 644.a \( 2^{2} \cdot 7 \cdot 23 \) \( 2^{12} \cdot 7 \cdot 23 \) $0$ $\Z/2\Z$ \(\Q \times \Q\) $[161796,1070662305,46065265919409,84410368]$ $[40449,23560804,14638854160,9253881697856,659456]$ $[108277681088425330677249/659456,389810454818831018649/164864,9297727292338785/256]$ $y^2 + (x^2 + x)y = -3x^6 - 13x^5 + 4x^4 + 51x^3 + 4x^2 - 13x - 3$
672.a.172032.1 672.a \( 2^{5} \cdot 3 \cdot 7 \) \( 2^{13} \cdot 3 \cdot 7 \) $0$ $\Z/4\Z$ \(\Q \times \Q\) $[16916,151117825,232872423961,-21504]$ $[16916,-88822256,277597802496,-798387183476800,-172032]$ $[-1352659309173012149/168,419870026410625699/168,-461744933079368]$ $y^2 + (x^3 + x)y = -x^6 - 16x^4 - 75x^2 + 56$
676.a.562432.1 676.a \( 2^{2} \cdot 13^{2} \) \( 2^{8} \cdot 13^{3} \) $0$ $\Z/21\Z$ \(\Q \times \Q\) $[1620,52953,29527389,71991296]$ $[405,4628,-8112,-6175936,562432]$ $[10896201253125/562432,5912281125/10816,-492075/208]$ $y^2 + (x^3 + 1)y = 2x^5 + 2x^4 + 4x^3 + 2x^2 + 2x$
688.a.704512.2 688.a \( 2^{4} \cdot 43 \) \( - 2^{14} \cdot 43 \) $0$ $\Z/10\Z$ \(\Q\) $[464,-248,-39602,-86]$ $[1856,146176,15688704,1937702912,-704512]$ $[-1344218660864/43,-57041383424/43,-3298550016/43]$ $y^2 = 2x^5 - 7x^4 - 8x^3 + 2x^2 + 4x + 1$
688.a.704512.1 688.a \( 2^{4} \cdot 43 \) \( 2^{14} \cdot 43 \) $0$ $\Z/10\Z$ \(\Q\) $[128,532,26830,86]$ $[512,5248,-408576,-59183104,704512]$ $[2147483648/43,42991616/43,-6537216/43]$ $y^2 = 2x^5 + 4x^3 + x^2 + 2x + 1$
708.a.181248.1 708.a \( 2^{2} \cdot 3 \cdot 59 \) \( - 2^{10} \cdot 3 \cdot 59 \) $0$ $\Z/2\Z$ \(\Q\) $[234100,3468879025,202585466081177,-23199744]$ $[58525,-1820975,60952909,62829762150,-181248]$ $[-686605237334059580078125/181248,365029741228054296875/181248,-208774418179643125/181248]$ $y^2 + (x^3 + 1)y = -x^6 - 4x^5 + 9x^4 + 48x^3 - 41x^2 - 98x - 36$
720.b.116640.1 720.b \( 2^{4} \cdot 3^{2} \cdot 5 \) \( 2^{5} \cdot 3^{6} \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/12\Z$ \(\Q \times \Q\) $[35416,45688,537039964,466560]$ $[17708,13057938,12831384960,14177105014959,116640]$ $[54412363190235229024/3645,251762275020280012/405,310461362928064/9]$ $y^2 + (x^3 + x)y = -6x^4 + 39x^2 - 90$
784.c.614656.1 784.c \( 2^{4} \cdot 7^{2} \) \( 2^{8} \cdot 7^{4} \) $0$ $\Z/2\Z\oplus\Z/6\Z$ \(\mathrm{M}_2(\Q)\) $[398,9016,912086,2401]$ $[796,2358,-2348,-1857293,614656]$ $[1248318403996/2401,9291226221/4802,-23245787/9604]$ $y^2 = x^5 - 4x^4 - 13x^3 - 9x^2 - x$
800.a.409600.1 800.a \( 2^{5} \cdot 5^{2} \) \( - 2^{14} \cdot 5^{2} \) $0$ $\Z/24\Z$ \(\Q \times \Q\) $[120,309,14889,50]$ $[480,6304,-151552,-28121344,409600]$ $[62208000,1702080,-85248]$ $y^2 = x^6 - 2x^2 + 1$
810.a.196830.1 810.a \( 2 \cdot 3^{4} \cdot 5 \) \( - 2 \cdot 3^{9} \cdot 5 \) $0$ $\Z/2\Z$ \(\mathsf{CM} \times \Q\) $[103200,92148840,2874875039973,-3240]$ $[154800,860236740,5905731060081,43549979813677800,-196830]$ $[-451609936896000000000,-16212110811776000000,-2156977131869584000/3]$ $y^2 + (x + 1)y = x^5 + 15x^4 + 20x^3 - 297x^2 + 94x - 8$
830.a.830000.1 830.a \( 2 \cdot 5 \cdot 83 \) \( - 2^{4} \cdot 5^{4} \cdot 83 \) $0$ $\Z/2\Z\oplus\Z/8\Z$ \(\Q\) $[15236,-229487,-1147645831,-106240000]$ $[3809,614082,133745600,33085071919,-830000]$ $[-801779343712318049/830000,-16967946642572289/415000,-4851113741084/2075]$ $y^2 + (x^2 + x)y = x^5 - 2x^4 + 16x^3 + 8x^2 + x$
847.d.456533.1 847.d \( 7 \cdot 11^{2} \) \( 7^{3} \cdot 11^{3} \) $0$ $\Z/15\Z$ \(\Q \times \Q\) $[90952,10132,303847072,1826132]$ $[45476,86167752,217689875480,618695823148744,456533]$ $[194496275421254111077376/456533,736713878289412204032/41503,10847340081772160/11]$ $y^2 + y = -x^6 - 9x^5 - 22x^4 + 3x^3 + 37x^2 - 24x + 4$
864.a.221184.1 864.a \( 2^{5} \cdot 3^{3} \) \( - 2^{13} \cdot 3^{3} \) $0$ $\Z/12\Z$ \(\mathsf{CM} \times \Q\) $[168,34560,-211428,-864]$ $[336,-87456,10192896,-1055934720,-221184]$ $[-19361664,14998704,-5202624]$ $y^2 + x^3y = x^5 - 4x^4 - 6x^3 + 33x^2 - 36x + 12$
864.a.442368.1 864.a \( 2^{5} \cdot 3^{3} \) \( 2^{14} \cdot 3^{3} \) $0$ $\Z/12\Z$ \(\mathsf{CM} \times \Q\) $[552,45,7083,54]$ $[2208,202656,24809472,3427464960,442368]$ $[118634674176,4931431104,273421056]$ $y^2 = x^6 - 4x^4 + 6x^2 - 3$
880.a.225280.1 880.a \( 2^{4} \cdot 5 \cdot 11 \) \( - 2^{12} \cdot 5 \cdot 11 \) $0$ $\Z/2\Z$ \(\Q \times \Q\) $[2342,111952,73574536,-880]$ $[4684,615622,103120196,26006137795,-225280]$ $[-2201833501574851/220,-494259267301121/1760,-35350660170809/3520]$ $y^2 = x^5 + 13x^4 + 55x^3 + 76x^2 - 44$
882.a.302526.1 882.a \( 2 \cdot 3^{2} \cdot 7^{2} \) \( - 2 \cdot 3^{2} \cdot 7^{5} \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[2572,-283391,165464399,38723328]$ $[643,29035,-3791761,-820283387,302526]$ $[109914468611443/302526,7718888172745/302526,-1567699793689/302526]$ $y^2 + (x^3 + 1)y = x^5 - 2x^4 - 5x^3 + 11x^2 - 12x + 5$
960.a.245760.1 960.a \( 2^{6} \cdot 3 \cdot 5 \) \( 2^{14} \cdot 3 \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[120,213,10095,30]$ $[480,7328,-15360,-15268096,245760]$ $[103680000,3297600,-14400]$ $y^2 = 2x^5 + x^4 + 4x^3 + x^2 + 2x$
960.a.368640.1 960.a \( 2^{6} \cdot 3 \cdot 5 \) \( 2^{13} \cdot 3^{2} \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[8952,6072,17987052,1440]$ $[17904,13340192,13237770240,14762078945024,368640]$ $[24952719973569408/5,1038436236963696/5,11510985848256]$ $y^2 = x^5 + 13x^4 + 44x^3 + 13x^2 + x$
960.a.983040.1 960.a \( 2^{6} \cdot 3 \cdot 5 \) \( - 2^{16} \cdot 3 \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[9,33,666,120]$ $[36,-298,-34260,-330541,983040]$ $[19683/320,-36207/2560,-46251/1024]$ $y^2 = x^5 - 2x^4 - x^3 - 2x^2 + x$
961.a.923521.1 961.a \( 31^{2} \) \( 31^{4} \) $0$ $\Z/5\Z$ \(\mathsf{RM}\) $[4100,78961,94151689,118210688]$ $[1025,40486,2121888,133954751,923521]$ $[1131408212890625/923521,1406419156250/29791,2319780000/961]$ $y^2 + (x^3 + x^2 + 1)y = -5x^4 + 4x^3 + 3x^2 - 2x - 3$
966.a.834624.1 966.a \( 2 \cdot 3 \cdot 7 \cdot 23 \) \( 2^{6} \cdot 3^{4} \cdot 7 \cdot 23 \) $0$ $\Z/2\Z\oplus\Z/12\Z$ \(\Q\) $[92,24673,-557265,-106831872]$ $[23,-1006,14336,-170577,-834624]$ $[-279841/36288,266087/18144,-736/81]$ $y^2 + (x^2 + x)y = x^5 - x^4 + x^3 + x^2 - x + 1$
968.a.234256.1 968.a \( 2^{3} \cdot 11^{2} \) \( - 2^{4} \cdot 11^{4} \) $1$ $\Z/5\Z$ \(\Q \times \Q\) $[23544,6117,47655081,29282]$ $[23544,23092586,30194746560,44409396210311,234256]$ $[452148675314325387264/14641,1712381980706754624/1331,785948064456960/11]$ $y^2 + x^3y = 6x^4 + 47x^2 + 121$
976.a.999424.1 976.a \( 2^{4} \cdot 61 \) \( 2^{14} \cdot 61 \) $0$ $\Z/29\Z$ \(\Q\) $[152,1012,68714,-124928]$ $[152,288,-24464,-950368,-999424]$ $[-4952198/61,-61731/61,551969/976]$ $y^2 + (x + 1)y = x^6 - 2x^5 + 2x^3 - x^2$
980.a.878080.1 980.a \( 2^{2} \cdot 5 \cdot 7^{2} \) \( - 2^{9} \cdot 5 \cdot 7^{3} \) $0$ $\Z/12\Z$ \(\Q \times \Q\) $[2508,50745,41700723,112394240]$ $[627,14266,359660,5497016,878080]$ $[96903107471907/878080,251175228777/62720,144278343/896]$ $y^2 + (x^3 + 1)y = -x^6 + x^5 - 4x^4 + 2x^3 - 4x^2 + x - 1$
990.a.240570.1 990.a \( 2 \cdot 3^{2} \cdot 5 \cdot 11 \) \( 2 \cdot 3^{7} \cdot 5 \cdot 11 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ \(\Q \times \Q\) $[153028,6848257,343366646113,30792960]$ $[38257,60697908,127876480380,301983618580299,240570]$ $[81951056110393451083057/240570,188813894774599018858/13365,7001861848004294/9]$ $y^2 + (x^2 + x)y = 3x^5 + 28x^4 + 72x^3 + 28x^2 + 3x$
1050.a.131250.1 1050.a \( 2 \cdot 3 \cdot 5^{2} \cdot 7 \) \( - 2 \cdot 3 \cdot 5^{5} \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[11868,198609,759217863,16800000]$ $[2967,358520,56735700,9949557875,131250]$ $[76641937806559869/43750,312136655012892/4375,475666111026/125]$ $y^2 + (x^2 + x)y = 3x^6 + 8x^5 + 15x^4 + 17x^3 + 15x^2 + 8x + 3$
1083.b.390963.1 1083.b \( 3 \cdot 19^{2} \) \( - 3 \cdot 19^{4} \) $0$ $\mathsf{trivial}$ \(\Q \times \Q\) $[150440,1945515892,68956865081488,-1563852]$ $[75220,-88500632,98386538568,-107931608328616,-390963]$ $[-2408056349828975363200000/390963,1982406707133537344000/20577,-27053302090985600/19]$ $y^2 + y = -x^6 + 3x^5 - 50x^4 + 95x^3 - 14x^2 - 33x - 6$
1104.b.141312.1 1104.b \( 2^{4} \cdot 3 \cdot 23 \) \( - 2^{11} \cdot 3 \cdot 23 \) $0$ $\Z/2\Z$ \(\Q \times \Q\) $[14220,9418737,54280328031,17664]$ $[14220,2146192,-16790479872,-60841690970176,141312]$ $[189267815942240625/46,2008843709918625/46,-24026098775400]$ $y^2 + (x^3 + x)y = -x^6 - 3x^4 + 29x^2 - 46$
1116.a.214272.1 1116.a \( 2^{2} \cdot 3^{2} \cdot 31 \) \( - 2^{8} \cdot 3^{3} \cdot 31 \) $0$ $\Z/39\Z$ \(\Q\) $[52,22201,238285,-27426816]$ $[13,-918,36,-210564,-214272]$ $[-371293/214272,37349/3968,-169/5952]$ $y^2 + (x^3 + 1)y = x^4 + 2x^3 + x^2 - x$
1125.a.151875.1 1125.a \( 3^{2} \cdot 5^{3} \) \( - 3^{5} \cdot 5^{4} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ \(\Q \times \Q\) $[8600,612100,1556297975,-607500]$ $[4300,668400,132975225,31258726875,-151875]$ $[-2352135088000000/243,-28342655360000/81,-437104339600/27]$ $y^2 + xy = 15x^5 + 50x^4 + 55x^3 + 22x^2 + 3x$
1136.a.290816.1 1136.a \( 2^{4} \cdot 71 \) \( 2^{12} \cdot 71 \) $0$ $\Z/14\Z$ \(\Q\) $[9252,17217,52921881,36352]$ $[9252,3555168,1815712832,1039938903360,290816]$ $[66203075280122793/284,1374792164318403/142,151781365064097/284]$ $y^2 + (x^3 + x^2)y = -5x^4 - 9x^3 + 25x^2 + 40x - 24$
1145.a.143125.1 1145.a \( 5 \cdot 229 \) \( - 5^{4} \cdot 229 \) $1$ $\Z/2\Z$ \(\Q\) $[5004,191097,289856403,18320000]$ $[1251,57246,3273124,204393402,143125]$ $[3063984390631251/143125,112077149104746/143125,5122442333124/143125]$ $y^2 + (x^3 + x^2 + x)y = 2x^4 + 4x^3 + 9x^2 + 10x + 9$
1152.a.147456.1 1152.a \( 2^{7} \cdot 3^{2} \) \( 2^{14} \cdot 3^{2} \) $0$ $\Z/8\Z$ \(\mathrm{M}_2(\Q)\) $[152,109,5469,18]$ $[608,14240,405504,10942208,147456]$ $[5071050752/9,195344320/9,1016576]$ $y^2 = x^6 - 2x^4 + 2x^2 - 1$
1164.b.670464.1 1164.b \( 2^{2} \cdot 3 \cdot 97 \) \( 2^{8} \cdot 3^{3} \cdot 97 \) $0$ $\Z/21\Z$ \(\Q\) $[372,4521,1271253,85819392]$ $[93,172,-10928,-261472,670464]$ $[257662359/24832,1281013/6208,-656363/4656]$ $y^2 + (x^2 + x + 1)y = 2x^5 - 2x^4 + x^3 - x^2$
1184.a.606208.2 1184.a \( 2^{5} \cdot 37 \) \( - 2^{14} \cdot 37 \) $0$ $\Z/8\Z$ \(\Q\) $[352,316,34242,74]$ $[1408,79232,5831680,483323904,606208]$ $[337748426752/37,13498597376/37,705633280/37]$ $y^2 = x^6 - 2x^5 + 5x^4 - 4x^3 + 6x^2 - 2x + 2$
1184.a.606208.1 1184.a \( 2^{5} \cdot 37 \) \( 2^{14} \cdot 37 \) $0$ $\Z/2\Z\oplus\Z/8\Z$ \(\Q\) $[176,496,29918,74]$ $[704,15360,140288,-34291712,606208]$ $[10554638336/37,327106560/37,4243712/37]$ $y^2 = 2x^5 + x^4 - 8x^3 - 8x^2 - 2x$
1197.a.410571.1 1197.a \( 3^{2} \cdot 7 \cdot 19 \) \( - 3^{2} \cdot 7^{4} \cdot 19 \) $0$ $\Z/10\Z$ \(\Q\) $[3296,706780,578353015,-1642284]$ $[1648,-4634,23921,4486963,-410571]$ $[-12155869717331968/410571,2962986082304/58653,-3419323136/21609]$ $y^2 + (x^2 + 1)y = x^5 + 12x^4 - 7x^3 - 3x^2 + x$
1200.a.450000.1 1200.a \( 2^{4} \cdot 3 \cdot 5^{2} \) \( - 2^{4} \cdot 3^{2} \cdot 5^{5} \) $0$ $\Z/2\Z\oplus\Z/8\Z$ \(\Q \times \Q\) $[18072,38904,233095932,1800000]$ $[9036,3395570,1698206400,953774351375,450000]$ $[418329622965299904/3125,3479436045234936/625,38515932506304/125]$ $y^2 + (x^3 + x)y = 4x^4 + 25x^2 + 45$
1269.b.102789.1 1269.b \( 3^{3} \cdot 47 \) \( - 3^{7} \cdot 47 \) $0$ $\Z/10\Z$ \(\Q\) $[91192,19900,603982075,1692]$ $[136788,779593356,5923938871071,50639487394179303,102789]$ $[197075993647247827966976/423,2737061778548953841408/141,152047414479420367856/141]$ $y^2 + (x^3 + x)y = -2x^6 - x^5 - 21x^4 - 8x^3 - 80x^2 - 16x - 103$
1269.b.102789.2 1269.b \( 3^{3} \cdot 47 \) \( 3^{7} \cdot 47 \) $0$ $\Z/10\Z$ \(\Q\) $[80,-140,-1027,1692]$ $[120,810,81,-161595,102789]$ $[102400000/423,640000/47,1600/141]$ $y^2 + xy = x^5 - x^4 + x^2 + x$
1270.a.325120.1 1270.a \( 2 \cdot 5 \cdot 127 \) \( 2^{9} \cdot 5 \cdot 127 \) $0$ $\Z/2\Z$ \(\Q\) $[239204,126763297,10436094933809,41615360]$ $[59801,143724846,437833820176,1381517230655315,325120]$ $[764790054928595680699001/325120,15368348330455841308623/162560,97860226229056869361/20320]$ $y^2 + (x^2 + x)y = x^5 + 17x^4 + 76x^3 + 14x^2 - 32x + 3$
1272.a.122112.1 1272.a \( 2^{3} \cdot 3 \cdot 53 \) \( - 2^{8} \cdot 3^{2} \cdot 53 \) $0$ $\Z/2\Z\oplus\Z/6\Z$ \(\Q\) $[124,-5027,-35457,15264]$ $[124,3992,-79504,-6448640,122112]$ $[114516604/477,29731418/477,-4775209/477]$ $y^2 + (x^2 + 1)y = 3x^5 + 4x^4 + 2x^3 - x^2 - x$
1300.a.130000.1 1300.a \( 2^{2} \cdot 5^{2} \cdot 13 \) \( - 2^{4} \cdot 5^{4} \cdot 13 \) $1$ $\Z/6\Z$ \(\Q \times \Q\) $[4600,9904,15140164,520000]$ $[2300,218766,27536704,3868964111,130000]$ $[6436343000000/13,266172592200/13,1120532032]$ $y^2 + (x^3 + x)y = 2x^4 + 9x^2 + 13$
1311.a.814131.1 1311.a \( 3 \cdot 19 \cdot 23 \) \( - 3^{4} \cdot 19 \cdot 23^{2} \) $0$ $\Z/2\Z\oplus\Z/8\Z$ \(\Q\) $[600,2040,860349,3256524]$ $[300,3410,-4761,-3264100,814131]$ $[30000000000/10051,3410000000/30153,-10000/19]$ $y^2 + xy = x^5 + 5x^4 + 5x^3 + 4x^2 + x$
1312.c.671744.1 1312.c \( 2^{5} \cdot 41 \) \( - 2^{14} \cdot 41 \) $0$ $\Z/22\Z$ \(\Q\) $[164,1441,58489,83968]$ $[164,160,1984,74944,671744]$ $[2825761/16,8405/8,1271/16]$ $y^2 + (x + 1)y = x^6 + 4x^5 + 7x^4 + 5x^3 + 2x^2$
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