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Label Class Conductor Discriminant Rank* Torsion $\textrm{End}^0(J_{\overline\Q})$ Igusa-Clebsch invariants Igusa invariants G2-invariants Equation
249.a.6723.1 249.a \( 3 \cdot 83 \) \( - 3^{4} \cdot 83 \) $0$ $\Z/28\Z$ \(\Q\) $[1932,87897,65765571,860544]$ $[483,6058,-161212,-28641190,6723]$ $[324526850403/83,25281736298/249,-4178776252/747]$ $y^2 + (x^3 + 1)y = -x^5 + x^3 + x^2 + 3x + 2$
294.a.8232.1 294.a \( 2 \cdot 3 \cdot 7^{2} \) \( 2^{3} \cdot 3 \cdot 7^{3} \) $0$ $\Z/12\Z$ \(\Q \times \Q\) $[7636,11785,29745701,1053696]$ $[1909,151354,15951264,1885732415,8232]$ $[25353016669288549/8232,75211396489919/588,49431027484/7]$ $y^2 + (x^3 + 1)y = -2x^4 + 4x^2 - 9x - 14$
360.a.6480.1 360.a \( 2^{3} \cdot 3^{2} \cdot 5 \) \( 2^{4} \cdot 3^{4} \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/2\Z\oplus\Z/8\Z$ \(\Q \times \Q\) $[2360,11992,9047820,25920]$ $[1180,56018,3453120,234166319,6480]$ $[28596971960000/81,1150492082200/81,6677950400/9]$ $y^2 + (x^3 + x)y = -3x^4 + 7x^2 - 5$
394.a.3152.1 394.a \( 2 \cdot 197 \) \( 2^{4} \cdot 197 \) $0$ $\Z/20\Z$ \(\Q\) $[80,-20,649,-12608]$ $[40,70,39,-835,-3152]$ $[-6400000/197,-280000/197,-3900/197]$ $y^2 + (x + 1)y = -x^5$
427.a.2989.1 427.a \( 7 \cdot 61 \) \( - 7^{2} \cdot 61 \) $0$ $\Z/14\Z$ \(\Q\) $[4564,-22439,-35962915,-382592]$ $[1141,55180,3641688,277583402,-2989]$ $[-39466820645749/61,-1672794336220/61,-96756008472/61]$ $y^2 + (x^3 + 1)y = x^5 - x^4 - 5x^3 + 4x^2 + 4x - 4$
450.a.2700.1 450.a \( 2 \cdot 3^{2} \cdot 5^{2} \) \( - 2^{2} \cdot 3^{3} \cdot 5^{2} \) $0$ $\Z/24\Z$ \(\Q \times \Q\) $[364,3529,393211,345600]$ $[91,198,0,-9801,2700]$ $[6240321451/2700,8289281/150,0]$ $y^2 + (x^3 + 1)y = x^5 + 3x^4 + 3x^3 + 3x^2 + x$
484.a.1936.1 484.a \( 2^{2} \cdot 11^{2} \) \( - 2^{4} \cdot 11^{2} \) $0$ $\Z/15\Z$ \(\Q \times \Q\) $[184,37,721,242]$ $[184,1386,15040,211591,1936]$ $[13181630464/121,49057344/11,31824640/121]$ $y^2 + y = x^6 + 2x^4 + x^2$
555.a.8325.1 555.a \( 3 \cdot 5 \cdot 37 \) \( 3^{2} \cdot 5^{2} \cdot 37 \) $0$ $\Z/2\Z\oplus\Z/10\Z$ \(\Q\) $[1264,18124,6869487,33300]$ $[632,13622,351361,9125317,8325]$ $[100828984082432/8325,3438682756096/8325,140342016064/8325]$ $y^2 + (x + 1)y = 3x^5 - 2x^4 - 4x^3 + x^2 + x$
578.a.2312.1 578.a \( 2 \cdot 17^{2} \) \( 2^{3} \cdot 17^{2} \) $0$ $\Z/12\Z$ \(\Q \times \Q\) $[228,705,135777,295936]$ $[57,106,-992,-16945,2312]$ $[601692057/2312,9815229/1156,-402876/289]$ $y^2 + (x^2 + x)y = x^5 - 2x^4 + 2x^3 - 2x^2 + x$
604.a.9664.1 604.a \( 2^{2} \cdot 151 \) \( 2^{6} \cdot 151 \) $0$ $\mathsf{trivial}$ \(\Q\) $[49556,-797087975,-23996873337603,1236992]$ $[12389,39607304,223396249616,299729401586052,9664]$ $[291864493641401980949/9664,9414430497536890397/1208,2143030742187944921/604]$ $y^2 + (x^2 + x + 1)y = 4x^5 + 9x^4 + 48x^3 - 4x^2 - 53x - 21$
604.a.9664.2 604.a \( 2^{2} \cdot 151 \) \( 2^{6} \cdot 151 \) $0$ $\Z/27\Z$ \(\Q\) $[116,6265,95277,1236992]$ $[29,-226,836,-6708,9664]$ $[20511149/9664,-2755957/4832,175769/2416]$ $y^2 + (x^3 + 1)y = -x^4 + x^3 + x^2 - x$
644.a.2576.1 644.a \( 2^{2} \cdot 7 \cdot 23 \) \( - 2^{4} \cdot 7 \cdot 23 \) $0$ $\Z/6\Z$ \(\Q \times \Q\) $[39036,4124865,50880984159,329728]$ $[9759,3796384,1910683600,1058457444236,2576]$ $[88516980336138032799/2576,220529201888022246/161,70640465629725]$ $y^2 + (x^2 + x)y = -5x^6 + 11x^5 - 20x^4 + 20x^3 - 20x^2 + 11x - 5$
676.a.5408.1 676.a \( 2^{2} \cdot 13^{2} \) \( - 2^{5} \cdot 13^{2} \) $0$ $\Z/21\Z$ \(\Q \times \Q\) $[204,3273,161211,692224]$ $[51,-28,0,-196,5408]$ $[345025251/5408,-928557/1352,0]$ $y^2 + (x^3 + x^2 + x)y = x^3 + 3x^2 + 3x + 1$
688.a.2752.1 688.a \( 2^{4} \cdot 43 \) \( - 2^{6} \cdot 43 \) $0$ $\Z/20\Z$ \(\Q\) $[32,112,-680,-344]$ $[32,-32,1344,10496,-2752]$ $[-524288/43,16384/43,-21504/43]$ $y^2 + y = 2x^5 - 5x^4 + 4x^3 - x$
708.a.2832.1 708.a \( 2^{2} \cdot 3 \cdot 59 \) \( 2^{4} \cdot 3 \cdot 59 \) $0$ $\Z/10\Z$ \(\Q\) $[148,2065,76361,362496]$ $[37,-29,-59,-756,2832]$ $[69343957/2832,-1468937/2832,-1369/48]$ $y^2 + (x^2 + x + 1)y = x^5$
720.a.6480.1 720.a \( 2^{4} \cdot 3^{2} \cdot 5 \) \( - 2^{4} \cdot 3^{4} \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[2360,11992,9047820,25920]$ $[1180,56018,3453120,234166319,6480]$ $[28596971960000/81,1150492082200/81,6677950400/9]$ $y^2 + (x^3 + x)y = 2x^4 + 7x^2 + 5$
726.a.1452.1 726.a \( 2 \cdot 3 \cdot 11^{2} \) \( - 2^{2} \cdot 3 \cdot 11^{2} \) $0$ $\Z/10\Z$ \(\Q \times \Q\) $[760,-69236,-16142609,-5808]$ $[380,17556,702601,-10306189,-1452]$ $[-1980879200000/363,-7297976000/11,-25363896100/363]$ $y^2 + (x^2 + 1)y = 2x^5 + 2x^4 + 6x^3 - 2x^2 - x$
762.a.3048.1 762.a \( 2 \cdot 3 \cdot 127 \) \( - 2^{3} \cdot 3 \cdot 127 \) $0$ $\Z/12\Z$ \(\Q\) $[428,3169,355487,390144]$ $[107,345,1823,19009,3048]$ $[14025517307/3048,140879945/1016,20871527/3048]$ $y^2 + (x^3 + x^2 + x)y = x^2 + x + 1$
768.a.1536.1 768.a \( 2^{8} \cdot 3 \) \( 2^{9} \cdot 3 \) $0$ $\Z/2\Z\oplus\Z/6\Z$ \(\Q\) $[134,82,3600,6]$ $[268,2774,35236,437043,1536]$ $[2700250214/3,417158281/12,39543601/24]$ $y^2 + y = 2x^5 - x^4 - 3x^3 + x$
768.a.4608.1 768.a \( 2^{8} \cdot 3 \) \( 2^{9} \cdot 3^{2} \) $0$ $\Z/2\Z\oplus\Z/6\Z$ \(\Q\) $[38,22,384,18]$ $[76,182,-476,-17325,4608]$ $[4952198/9,624169/36,-42959/72]$ $y^2 + (x^3 + x^2 + x + 1)y = -x^3 - x^2 - x - 1$
784.a.1568.1 784.a \( 2^{4} \cdot 7^{2} \) \( 2^{5} \cdot 7^{2} \) $0$ $\Z/12\Z$ \(\Q \times \Q\) $[792,120,15228,6272]$ $[396,6514,144256,3673295,1568]$ $[304316815968/49,12641055372/49,14427072]$ $y^2 + (x^3 + x)y = -2x^4 + 3x^2 - 2$
800.a.1600.1 800.a \( 2^{5} \cdot 5^{2} \) \( 2^{6} \cdot 5^{2} \) $0$ $\Z/12\Z$ \(\Q \times \Q\) $[0,84,936,200]$ $[0,-56,832,-784,-1600]$ $[0,-134456/625,728/25]$ $y^2 + (x^3 + x^2 + x + 1)y = -x^4 - x^2$
800.a.8000.1 800.a \( 2^{5} \cdot 5^{2} \) \( 2^{6} \cdot 5^{3} \) $0$ $\Z/4\Z$ \(\Q \times \Q\) $[192,11604,322392,-1000]$ $[192,-6200,142400,-2774800,-8000]$ $[-4076863488/125,27426816/5,-3280896/5]$ $y^2 + (x^3 + x^2 + x + 1)y = -x^6 + 2x^4 + 4x^3 + 2x^2 - 1$
807.a.2421.1 807.a \( 3 \cdot 269 \) \( 3^{2} \cdot 269 \) $0$ $\Z/8\Z$ \(\Q\) $[680,640,153059,9684]$ $[340,4710,84049,1598140,2421]$ $[4543542400000/2421,61707280000/807,9716064400/2421]$ $y^2 + (x^3 + x)y = x^5 - 2x^3 - x^2 + 2x - 1$
830.a.6640.1 830.a \( 2 \cdot 5 \cdot 83 \) \( - 2^{4} \cdot 5 \cdot 83 \) $0$ $\Z/16\Z$ \(\Q\) $[652,4273,1339719,849920]$ $[163,929,-521,-236991,6640]$ $[115063617043/6640,4023263963/6640,-13842449/6640]$ $y^2 + (x^3 + 1)y = -x^5 + x^4 - 2x^2 + x + 1$
834.a.1668.1 834.a \( 2 \cdot 3 \cdot 139 \) \( 2^{2} \cdot 3 \cdot 139 \) $0$ $\Z/8\Z$ \(\Q\) $[372,3345,401289,213504]$ $[93,221,-111,-14791,1668]$ $[2318961231/556,59254299/556,-320013/556]$ $y^2 + (x^3 + 1)y = -x^2 + x - 1$
847.b.9317.1 847.b \( 7 \cdot 11^{2} \) \( 7 \cdot 11^{3} \) $0$ $\Z/10\Z$ \(\Q \times \Q\) $[304,5932,452465,-37268]$ $[152,-26,-401,-15407,-9317]$ $[-81136812032/9317,91307008/9317,9264704/9317]$ $y^2 + (x^2 + 1)y = x^5 + 2x^4 - 3x^3 + 2x^2 - x$
847.c.9317.1 847.c \( 7 \cdot 11^{2} \) \( 7 \cdot 11^{3} \) $0$ $\Z/8\Z$ \(\Q\) $[424,3520,581427,37268]$ $[212,1286,-7999,-837396,9317]$ $[428232184832/9317,12253172608/9317,-359507056/9317]$ $y^2 + (x^3 + x^2)y = x^4 + x^3 - x - 2$
856.a.1712.1 856.a \( 2^{3} \cdot 107 \) \( - 2^{4} \cdot 107 \) $0$ $\Z/2\Z\oplus\Z/6\Z$ \(\Q\) $[32,-368,-11044,-6848]$ $[16,72,964,2560,-1712]$ $[-65536/107,-18432/107,-15424/107]$ $y^2 + (x^3 + x)y = -x^4 - x^3 + x$
862.a.6896.1 862.a \( 2 \cdot 431 \) \( - 2^{4} \cdot 431 \) $0$ $\Z/2\Z\oplus\Z/8\Z$ \(\Q\) $[932,12385,3688145,-882688]$ $[233,1746,11456,-94817,-6896]$ $[-686719856393/6896,-11042871201/3448,-38870924/431]$ $y^2 + (x^2 + x)y = 4x^5 + 6x^4 - 3x^2 - x$
864.a.1728.1 864.a \( 2^{5} \cdot 3^{3} \) \( - 2^{6} \cdot 3^{3} \) $0$ $\Z/12\Z$ \(\mathsf{CM} \times \Q\) $[96,180,5256,216]$ $[96,264,576,-3600,1728]$ $[4718592,135168,3072]$ $y^2 + (x^3 + x^2 + x + 1)y = x^4 + x^2$
886.a.3544.1 886.a \( 2 \cdot 443 \) \( 2^{3} \cdot 443 \) $0$ $\Z/15\Z$ \(\Q\) $[232,1180,93881,-14176]$ $[116,364,-481,-47073,-3544]$ $[-2625427072/443,-71020768/443,809042/443]$ $y^2 + (x^3 + x)y = -x^4 - x + 1$
909.a.8181.1 909.a \( 3^{2} \cdot 101 \) \( 3^{4} \cdot 101 \) $0$ $\Z/2\Z\oplus\Z/8\Z$ \(\Q\) $[1384,44560,19431635,32724]$ $[692,12526,35569,-33071732,8181]$ $[158683025503232/8181,4150789321088/8181,17032713616/8181]$ $y^2 + xy = 3x^5 - 7x^4 + x^3 + 6x^2 - 3x$
932.a.3728.1 932.a \( 2^{2} \cdot 233 \) \( - 2^{4} \cdot 233 \) $1$ $\mathsf{trivial}$ \(\Q\) $[8,229,527,-466]$ $[8,-150,-128,-5881,-3728]$ $[-2048/233,4800/233,512/233]$ $y^2 + y = x^6 - 2x^5 + x^4 + x^2 - x$
936.a.1872.1 936.a \( 2^{3} \cdot 3^{2} \cdot 13 \) \( - 2^{4} \cdot 3^{2} \cdot 13 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[45352,11224,169415364,7488]$ $[22676,21423170,26983749312,38232821637503,1872]$ $[374724646811252438336/117,15612163699641478120/117,7411896491650496]$ $y^2 + (x^3 + x)y = -x^6 - 9x^4 - 32x^2 - 39$
968.a.1936.1 968.a \( 2^{3} \cdot 11^{2} \) \( - 2^{4} \cdot 11^{2} \) $1$ $\Z/5\Z$ \(\Q \times \Q\) $[120,357,14937,242]$ $[120,362,-1344,-73081,1936]$ $[1555200000/121,39096000/121,-1209600/121]$ $y^2 + y = x^6 - x^4$
970.a.1940.1 970.a \( 2 \cdot 5 \cdot 97 \) \( 2^{2} \cdot 5 \cdot 97 \) $0$ $\Z/10\Z$ \(\Q\) $[24,684,4887,7760]$ $[12,-108,-159,-3393,1940]$ $[62208/485,-46656/485,-5724/485]$ $y^2 + (x + 1)y = x^5 + x^4 + x^3 + x^2$
980.a.7840.1 980.a \( 2^{2} \cdot 5 \cdot 7^{2} \) \( 2^{5} \cdot 5 \cdot 7^{2} \) $0$ $\Z/12\Z$ \(\Q \times \Q\) $[276,3945,280149,1003520]$ $[69,34,20,56,7840]$ $[1564031349/7840,5584653/3920,4761/392]$ $y^2 + (x^2 + x + 1)y = -x^6 + 3x^5 - 3x^4 - x$
990.a.8910.1 990.a \( 2 \cdot 3^{2} \cdot 5 \cdot 11 \) \( 2 \cdot 3^{4} \cdot 5 \cdot 11 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ \(\Q \times \Q\) $[3268,252577,318023313,1140480]$ $[817,17288,-766260,-231227341,8910]$ $[364007458703857/8910,4713906106372/4455,-57404054]$ $y^2 + (x^2 + x)y = 3x^5 + 4x^4 + 7x^3 + 4x^2 + 3x$
1012.a.4048.1 1012.a \( 2^{2} \cdot 11 \cdot 23 \) \( 2^{4} \cdot 11 \cdot 23 \) $0$ $\Z/15\Z$ \(\Q\) $[140,2425,78163,-518144]$ $[35,-50,-4,-660,-4048]$ $[-52521875/4048,1071875/2024,1225/1012]$ $y^2 + (x^3 + 1)y = x^4 + x^3 + x^2 + x$
1038.a.1038.2 1038.a \( 2 \cdot 3 \cdot 173 \) \( - 2 \cdot 3 \cdot 173 \) $0$ $\Z/6\Z$ \(\Q\) $[844,4129,1133983,132864]$ $[211,1683,16079,140045,1038]$ $[418227202051/1038,5269995291/346,715853159/1038]$ $y^2 + (x^3 + 1)y = x^4 + 2x^2 + x + 1$
1038.a.1038.1 1038.a \( 2 \cdot 3 \cdot 173 \) \( 2 \cdot 3 \cdot 173 \) $0$ $\Z/6\Z$ \(\Q\) $[109988,334849,12332566337,132864]$ $[27497,31489590,48060441688,82480921681709,1038]$ $[15719059879327073637257/1038,109111794064913809345/173,18168889743107727596/519]$ $y^2 + (x^2 + x)y = x^5 - 12x^4 + 26x^3 + 46x^2 + 21x + 3$
1042.a.1042.1 1042.a \( 2 \cdot 521 \) \( 2 \cdot 521 \) $0$ $\Z/9\Z$ \(\Q\) $[480,3912,728889,-4168]$ $[240,1748,-5521,-1095136,-1042]$ $[-398131200000/521,-12082176000/521,159004800/521]$ $y^2 + (x^3 + x)y = -x^4 - x^3 - x^2 + 2x + 2$
1047.a.3141.1 1047.a \( 3 \cdot 349 \) \( 3^{2} \cdot 349 \) $0$ $\Z/10\Z$ \(\Q\) $[8,604,1017,-12564]$ $[4,-100,-1,-2501,-3141]$ $[-1024/3141,6400/3141,16/3141]$ $y^2 + (x^3 + x)y = x$
1051.a.1051.1 1051.a \( 1051 \) \( -1051 \) $1$ $\mathsf{trivial}$ \(\Q\) $[96,-144,144,4204]$ $[48,120,-80,-4560,1051]$ $[254803968/1051,13271040/1051,-184320/1051]$ $y^2 + y = x^5 - x^4 + x^2 - x$
1051.b.1051.1 1051.b \( 1051 \) \( -1051 \) $0$ $\Z/8\Z$ \(\Q\) $[64,-200,185,4204]$ $[32,76,-241,-3372,1051]$ $[33554432/1051,2490368/1051,-246784/1051]$ $y^2 + (x + 1)y = -x^5 - x^4$
1051.b.1051.2 1051.b \( 1051 \) \( -1051 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ \(\Q\) $[6176,-50240,-103225225,-4204]$ $[3088,405696,72449921,14784027908,-1051]$ $[-280793117300359168/1051,-11946277554880512/1051,-690863899476224/1051]$ $y^2 + xy = x^5 + 8x^4 + 16x^3 + x$
1055.a.1055.1 1055.a \( 5 \cdot 211 \) \( - 5 \cdot 211 \) $0$ $\Z/6\Z$ \(\Q\) $[500,-3023,-525127,-135040]$ $[125,777,7441,81599,-1055]$ $[-6103515625/211,-303515625/211,-23253125/211]$ $y^2 + (x^3 + 1)y = -x^4 + x^2 - x - 1$
1062.a.6372.1 1062.a \( 2 \cdot 3^{2} \cdot 59 \) \( 2^{2} \cdot 3^{3} \cdot 59 \) $1$ $\Z/2\Z$ \(\Q\) $[300,2601,306603,-815616]$ $[75,126,-1024,-23169,-6372]$ $[-87890625/236,-984375/118,160000/177]$ $y^2 + (x^3 + 1)y = x^5 - x^4 + x^2 - x$
1069.a.1069.1 1069.a \( 1069 \) \( 1069 \) $0$ $\Z/7\Z$ \(\Q\) $[244,3193,263789,136832]$ $[61,22,-884,-13602,1069]$ $[844596301/1069,4993582/1069,-3289364/1069]$ $y^2 + (x^2 + x + 1)y = x^5 + x^3$
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