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Label Class Conductor Rank* Torsion $\textrm{End}^0(J_{\overline\Q})$ Igusa-Clebsch invariants Igusa invariants G2-invariants Equation
676.b.17576.1 676.b \( 2^{2} \cdot 13^{2} \) $0$ $\Z/3\Z\oplus\Z/3\Z$ \(\mathrm{M}_2(\Q)\) $[1244,1249,129167,2249728]$ $[311,3978,72332,1667692,17576]$ $[2909390022551/17576,4602275343/676,10349147/26]$ $y^2 + (x^2 + x)y = -x^6 + 3x^5 - 6x^4 + 6x^3 - 6x^2 + 3x - 1$
713.b.713.1 713.b \( 23 \cdot 31 \) $0$ $\Z/9\Z$ \(\Q\) $[92,73,6379,-91264]$ $[23,19,-41,-326,-713]$ $[-279841/31,-10051/31,943/31]$ $y^2 + (x^3 + x + 1)y = -x^4$
745.a.745.1 745.a \( 5 \cdot 149 \) $0$ $\Z/9\Z$ \(\Q\) $[124,1417,38763,95360]$ $[31,-19,39,212,745]$ $[28629151/745,-566029/745,37479/745]$ $y^2 + (x^3 + x + 1)y = -x$
862.b.862.1 862.b \( 2 \cdot 431 \) $0$ $\Z/9\Z$ \(\Q\) $[552,696,112755,3448]$ $[276,3058,45033,769436,862]$ $[800784050688/431,32146576704/431,1715216904/431]$ $y^2 + (x^3 + x)y = -2x^4 + 3x^2 - x - 1$
1042.a.1042.1 1042.a \( 2 \cdot 521 \) $0$ $\Z/9\Z$ \(\Q\) $[480,3912,728889,-4168]$ $[240,1748,-5521,-1095136,-1042]$ $[-398131200000/521,-12082176000/521,159004800/521]$ $y^2 + (x^3 + x)y = -x^4 - x^3 - x^2 + 2x + 2$
1696.b.434176.1 1696.b \( 2^{5} \cdot 53 \) $0$ $\Z/9\Z$ \(\Q \times \Q\) $[11236,7908289,22291799553,54272]$ $[11236,-11872,-76224768,-214150609408,434176]$ $[3299763591802133/8,-155150527903/4,-44328573381/2]$ $y^2 + xy = x^6 - 2x^5 + 2x^4 + 9x^3 - 12x^2 + 3x + 26$
2230.a.8920.1 2230.a \( 2 \cdot 5 \cdot 223 \) $0$ $\Z/9\Z$ \(\Q\) $[600,1488,910149,-35680]$ $[300,3502,-17961,-4413076,-8920]$ $[-60750000000/223,-2363850000/223,40412250/223]$ $y^2 + xy = x^5 + x^4 - x^3 + 2x^2 - 3x + 1$
2404.a.4808.1 2404.a \( 2^{2} \cdot 601 \) $0$ $\Z/9\Z$ \(\Q\) $[20,-3623,-42723,615424]$ $[5,152,384,-5296,4808]$ $[3125/4808,2375/601,1200/601]$ $y^2 + (x^3 + 1)y = -x^4 + x^2 + x$
2673.a.8019.1 2673.a \( 3^{5} \cdot 11 \) $0$ $\Z/9\Z$ \(\Q\) $[108,-639,-15921,4224]$ $[81,513,1809,-29160,8019]$ $[4782969/11,373977/11,16281/11]$ $y^2 + (x^3 + x + 1)y = -2x^4 + 2x^2 + x$
2768.a.354304.1 2768.a \( 2^{4} \cdot 173 \) $1$ $\Z/9\Z$ \(\Q\) $[76,889,21843,-44288]$ $[76,-352,-5888,-142848,-354304]$ $[-2476099/346,75449/173,16606/173]$ $y^2 + y = x^6 - 4x^4 - 5x^3 - 2x^2$
2810.a.89920.1 2810.a \( 2 \cdot 5 \cdot 281 \) $0$ $\Z/9\Z$ \(\Q\) $[3000,168,-70221,359680]$ $[1500,93722,7831969,741035054,89920]$ $[23730468750000/281,988474218750/281,220274128125/1124]$ $y^2 + xy = -x^6 - 3x^5 + 5x^3 - 3x + 1$
2916.a.5832.1 2916.a \( 2^{2} \cdot 3^{6} \) $0$ $\Z/3\Z\oplus\Z/3\Z$ \(\mathrm{M}_2(\Q)\) $[4,369,1257,-3072]$ $[3,-138,-356,-5028,-5832]$ $[-1/24,23/36,89/162]$ $y^2 + (x^3 + 1)y = x^3$
2916.b.11664.1 2916.b \( 2^{2} \cdot 3^{6} \) $0$ $\Z/3\Z\oplus\Z/3\Z$ \(\mathrm{M}_2(\mathsf{CM})\) $[40,45,555,6]$ $[120,330,-320,-36825,11664]$ $[6400000/3,440000/9,-32000/81]$ $y^2 + y = x^6$
3274.a.13096.1 3274.a \( 2 \cdot 1637 \) $0$ $\Z/9\Z$ \(\Q\) $[864,17376,4198167,52384]$ $[432,4880,67681,1355948,13096]$ $[1880739938304/1637,49179156480/1637,1578862368/1637]$ $y^2 + xy = x^5 - 4x^3 + 3x + 1$
3428.a.6856.1 3428.a \( 2^{2} \cdot 857 \) $0$ $\Z/9\Z$ \(\Q\) $[236,7129,366307,877568]$ $[59,-152,256,-2000,6856]$ $[714924299/6856,-3902201/857,111392/857]$ $y^2 + (x^3 + 1)y = x^4 + x^2 - x$
3568.d.913408.1 3568.d \( 2^{4} \cdot 223 \) $1$ $\Z/9\Z$ \(\Q\) $[20,4297,2661,114176]$ $[20,-2848,13568,-1959936,913408]$ $[3125/892,-11125/446,1325/223]$ $y^2 + x^3y = x^4 - 5x^3 + 5x^2 - 2x + 1$
4132.a.66112.1 4132.a \( 2^{2} \cdot 1033 \) $0$ $\Z/9\Z$ \(\Q\) $[948,10569,4333701,8462336]$ $[237,1900,-384,-925252,66112]$ $[747724704957/66112,6323225175/16528,-337014/1033]$ $y^2 + (x^3 + 1)y = x^3 - 2x^2 + 2x - 2$
4752.d.608256.1 4752.d \( 2^{4} \cdot 3^{3} \cdot 11 \) $0$ $\Z/9\Z$ \(\Q\) $[4428,5769,8489115,76032]$ $[4428,813120,198158336,54070244352,608256]$ $[61570735315641/22,116062274790,70264159344/11]$ $y^2 + x^3y = x^5 + 5x^4 + 11x^3 + 26x^2 + 28x + 33$
4900.a.98000.1 4900.a \( 2^{2} \cdot 5^{2} \cdot 7^{2} \) $0$ $\Z/3\Z\oplus\Z/3\Z$ \(\Q \times \Q\) $[1112,1549,528677,12250]$ $[1112,50490,3032000,205585975,98000]$ $[106268353943552/6125,867820181184/1225,1874600704/49]$ $y^2 + y = x^6 + 4x^4 + 4x^2 + 1$
7012.a.112192.1 7012.a \( 2^{2} \cdot 1753 \) $0$ $\Z/9\Z$ \(\Q\) $[1132,109273,29658339,14360576]$ $[283,-1216,-1536,-478336,112192]$ $[1815232161643/112192,-430638553/1753,-1922136/1753]$ $y^2 + (x^3 + 1)y = 2x^4 + 4x^2 - 2x$
7562.a.241984.1 7562.a \( 2 \cdot 19 \cdot 199 \) $0$ $\Z/9\Z$ \(\Q\) $[2544,102576,97720377,-967936]$ $[1272,50320,-53169,-649933342,-241984]$ $[-52030210457088/3781,-1618161978240/3781,1344165489/3781]$ $y^2 + (x^2 + 1)y = x^6 - 3x^5 + 2x^4 - x^3 - x^2 + 3x + 1$
10260.b.164160.1 10260.b \( 2^{2} \cdot 3^{3} \cdot 5 \cdot 19 \) $1$ $\Z/9\Z$ \(\Q\) $[3348,18297,16345485,21012480]$ $[837,28428,1307584,71574156,164160]$ $[15214704636591/6080,154347260373/1520,530123157/95]$ $y^2 + (x^3 + 1)y = -2x^4 + 6x^2 - 4$
10449.a.31347.1 10449.a \( 3^{5} \cdot 43 \) $0$ $\Z/9\Z$ \(\Q\) $[180,3393,141489,16512]$ $[135,-513,351,-53946,31347]$ $[61509375/43,-1731375/43,8775/43]$ $y^2 + (x^3 + x + 1)y = x^4 + 2x^2 - 2x$
11536.a.369152.1 11536.a \( 2^{4} \cdot 7 \cdot 103 \) $0$ $\Z/9\Z$ \(\Q\) $[100,397,12333,-46144]$ $[100,152,-1296,-38176,-369152]$ $[-19531250/721,-296875/721,50625/1442]$ $y^2 + (x + 1)y = x^6 - x^4 + x^3$
11728.d.187648.1 11728.d \( 2^{4} \cdot 733 \) $0$ $\Z/9\Z$ \(\Q\) $[224,3592,191172,750592]$ $[112,-76,636,16364,187648]$ $[68841472/733,-417088/733,31164/733]$ $y^2 + (x^3 + x)y = x^3 - x + 1$
11792.b.377344.1 11792.b \( 2^{4} \cdot 11 \cdot 67 \) $0$ $\Z/9\Z$ \(\Q\) $[116,1069,28477,47168]$ $[116,-152,1264,30880,377344]$ $[41022298/737,-463391/737,66439/1474]$ $y^2 + (x + 1)y = x^6 + x^4 - x^3$
17689.d.866761.1 17689.d \( 7^{2} \cdot 19^{2} \) $2$ $\Z/9\Z$ \(\mathsf{RM}\) $[3196,1064809,806830683,-110945408]$ $[799,-17767,-178217,-114515418,-866761]$ $[-325637113603999/866761,9062633983033/866761,113773911017/866761]$ $y^2 + (x^3 + x^2 + 1)y = 2x^4 - 2x^2 - 7x + 5$
23012.a.368192.1 23012.a \( 2^{2} \cdot 11 \cdot 523 \) $0$ $\Z/9\Z$ \(\Q\) $[84,368889,-132834675,-47128576]$ $[21,-15352,1934608,-48764284,-368192]$ $[-4084101/368192,17771859/46024,-53322633/23012]$ $y^2 + (x^2 + x + 1)y = 4x^5 + 8x^4 + x^2 + x$
26244.c.157464.1 26244.c \( 2^{2} \cdot 3^{8} \) $0$ $\Z/3\Z\oplus\Z/3\Z$ \(\mathrm{M}_2(\Q)\) $[60,945,2295,82944]$ $[45,-270,3780,24300,157464]$ $[9375/8,-625/4,875/18]$ $y^2 + (x^3 + 1)y = 2x^3$
26244.d.314928.1 26244.d \( 2^{2} \cdot 3^{8} \) $1$ $\Z/3\Z\oplus\Z/3\Z$ \(\mathrm{M}_2(\Q)\) $[24,189,1107,-162]$ $[72,-918,-3024,-265113,-314928]$ $[-6144,1088,448/9]$ $y^2 + y = x^6 - 2x^3$
26244.e.472392.1 26244.e \( 2^{2} \cdot 3^{8} \) $0$ $\Z/3\Z\oplus\Z/3\Z$ \(\mathrm{M}_2(\Q)\) $[356,3969,419553,248832]$ $[267,1482,-2884,-741588,472392]$ $[5584059449/1944,174127343/2916,-5711041/13122]$ $y^2 + (x^3 + 1)y = 2$
31775.a.158875.1 31775.a \( 5^{2} \cdot 31 \cdot 41 \) $0$ $\Z/9\Z$ \(\Q\) $[1892,166729,81871317,-20336000]$ $[473,2375,20625,1028750,-158875]$ $[-23675856753593/158875,-2010652523/1271,-36915285/1271]$ $y^2 + (x^3 + x + 1)y = -3x^4 + 6x^2 + 2x$
50220.a.803520.1 50220.a \( 2^{2} \cdot 3^{4} \cdot 5 \cdot 31 \) $0$ $\Z/9\Z$ \(\Q\) $[9036,1201257,4222582731,-102850560]$ $[2259,162576,-554256,-6920755020,-803520]$ $[-726266706536979/9920,-1446105990699/620,2182417641/620]$ $y^2 + (x^3 + 1)y = -x^5 - x^4 + x^3 + 7x^2 + 16x + 10$
52488.a.629856.1 52488.a \( 2^{3} \cdot 3^{8} \) $1$ $\Z/3\Z\oplus\Z/3\Z$ \(\Q \times \Q\) $[264,15984,2059452,10368]$ $[396,-17442,-3397248,-412383393,629856]$ $[15460896,-1719652,-7612352/9]$ $y^2 + (x^3 + x)y = x^4 - 7x^2 + 6$
68225.a.341125.1 68225.a \( 5^{2} \cdot 2729 \) $0$ $\Z/9\Z$ \(\Q\) $[2108,334729,172160683,43664000]$ $[527,-2375,-10625,-2810000,341125]$ $[40649300451407/341125,-2780900477/2729,-23606965/2729]$ $y^2 + (x^3 + x + 1)y = 2x^4 + 6x^2 - 3x$
98172.a.589032.1 98172.a \( 2^{2} \cdot 3^{5} \cdot 101 \) $0$ $\Z/9\Z$ \(\Q\) $[1116,66897,19025703,-310272]$ $[837,4104,55296,7359984,-589032]$ $[-563507579133/808,-412635141/101,-6642432/101]$ $y^2 + (x^3 + 1)y = -3x^4 + 9x^2 + 3x$
150660.a.903960.1 150660.a \( 2^{2} \cdot 3^{5} \cdot 5 \cdot 31 \) $0$ $\Z/9\Z$ \(\Q\) $[1188,99153,29008089,476160]$ $[891,-4104,-38016,-12678768,903960]$ $[770301940419/1240,-497763387/155,-5174928/155]$ $y^2 + (x^3 + 1)y = 3x^4 + 9x^2 - 3x$
163782.b.491346.1 163782.b \( 2 \cdot 3^{5} \cdot 337 \) $0$ $\Z/9\Z$ \(\Q\) $[30672,-3816,-40481955,8088]$ $[46008,88203060,225480683961,648533878578522,491346]$ $[141386924928583581696/337,5891504205359139840/337,327354660820051488/337]$ $y^2 + (x^2 + 1)y = -2x^6 + 17x^4 - 9x^3 - 26x^2 - 6x + 32$
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