| Label |
Class |
Conductor |
Discriminant |
Rank* |
2-Selmer rank |
Torsion |
$\textrm{End}^0(J_{\overline\Q})$ |
$\textrm{End}^0(J)$ |
$\GL_2\textsf{-type}$ |
Sato-Tate |
Nonmaximal primes |
$\Q$-simple |
\(\overline{\Q}\)-simple |
\(\Aut(X)\) |
\(\Aut(X_{\overline{\Q}})\) |
$\Q$-points |
$\Q$-Weierstrass points |
mod-$\ell$ images |
Locally solvable |
Square Ш* |
Analytic Ш* |
Tamagawa |
Regulator |
Real period |
Leading coefficient |
Igusa-Clebsch invariants |
Igusa invariants |
G2-invariants |
Equation |
| 1008.a.27216.1 |
1008.a |
\( 2^{4} \cdot 3^{2} \cdot 7 \) |
\( 2^{4} \cdot 3^{5} \cdot 7 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/8\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(12.167487\) |
\(0.380234\) |
$[8456,9496,26675348,108864]$ |
$[4228,743250,173847744,45651924783,27216]$ |
$[12063042849801664/243,167186257609000/81,3083035208512/27]$ |
$y^2 + (x^3 + x)y = -4x^4 + 15x^2 - 21$ |
| 1012.a.4048.1 |
1012.a |
\( 2^{2} \cdot 11 \cdot 23 \) |
\( 2^{4} \cdot 11 \cdot 23 \) |
$0$ |
$0$ |
$\Z/15\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(18.518969\) |
\(0.411533\) |
$[140,2425,78163,-518144]$ |
$[35,-50,-4,-660,-4048]$ |
$[-52521875/4048,1071875/2024,1225/1012]$ |
$y^2 + (x^3 + 1)y = x^4 + x^3 + x^2 + x$ |
| 1038.a.1038.2 |
1038.a |
\( 2 \cdot 3 \cdot 173 \) |
\( - 2 \cdot 3 \cdot 173 \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.15.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(15.397347\) |
\(0.427704\) |
$[844,4129,1133983,132864]$ |
$[211,1683,16079,140045,1038]$ |
$[418227202051/1038,5269995291/346,715853159/1038]$ |
$y^2 + (x^3 + 1)y = x^4 + 2x^2 + x + 1$ |
| 1038.a.1038.1 |
1038.a |
\( 2 \cdot 3 \cdot 173 \) |
\( 2 \cdot 3 \cdot 173 \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(15.397347\) |
\(0.427704\) |
$[109988,334849,12332566337,132864]$ |
$[27497,31489590,48060441688,82480921681709,1038]$ |
$[15719059879327073637257/1038,109111794064913809345/173,18168889743107727596/519]$ |
$y^2 + (x^2 + x)y = x^5 - 12x^4 + 26x^3 + 46x^2 + 21x + 3$ |
| 1042.a.1042.1 |
1042.a |
\( 2 \cdot 521 \) |
\( 2 \cdot 521 \) |
$0$ |
$0$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(30.423017\) |
\(0.375593\) |
$[480,3912,728889,-4168]$ |
$[240,1748,-5521,-1095136,-1042]$ |
$[-398131200000/521,-12082176000/521,159004800/521]$ |
$y^2 + (x^3 + x)y = -x^4 - x^3 - x^2 + 2x + 2$ |
| 1047.a.3141.1 |
1047.a |
\( 3 \cdot 349 \) |
\( 3^{2} \cdot 349 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(17.821680\) |
\(0.356434\) |
$[8,604,1017,-12564]$ |
$[4,-100,-1,-2501,-3141]$ |
$[-1024/3141,6400/3141,16/3141]$ |
$y^2 + (x^3 + x)y = x$ |
| 1050.a.131250.1 |
1050.a |
\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
\( - 2 \cdot 3 \cdot 5^{5} \cdot 7 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.6, 3.90.1 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(6.612551\) |
\(0.413284\) |
$[11868,198609,759217863,16800000]$ |
$[2967,358520,56735700,9949557875,131250]$ |
$[76641937806559869/43750,312136655012892/4375,475666111026/125]$ |
$y^2 + (x^2 + x)y = 3x^6 + 8x^5 + 15x^4 + 17x^3 + 15x^2 + 8x + 3$ |
| 1051.a.1051.1 |
1051.a |
\( 1051 \) |
\( -1051 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.007925\) |
\(23.437821\) |
\(0.185743\) |
$[96,-144,144,4204]$ |
$[48,120,-80,-4560,1051]$ |
$[254803968/1051,13271040/1051,-184320/1051]$ |
$y^2 + y = x^5 - x^4 + x^2 - x$ |
| 1051.b.1051.1 |
1051.b |
\( 1051 \) |
\( -1051 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(23.331720\) |
\(0.364558\) |
$[64,-200,185,4204]$ |
$[32,76,-241,-3372,1051]$ |
$[33554432/1051,2490368/1051,-246784/1051]$ |
$y^2 + (x + 1)y = -x^5 - x^4$ |
| 1051.b.1051.2 |
1051.b |
\( 1051 \) |
\( -1051 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(5.832930\) |
\(0.364558\) |
$[6176,-50240,-103225225,-4204]$ |
$[3088,405696,72449921,14784027908,-1051]$ |
$[-280793117300359168/1051,-11946277554880512/1051,-690863899476224/1051]$ |
$y^2 + xy = x^5 + 8x^4 + 16x^3 + x$ |
| 1055.a.1055.1 |
1055.a |
\( 5 \cdot 211 \) |
\( - 5 \cdot 211 \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(15.577626\) |
\(0.432712\) |
$[500,-3023,-525127,-135040]$ |
$[125,777,7441,81599,-1055]$ |
$[-6103515625/211,-303515625/211,-23253125/211]$ |
$y^2 + (x^3 + 1)y = -x^4 + x^2 - x - 1$ |
| 1062.a.6372.1 |
1062.a |
\( 2 \cdot 3^{2} \cdot 59 \) |
\( 2^{2} \cdot 3^{3} \cdot 59 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$11$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.008698\) |
\(21.575863\) |
\(0.187677\) |
$[300,2601,306603,-815616]$ |
$[75,126,-1024,-23169,-6372]$ |
$[-87890625/236,-984375/118,160000/177]$ |
$y^2 + (x^3 + 1)y = x^5 - x^4 + x^2 - x$ |
| 1069.a.1069.1 |
1069.a |
\( 1069 \) |
\( 1069 \) |
$0$ |
$0$ |
$\Z/7\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(14.937046\) |
\(0.304838\) |
$[244,3193,263789,136832]$ |
$[61,22,-884,-13602,1069]$ |
$[844596301/1069,4993582/1069,-3289364/1069]$ |
$y^2 + (x^2 + x + 1)y = x^5 + x^3$ |
| 1070.a.2140.1 |
1070.a |
\( 2 \cdot 5 \cdot 107 \) |
\( - 2^{2} \cdot 5 \cdot 107 \) |
$1$ |
$2$ |
$\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.054349\) |
\(27.743934\) |
\(0.188481\) |
$[12,3321,141939,273920]$ |
$[3,-138,-1856,-6153,2140]$ |
$[243/2140,-1863/1070,-4176/535]$ |
$y^2 + (x^3 + 1)y = x^3 - x$ |
| 1077.a.1077.2 |
1077.a |
\( 3 \cdot 359 \) |
\( - 3 \cdot 359 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.035633\) |
\(21.235034\) |
\(0.189165\) |
$[268,2233,175667,137856]$ |
$[67,94,-12,-2410,1077]$ |
$[1350125107/1077,28271722/1077,-17956/359]$ |
$y^2 + (x^3 + 1)y = x^4 + x^3 + 2x^2 + x$ |
| 1077.a.1077.1 |
1077.a |
\( 3 \cdot 359 \) |
\( 3 \cdot 359 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.035633\) |
\(21.235034\) |
\(0.189165\) |
$[155924,161593,8379938029,137856]$ |
$[38981,63306532,137068427976,333836849266358,1077]$ |
$[90004636142290020118901/1077,3749794358746968581012/1077,69425997674312689112/359]$ |
$y^2 + (x^3 + 1)y = 5x^5 + 34x^4 + 80x^3 - x^2 - 90x + 32$ |
| 1077.b.1077.1 |
1077.b |
\( 3 \cdot 359 \) |
\( 3 \cdot 359 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(10.157286\) |
\(0.406291\) |
$[320,544,55360,4308]$ |
$[160,976,7360,56256,1077]$ |
$[104857600000/1077,3997696000/1077,188416000/1077]$ |
$y^2 + x^3y = x^5 + x^4 - x - 2$ |
| 1077.b.1077.2 |
1077.b |
\( 3 \cdot 359 \) |
\( 3 \cdot 359 \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.406291\) |
\(0.406291\) |
$[107840,22281904,765878465200,4308]$ |
$[53920,117426616,333407026000,1047074174177136,1077]$ |
$[455773864377135923200000/1077,18408406506675601408000/1077,969336384916326400000/1077]$ |
$y^2 + y = x^5 + 14x^4 + 38x^3 - 79x^2 + 15x - 1$ |
| 1083.a.1083.1 |
1083.a |
\( 3 \cdot 19^{2} \) |
\( - 3 \cdot 19^{2} \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.15.2, 3.720.4 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.075149\) |
\(22.662454\) |
\(0.189229\) |
$[56,244,928,4332]$ |
$[28,-8,264,1832,1083]$ |
$[17210368/1083,-175616/1083,68992/361]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^3$ |
| 1083.a.20577.1 |
1083.a |
\( 3 \cdot 19^{2} \) |
\( 3 \cdot 19^{3} \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.15.2, 3.2160.20 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.075149\) |
\(7.554151\) |
\(0.189229\) |
$[904,13684,4578992,82308]$ |
$[452,6232,-8664,-10688488,20577]$ |
$[18866536236032/20577,30289293824/1083,-1634432/19]$ |
$y^2 + x^3y = x^5 - 5x^4 + 11x^3 - 13x^2 + 9x - 3$ |
| 1083.b.87723.1 |
1083.b |
\( 3 \cdot 19^{2} \) |
\( - 3^{5} \cdot 19^{2} \) |
$0$ |
$1$ |
$\Z/15\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.15.2, 3.720.4 |
|
|
$2$ |
\( 5 \) |
\(1.000000\) |
\(5.981341\) |
\(0.265837\) |
$[5464,8692,15768656,350892]$ |
$[2732,309544,46549080,7838649656,87723]$ |
$[152196082896530432/87723,6311963449851392/87723,1429770125440/361]$ |
$y^2 + y = -x^6 - 3x^5 - 8x^4 - 11x^3 - 14x^2 - 9x - 6$ |
| 1083.b.390963.1 |
1083.b |
\( 3 \cdot 19^{2} \) |
\( - 3 \cdot 19^{4} \) |
$0$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.15.2, 3.720.5 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(0.132919\) |
\(0.265837\) |
$[150440,1945515892,68956865081488,-1563852]$ |
$[75220,-88500632,98386538568,-107931608328616,-390963]$ |
$[-2408056349828975363200000/390963,1982406707133537344000/20577,-27053302090985600/19]$ |
$y^2 + y = -x^6 + 3x^5 - 50x^4 + 95x^3 - 14x^2 - 33x - 6$ |
| 1088.a.1088.1 |
1088.a |
\( 2^{6} \cdot 17 \) |
\( - 2^{6} \cdot 17 \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q\) |
|
$N(\mathrm{SU}(2)\times\mathrm{SU}(2))$ |
|
✓ |
|
$C_2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.1, 3.2880.5 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(15.720126\) |
\(0.436670\) |
$[196,28,632,136]$ |
$[196,1582,17884,250635,1088]$ |
$[4519603984/17,186120718/17,631463]$ |
$y^2 + (x^3 + x^2 + x + 1)y = x^4 + x^3 + 2x^2 + x + 1$ |
| 1088.b.2176.1 |
1088.b |
\( 2^{6} \cdot 17 \) |
\( - 2^{7} \cdot 17 \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.45.1, 3.2160.5 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(5.893944\) |
\(0.491162\) |
$[7572,68115,166006308,272]$ |
$[7572,2343556,952909568,430794130940,2176]$ |
$[194465720403941544/17,7948719687495546/17,25108109106912]$ |
$y^2 + (x^3 + x)y = 4x^4 + 24x^2 + 34$ |
| 1088.b.2176.2 |
1088.b |
\( 2^{6} \cdot 17 \) |
\( 2^{7} \cdot 17 \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.1, 3.2160.5 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(23.575776\) |
\(0.491162\) |
$[7572,68115,166006308,272]$ |
$[7572,2343556,952909568,430794130940,2176]$ |
$[194465720403941544/17,7948719687495546/17,25108109106912]$ |
$y^2 + (x^3 + x)y = -5x^4 + 24x^2 - 34$ |
| 1091.a.1091.1 |
1091.a |
\( 1091 \) |
\( 1091 \) |
$1$ |
$1$ |
$\Z/7\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.339399\) |
\(27.506563\) |
\(0.190525\) |
$[276,1305,42813,139648]$ |
$[69,144,1208,15654,1091]$ |
$[1564031349/1091,47305296/1091,5751288/1091]$ |
$y^2 + (x^2 + x + 1)y = x^5 - 2x^3 - x^2$ |
| 1094.a.2188.1 |
1094.a |
\( 2 \cdot 547 \) |
\( 2^{2} \cdot 547 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.003585\) |
\(26.605542\) |
\(0.190768\) |
$[20,3001,-30387,280064]$ |
$[5,-124,596,-3099,2188]$ |
$[3125/2188,-3875/547,3725/547]$ |
$y^2 + (x^3 + 1)y = x^4 - x^2$ |
| 1104.a.17664.1 |
1104.a |
\( 2^{4} \cdot 3 \cdot 23 \) |
\( 2^{8} \cdot 3 \cdot 23 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(1.000000\) |
\(8.907497\) |
\(0.445375\) |
$[88,160,4888,69]$ |
$[176,864,-1280,-242944,17664]$ |
$[659664896/69,6133248/23,-154880/69]$ |
$y^2 = x^5 - 2x^4 + 4x^3 - 4x^2 + 3x - 1$ |
| 1104.b.141312.1 |
1104.b |
\( 2^{4} \cdot 3 \cdot 23 \) |
\( - 2^{11} \cdot 3 \cdot 23 \) |
$0$ |
$2$ |
$\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.90.1 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(0.712625\) |
\(0.356313\) |
$[14220,9418737,54280328031,17664]$ |
$[14220,2146192,-16790479872,-60841690970176,141312]$ |
$[189267815942240625/46,2008843709918625/46,-24026098775400]$ |
$y^2 + (x^3 + x)y = -x^6 - 3x^4 + 29x^2 - 46$ |
| 1109.a.1109.1 |
1109.a |
\( 1109 \) |
\( 1109 \) |
$0$ |
$0$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.288506\) |
\(0.288506\) |
$[38880,87301728,855606760992,4436]$ |
$[19440,1196112,510249312,2122140677184,1109]$ |
$[2776395315422822400000/1109,8787404722987008000/1109,192830154395443200/1109]$ |
$y^2 + y = x^5 - 6x^4 - 36x^3 - 6x^2 + 63x - 36$ |
| 1109.b.1109.1 |
1109.b |
\( 1109 \) |
\( 1109 \) |
$0$ |
$0$ |
$\Z/7\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(21.606017\) |
\(0.440939\) |
$[248,-32,-10424,4436]$ |
$[124,646,5388,62699,1109]$ |
$[29316250624/1109,1231679104/1109,82845888/1109]$ |
$y^2 + y = x^5 - x^4 - x^3 + x^2 + x$ |
| 1109.c.1109.1 |
1109.c |
\( 1109 \) |
\( 1109 \) |
$0$ |
$0$ |
$\Z/5\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(9.552149\) |
\(0.382086\) |
$[392,292,36703,4436]$ |
$[196,1552,16001,181873,1109]$ |
$[289254654976/1109,11685839872/1109,614694416/1109]$ |
$y^2 + (x^3 + x)y = x^5 - 2x^3 - 2x^2 - 1$ |
| 1116.a.214272.1 |
1116.a |
\( 2^{2} \cdot 3^{2} \cdot 31 \) |
\( - 2^{8} \cdot 3^{3} \cdot 31 \) |
$0$ |
$0$ |
$\Z/39\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3,13$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
2.10.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3 \cdot 13 \) |
\(1.000000\) |
\(16.984099\) |
\(0.435490\) |
$[52,22201,238285,-27426816]$ |
$[13,-918,36,-210564,-214272]$ |
$[-371293/214272,37349/3968,-169/5952]$ |
$y^2 + (x^3 + 1)y = x^4 + 2x^3 + x^2 - x$ |
| 1122.a.1122.1 |
1122.a |
\( 2 \cdot 3 \cdot 11 \cdot 17 \) |
\( 2 \cdot 3 \cdot 11 \cdot 17 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.180.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(6.820719\) |
\(0.426295\) |
$[56004,288321,5331417537,143616]$ |
$[14001,8155820,6325887612,5512838145803,1122]$ |
$[179338702480653356667/374,3730727674118765970/187,1105214886926046]$ |
$y^2 + (x^2 + x)y = x^5 + 7x^4 - 43x^2 + 51x - 17$ |
| 1122.b.2244.1 |
1122.b |
\( 2 \cdot 3 \cdot 11 \cdot 17 \) |
\( 2^{2} \cdot 3 \cdot 11 \cdot 17 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.180.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(30.724131\) |
\(0.426724\) |
$[1828,153793,73850145,287232]$ |
$[457,2294,8704,-321177,2244]$ |
$[19933382494057/2244,109474259971/1122,26732672/33]$ |
$y^2 + (x^2 + x)y = x^5 + 7x^4 + 5x^3 - x^2 - x$ |
| 1123.a.1123.1 |
1123.a |
\( 1123 \) |
\( -1123 \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(21.491845\) |
\(0.335810\) |
$[24,-672,-75,4492]$ |
$[12,118,-361,-4564,1123]$ |
$[248832/1123,203904/1123,-51984/1123]$ |
$y^2 + (x^3 + x)y = -x^4 - x^2 - x$ |
| 1125.a.151875.1 |
1125.a |
\( 3^{2} \cdot 5^{3} \) |
\( - 3^{5} \cdot 5^{4} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3, 3.80.4 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(1.964402\) |
\(0.491100\) |
$[8600,612100,1556297975,-607500]$ |
$[4300,668400,132975225,31258726875,-151875]$ |
$[-2352135088000000/243,-28342655360000/81,-437104339600/27]$ |
$y^2 + xy = 15x^5 + 50x^4 + 55x^3 + 22x^2 + 3x$ |
| 1127.a.1127.1 |
1127.a |
\( 7^{2} \cdot 23 \) |
\( - 7^{2} \cdot 23 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
2.40.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.006656\) |
\(25.743921\) |
\(0.171351\) |
$[60,105,37947,144256]$ |
$[15,5,-501,-1885,1127]$ |
$[759375/1127,16875/1127,-112725/1127]$ |
$y^2 + (x^3 + x + 1)y = -x^4 + x^3 - x^2 - x$ |
| 1136.a.9088.1 |
1136.a |
\( 2^{4} \cdot 71 \) |
\( - 2^{7} \cdot 71 \) |
$0$ |
$1$ |
$\Z/14\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 7 \) |
\(1.000000\) |
\(13.476708\) |
\(0.481311\) |
$[432,1368,174708,36352]$ |
$[216,1716,17596,214020,9088]$ |
$[3673320192/71,135104112/71,6413742/71]$ |
$y^2 + (x^3 + x)y = x^4 - x^3 + 2x^2 - x + 1$ |
| 1136.a.290816.1 |
1136.a |
\( 2^{4} \cdot 71 \) |
\( 2^{12} \cdot 71 \) |
$0$ |
$1$ |
$\Z/14\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 7 \) |
\(1.000000\) |
\(13.476708\) |
\(0.481311\) |
$[9252,17217,52921881,36352]$ |
$[9252,3555168,1815712832,1039938903360,290816]$ |
$[66203075280122793/284,1374792164318403/142,151781365064097/284]$ |
$y^2 + (x^3 + x^2)y = -5x^4 - 9x^3 + 25x^2 + 40x - 24$ |
| 1137.a.1137.1 |
1137.a |
\( 3 \cdot 379 \) |
\( 3 \cdot 379 \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(15.522353\) |
\(0.431176\) |
$[148,-191,28401,145536]$ |
$[37,65,-359,-4377,1137]$ |
$[69343957/1137,3292445/1137,-491471/1137]$ |
$y^2 + (x^2 + x + 1)y = x^5 + x^4 + x^3$ |
| 1142.a.2284.1 |
1142.a |
\( 2 \cdot 571 \) |
\( - 2^{2} \cdot 571 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(16.871340\) |
\(0.337427\) |
$[472,-2876,-427657,-9136]$ |
$[236,2800,46521,784739,-2284]$ |
$[-183020620544/571,-9200979200/571,-647758404/571]$ |
$y^2 + (x^3 + x^2)y = -x^4 - x^3 + x^2 - x - 2$ |
| 1142.b.9136.1 |
1142.b |
\( 2 \cdot 571 \) |
\( - 2^{4} \cdot 571 \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(17.757282\) |
\(0.493258\) |
$[864,-4488,-1442025,-36544]$ |
$[432,8524,257089,9600968,-9136]$ |
$[-940369969152/571,-42951140352/571,-2998686096/571]$ |
$y^2 + (x + 1)y = -x^5 + 3x^4 - 6x^2 + x + 3$ |
| 1145.a.1145.1 |
1145.a |
\( 5 \cdot 229 \) |
\( 5 \cdot 229 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.026504\) |
\(29.585150\) |
\(0.196028\) |
$[468,5337,771165,146560]$ |
$[117,348,224,-23724,1145]$ |
$[21924480357/1145,557361324/1145,3066336/1145]$ |
$y^2 + (x^3 + 1)y = -3x^4 + 3x^3 - x$ |
| 1145.a.143125.1 |
1145.a |
\( 5 \cdot 229 \) |
\( - 5^{4} \cdot 229 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.026504\) |
\(7.396287\) |
\(0.196028\) |
$[5004,191097,289856403,18320000]$ |
$[1251,57246,3273124,204393402,143125]$ |
$[3063984390631251/143125,112077149104746/143125,5122442333124/143125]$ |
$y^2 + (x^3 + x^2 + x)y = 2x^4 + 4x^3 + 9x^2 + 10x + 9$ |
| 1146.a.2292.1 |
1146.a |
\( 2 \cdot 3 \cdot 191 \) |
\( 2^{2} \cdot 3 \cdot 191 \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.30.3, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(9.256014\) |
\(0.514223\) |
$[104,1096,61011,9168]$ |
$[52,-70,-3815,-50820,2292]$ |
$[95051008/573,-2460640/573,-2578940/573]$ |
$y^2 + xy = x^5 + 3x^4 + 5x^3 + 4x^2 + 2x$ |
| 1147.a.35557.1 |
1147.a |
\( 31 \cdot 37 \) |
\( 31^{2} \cdot 37 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(11.458568\) |
\(0.358080\) |
$[3712,11944,14677639,142228]$ |
$[1856,141540,14195057,1578113548,35557]$ |
$[22023678539595776/35557,904926084464640/35557,48898223869952/35557]$ |
$y^2 + xy = x^5 + 8x^4 + 18x^3 + 8x^2 + x$ |
| 1147.a.35557.2 |
1147.a |
\( 31 \cdot 37 \) |
\( 31^{2} \cdot 37 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(2.864642\) |
\(0.358080\) |
$[12352,2309104,8338761079,142228]$ |
$[6176,1204440,279006977,68117844088,35557]$ |
$[8985379753611493376/35557,283731159059005440/35557,10642156427543552/35557]$ |
$y^2 + xy = x^5 + 6x^4 - 32x^2 + x$ |
| 1148.a.8036.1 |
1148.a |
\( 2^{2} \cdot 7 \cdot 41 \) |
\( 2^{2} \cdot 7^{2} \cdot 41 \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.90.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(22.531311\) |
\(0.450626\) |
$[3540,152577,168647985,1028608]$ |
$[885,26277,825045,9921024,8036]$ |
$[542895639553125/8036,18214010942625/8036,646195870125/8036]$ |
$y^2 + (x^3 + 1)y = x^5 - x^4 - 6x^3 + x^2 + 5x - 1$ |
| 1148.a.47068.1 |
1148.a |
\( 2^{2} \cdot 7 \cdot 41 \) |
\( - 2^{2} \cdot 7 \cdot 41^{2} \) |
$0$ |
$1$ |
$\Z/10\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.90.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(22.531311\) |
\(0.450626\) |
$[1236,129537,36025137,-6024704]$ |
$[309,-1419,31221,1908432,-47068]$ |
$[-2817036000549/47068,41865649551/47068,-2981012301/47068]$ |
$y^2 + (x^2 + x + 1)y = x^5 + 2x^4 - 5x^3 + x$ |
