| 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 |
| 713.a.713.1 |
713.a |
\( 23 \cdot 31 \) |
\( 23 \cdot 31 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
2.20.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.004592\) |
\(27.957889\) |
\(0.128395\) |
$[36,1305,-2547,91264]$ |
$[9,-51,173,-261,713]$ |
$[59049/713,-37179/713,14013/713]$ |
$y^2 + (x^3 + x + 1)y = -x^5 - x$ |
| 743.a.743.1 |
743.a |
\( 743 \) |
\( -743 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.004577\) |
\(28.765391\) |
\(0.131656\) |
$[28,1945,15219,95104]$ |
$[7,-79,-53,-1653,743]$ |
$[16807/743,-27097/743,-2597/743]$ |
$y^2 + (x^3 + x + 1)y = -x^4 + x^2$ |
| 893.a.893.1 |
893.a |
\( 19 \cdot 47 \) |
\( 19 \cdot 47 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.006429\) |
\(23.402435\) |
\(0.150459\) |
$[156,-519,-11805,-114304]$ |
$[39,85,67,-1153,-893]$ |
$[-90224199/893,-5042115/893,-101907/893]$ |
$y^2 + (x^3 + x + 1)y = -x^4 - x^2$ |
| 953.a.953.1 |
953.a |
\( 953 \) |
\( -953 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.006276\) |
\(24.886682\) |
\(0.156194\) |
$[92,1513,26203,121984]$ |
$[23,-41,67,-35,953]$ |
$[6436343/953,-498847/953,35443/953]$ |
$y^2 + (x^3 + x + 1)y = x^3 + x^2$ |
| 968.a.1936.1 |
968.a |
\( 2^{3} \cdot 11^{2} \) |
\( - 2^{4} \cdot 11^{2} \) |
$1$ |
$1$ |
$\Z/5\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$8$ |
$0$ |
2.60.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.080529\) |
\(26.986750\) |
\(0.173857\) |
$[120,357,14937,242]$ |
$[120,362,-1344,-73081,1936]$ |
$[1555200000/121,39096000/121,-1209600/121]$ |
$y^2 + y = x^6 - x^4$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.035633\) |
\(21.235034\) |
\(0.189165\) |
$[268,2233,175667,137856]$ |
$[67,94,-12,-2410,1077]$ |
$[1350125107/1077,28271722/1077,-17956/359]$ |
$y^2 + (x^3 + 1)y = x^4 + x^3 + 2x^2 + x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 3 \cdot 13 \) |
\(1.000000\) |
\(16.984099\) |
\(0.435490\) |
$[52,22201,238285,-27426816]$ |
$[13,-918,36,-210564,-214272]$ |
$[-371293/214272,37349/3968,-169/5952]$ |
$y^2 + (x^3 + 1)y = x^4 + 2x^3 + x^2 - x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.006656\) |
\(25.743921\) |
\(0.171351\) |
$[60,105,37947,144256]$ |
$[15,5,-501,-1885,1127]$ |
$[759375/1127,16875/1127,-112725/1127]$ |
$y^2 + (x^3 + x + 1)y = -x^4 + x^3 - x^2 - x$ |
| 1343.a.1343.1 |
1343.a |
\( 17 \cdot 79 \) |
\( 17 \cdot 79 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.007639\) |
\(24.541872\) |
\(0.187477\) |
$[220,649,72811,-171904]$ |
$[55,99,-213,-5379,-1343]$ |
$[-503284375/1343,-16471125/1343,644325/1343]$ |
$y^2 + (x^3 + x + 1)y = x^5 - 2x^4 - x$ |
| 1343.b.1343.1 |
1343.b |
\( 17 \cdot 79 \) |
\( 17 \cdot 79 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.013205\) |
\(18.431116\) |
\(0.243377\) |
$[708,-32871,-7418931,171904]$ |
$[177,2675,48537,358856,1343]$ |
$[173726604657/1343,14833498275/1343,1520615673/1343]$ |
$y^2 + (x^3 + x + 1)y = -3x^4 + x^3 + 2x^2 + x$ |
| 1468.a.2936.1 |
1468.a |
\( 2^{2} \cdot 367 \) |
\( - 2^{3} \cdot 367 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.003870\) |
\(22.107029\) |
\(0.256637\) |
$[220,-719,27031,375808]$ |
$[55,156,-448,-12244,2936]$ |
$[503284375/2936,6488625/734,-169400/367]$ |
$y^2 + (x^3 + x + 1)y = -x^5 - x^2$ |
| 1544.a.3088.1 |
1544.a |
\( 2^{3} \cdot 193 \) |
\( - 2^{4} \cdot 193 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.005918\) |
\(20.256903\) |
\(0.239772\) |
$[40,109,589,386]$ |
$[40,-6,432,4311,3088]$ |
$[6400000/193,-24000/193,43200/193]$ |
$y^2 + (x^3 + x^2 + x + 1)y = x^2$ |
| 1549.a.1549.1 |
1549.a |
\( 1549 \) |
\( 1549 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.011914\) |
\(22.603960\) |
\(0.269299\) |
$[772,673,79825,198272]$ |
$[193,1524,17036,241343,1549]$ |
$[267785184193/1549,10956122868/1549,634573964/1549]$ |
$y^2 + (x^3 + x + 1)y = -x^5 + x^3 - 3x$ |
| 1568.b.12544.1 |
1568.b |
\( 2^{5} \cdot 7^{2} \) |
\( - 2^{8} \cdot 7^{2} \) |
$1$ |
$2$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$8$ |
$0$ |
2.180.4, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.119960\) |
\(20.050461\) |
\(0.267250\) |
$[116,445,16259,1568]$ |
$[116,264,-1280,-54544,12544]$ |
$[82044596/49,1609674/49,-67280/49]$ |
$y^2 + (x^3 + x)y = -x^4 + 1$ |
| 1575.a.23625.1 |
1575.a |
\( 3^{2} \cdot 5^{2} \cdot 7 \) |
\( 3^{3} \cdot 5^{3} \cdot 7 \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$2$ |
2.180.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.054364\) |
\(17.779771\) |
\(0.241646\) |
$[5748,48105,93031605,3024000]$ |
$[1437,84036,6376864,525376068,23625]$ |
$[226944716565591/875,9235744556604/875,1463114053024/2625]$ |
$y^2 + (x^3 + 1)y = x^5 - x^4 - 6x^3 + 2x^2 + 7x - 4$ |
| 1612.a.3224.1 |
1612.a |
\( 2^{2} \cdot 13 \cdot 31 \) |
\( 2^{3} \cdot 13 \cdot 31 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.004500\) |
\(20.032411\) |
\(0.270409\) |
$[156,609,32271,-412672]$ |
$[39,38,-36,-712,-3224]$ |
$[-6940323/248,-86697/124,1053/62]$ |
$y^2 + (x^3 + x + 1)y = x^3 + 2x^2 + x$ |
| 1721.a.1721.1 |
1721.a |
\( 1721 \) |
\( -1721 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.009817\) |
\(25.739030\) |
\(0.252677\) |
$[108,2937,92403,220288]$ |
$[27,-92,-320,-4276,1721]$ |
$[14348907/1721,-1810836/1721,-233280/1721]$ |
$y^2 + (x^3 + 1)y = x^2 - x$ |
| 1844.a.3688.1 |
1844.a |
\( 2^{2} \cdot 461 \) |
\( 2^{3} \cdot 461 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.003840\) |
\(26.051771\) |
\(0.300117\) |
$[92,5569,279551,-472064]$ |
$[23,-210,-2372,-24664,-3688]$ |
$[-6436343/3688,1277535/1844,313697/922]$ |
$y^2 + (x^3 + x^2 + 1)y = x^4 + x^3 - x^2 - x$ |
| 1863.b.1863.1 |
1863.b |
\( 3^{4} \cdot 23 \) |
\( - 3^{4} \cdot 23 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
2.40.2, 3.80.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.017029\) |
\(17.775845\) |
\(0.302697\) |
$[516,-3591,-633123,-238464]$ |
$[129,843,8401,93270,-1863]$ |
$[-441025329/23,-22341467/23,-15533449/207]$ |
$y^2 + (x^3 + x + 1)y = -x^6 + x^4 - x^2 - x$ |
| 1900.a.3800.1 |
1900.a |
\( 2^{2} \cdot 5^{2} \cdot 19 \) |
\( - 2^{3} \cdot 5^{2} \cdot 19 \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
3.960.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.036896\) |
\(24.860296\) |
\(0.305748\) |
$[28,4465,38775,486400]$ |
$[7,-184,-176,-8772,3800]$ |
$[16807/3800,-7889/475,-1078/475]$ |
$y^2 + (x^3 + x + 1)y = x^3 - x$ |
| 1915.a.1915.1 |
1915.a |
\( 5 \cdot 383 \) |
\( 5 \cdot 383 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.011348\) |
\(27.602892\) |
\(0.313229\) |
$[540,5361,1155735,-245120]$ |
$[135,536,-1980,-138649,-1915]$ |
$[-8968066875/383,-263752200/383,7217100/383]$ |
$y^2 + (x^3 + x + 1)y = x^6 - 2x^4 - x$ |
| 1929.a.52083.1 |
1929.a |
\( 3 \cdot 643 \) |
\( - 3^{4} \cdot 643 \) |
$1$ |
$2$ |
$\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.079463\) |
\(14.021063\) |
\(0.278540\) |
$[8980,-117815,-379558107,-6666624]$ |
$[2245,214910,28402156,4394133030,-52083]$ |
$[-57027157741403125/52083,-2431675729823750/52083,-143147576293900/52083]$ |
$y^2 + (x^2 + x + 1)y = 9x^5 + 6x^3 + 7x^2 + 2x$ |
| 2036.a.8144.1 |
2036.a |
\( 2^{2} \cdot 509 \) |
\( - 2^{4} \cdot 509 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.004448\) |
\(24.450682\) |
\(0.326289\) |
$[376,4096,563684,32576]$ |
$[188,790,-11600,-701225,8144]$ |
$[14678080448/509,328080680/509,-25624400/509]$ |
$y^2 + (x + 1)y = x^6 - 2x^5 + x^3$ |
| 2054.a.4108.1 |
2054.a |
\( 2 \cdot 13 \cdot 79 \) |
\( - 2^{2} \cdot 13 \cdot 79 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.025629\) |
\(25.585662\) |
\(0.327866\) |
$[328,2488,259883,-16432]$ |
$[164,706,225,-115384,-4108]$ |
$[-29659187456/1027,-778531616/1027,-1512900/1027]$ |
$y^2 + (x + 1)y = x^5 + 2x^4 - x^3 - 2x^2$ |
| 2060.a.4120.1 |
2060.a |
\( 2^{2} \cdot 5 \cdot 103 \) |
\( 2^{3} \cdot 5 \cdot 103 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.004115\) |
\(25.814688\) |
\(0.318682\) |
$[196,3841,146497,527360]$ |
$[49,-60,416,4196,4120]$ |
$[282475249/4120,-352947/206,124852/515]$ |
$y^2 + (x^3 + x + 1)y = -x^5 + x^4 - x^2 - x$ |
| 2094.a.12564.1 |
2094.a |
\( 2 \cdot 3 \cdot 349 \) |
\( 2^{2} \cdot 3^{2} \cdot 349 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.014693\) |
\(22.539432\) |
\(0.331172\) |
$[392,2200,166747,50256]$ |
$[196,1234,18865,543696,12564]$ |
$[72313663744/3141,2322861856/3141,181179460/3141]$ |
$y^2 + (x + 1)y = x^5 - 2x^4 - x^3 + 2x^2$ |
| 2156.b.34496.1 |
2156.b |
\( 2^{2} \cdot 7^{2} \cdot 11 \) |
\( 2^{6} \cdot 7^{2} \cdot 11 \) |
$1$ |
$2$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$8$ |
$2$ |
2.90.3, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.123039\) |
\(21.055838\) |
\(0.287853\) |
$[2916,41745,37024569,4415488]$ |
$[729,20404,734800,29836496,34496]$ |
$[205891132094649/34496,1976231914389/8624,2218766175/196]$ |
$y^2 + (x^2 + x)y = 2x^5 - x^4 - 5x^3 + 3x + 1$ |
| 2165.a.270625.1 |
2165.a |
\( 5 \cdot 433 \) |
\( - 5^{4} \cdot 433 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.015455\) |
\(18.315548\) |
\(0.283063\) |
$[468,451353,-38126979,-34640000]$ |
$[117,-18236,1144456,-49662586,-270625]$ |
$[-21924480357/270625,29207014668/270625,-15666458184/270625]$ |
$y^2 + (x^2 + x + 1)y = x^5 + 6x^4 - 4x^3 + x$ |
| 2172.a.4344.1 |
2172.a |
\( 2^{2} \cdot 3 \cdot 181 \) |
\( 2^{3} \cdot 3 \cdot 181 \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
3.80.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.050582\) |
\(19.546677\) |
\(0.329567\) |
$[124,577,37151,-556032]$ |
$[31,16,-240,-1924,-4344]$ |
$[-28629151/4344,-59582/543,9610/181]$ |
$y^2 + (x^3 + x + 1)y = -x^4 + x^3 - 2x^2$ |
| 2225.a.11125.1 |
2225.a |
\( 5^{2} \cdot 89 \) |
\( 5^{3} \cdot 89 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
2.90.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.020059\) |
\(19.135597\) |
\(0.287882\) |
$[1428,14169,6902493,1424000]$ |
$[357,4720,68000,499400,11125]$ |
$[5798839393557/11125,42951332592/2225,69332256/89]$ |
$y^2 + (x^3 + 1)y = -3x^4 + 4x^2 + 2x$ |
| 2238.a.13428.1 |
2238.a |
\( 2 \cdot 3 \cdot 373 \) |
\( 2^{2} \cdot 3^{2} \cdot 373 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.020178\) |
\(17.090804\) |
\(0.344854\) |
$[0,1128,5193,-53712]$ |
$[0,-188,577,-8836,13428]$ |
$[0,-14678080448/11269449,-27119/3357]$ |
$y^2 + (x + 1)y = -x^5 - x^4 + x^2$ |
| 2251.a.2251.2 |
2251.a |
\( 2251 \) |
\( -2251 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.054433\) |
\(25.327768\) |
\(0.344667\) |
$[304,1612,166103,-9004]$ |
$[152,694,1017,-81763,-2251]$ |
$[-81136812032/2251,-2437194752/2251,-23496768/2251]$ |
$y^2 + xy = x^5 + x^4 - 2x^3 - x^2 + x$ |
| 2326.a.4652.1 |
2326.a |
\( 2 \cdot 1163 \) |
\( - 2^{2} \cdot 1163 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.037209\) |
\(18.916572\) |
\(0.351931\) |
$[32,-968,2137,18608]$ |
$[16,172,-945,-11176,4652]$ |
$[262144/1163,176128/1163,-60480/1163]$ |
$y^2 + (x + 1)y = -x^5 + x^4 - x^2$ |
| 2348.b.37568.1 |
2348.b |
\( 2^{2} \cdot 587 \) |
\( 2^{6} \cdot 587 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.007204\) |
\(16.450123\) |
\(0.355517\) |
$[4,-15839,-1111055,4808704]$ |
$[1,660,15248,-105088,37568]$ |
$[1/37568,165/9392,953/2348]$ |
$y^2 + (x^3 + x + 1)y = x^5 - 4x^4 + 2x^3 - x^2$ |
| 2390.a.4780.1 |
2390.a |
\( 2 \cdot 5 \cdot 239 \) |
\( - 2^{2} \cdot 5 \cdot 239 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.026165\) |
\(27.152397\) |
\(0.355215\) |
$[224,1984,112487,-19120]$ |
$[112,192,1041,19932,-4780]$ |
$[-4405854208/1195,-67436544/1195,-3264576/1195]$ |
$y^2 + (x + 1)y = x^5 + x^4 - 2x^3 - x^2$ |
| 2457.a.95823.1 |
2457.a |
\( 3^{3} \cdot 7 \cdot 13 \) |
\( - 3^{4} \cdot 7 \cdot 13^{2} \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$2$ |
2.180.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.066494\) |
\(18.983107\) |
\(0.315567\) |
$[1932,57897,45198315,12265344]$ |
$[483,7308,-43264,-18575844,95823]$ |
$[46360978629/169,1452301788/169,-947968/9]$ |
$y^2 + (x^3 + 1)y = x^5 - x^4 - 3x^3 + 6x^2 - 6x + 2$ |
| 2493.a.7479.1 |
2493.a |
\( 3^{2} \cdot 277 \) |
\( 3^{3} \cdot 277 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.030434\) |
\(14.572014\) |
\(0.332614\) |
$[76,6265,-26669,-957312]$ |
$[19,-246,1764,-6750,-7479]$ |
$[-2476099/7479,562438/2493,-70756/831]$ |
$y^2 + (x^3 + 1)y = -x^4 + 2x^3 - 2x^2 + x$ |
| 2564.a.5128.1 |
2564.a |
\( 2^{2} \cdot 641 \) |
\( 2^{3} \cdot 641 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.005567\) |
\(22.252329\) |
\(0.371645\) |
$[4,481,-147055,656384]$ |
$[1,-20,2048,412,5128]$ |
$[1/5128,-5/1282,256/641]$ |
$y^2 + (x^3 + x + 1)y = -2x^2$ |
| 2690.a.26900.1 |
2690.a |
\( 2 \cdot 5 \cdot 269 \) |
\( 2^{2} \cdot 5^{2} \cdot 269 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.019137\) |
\(19.757537\) |
\(0.378103\) |
$[72,768,-48429,107600]$ |
$[36,-74,6769,59552,26900]$ |
$[15116544/6725,-863136/6725,2193156/6725]$ |
$y^2 + (x^3 + x)y = -2x^4 + 3x^2 - 3x + 1$ |
| 2768.a.354304.1 |
2768.a |
\( 2^{4} \cdot 173 \) |
\( 2^{11} \cdot 173 \) |
$1$ |
$1$ |
$\Z/9\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
3.80.1 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(0.305902\) |
\(13.034562\) |
\(0.443033\) |
$[76,889,21843,-44288]$ |
$[76,-352,-5888,-142848,-354304]$ |
$[-2476099/346,75449/173,16606/173]$ |
$y^2 + y = x^6 - 4x^4 - 5x^3 - 2x^2$ |
| 2780.a.5560.1 |
2780.a |
\( 2^{2} \cdot 5 \cdot 139 \) |
\( - 2^{3} \cdot 5 \cdot 139 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.005108\) |
\(25.346337\) |
\(0.388423\) |
$[68,7057,98201,-711680]$ |
$[17,-282,36,-19728,-5560]$ |
$[-1419857/5560,692733/2780,-2601/1390]$ |
$y^2 + (x^3 + x + 1)y = -x^5 + x^3 + x^2 - 7x + 4$ |
| 2836.a.5672.1 |
2836.a |
\( 2^{2} \cdot 709 \) |
\( 2^{3} \cdot 709 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.006682\) |
\(19.554837\) |
\(0.391973\) |
$[28,3505,44695,-726016]$ |
$[7,-144,-336,-5772,-5672]$ |
$[-16807/5672,6174/709,2058/709]$ |
$y^2 + (x^3 + x + 1)y = x^5 + x^2$ |
| 2837.a.2837.2 |
2837.a |
\( 2837 \) |
\( 2837 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.061446\) |
\(25.246160\) |
\(0.387816\) |
$[336,2028,224535,11348]$ |
$[168,838,1801,-99919,2837]$ |
$[133827821568/2837,3973487616/2837,50831424/2837]$ |
$y^2 + xy = x^5 - x^4 - 2x^3 + x^2 + x$ |
| 2859.a.77193.1 |
2859.a |
\( 3 \cdot 953 \) |
\( - 3^{4} \cdot 953 \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
2.10.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.115762\) |
\(14.608476\) |
\(0.375801\) |
$[988,69913,17187731,9880704]$ |
$[247,-371,-3969,-279496,77193]$ |
$[919358226007/77193,-5590681733/77193,-2989441/953]$ |
$y^2 + (x^3 + x + 1)y = 2x^5 + 4x^4 + x^3 + 2x^2$ |
| 2873.a.48841.1 |
2873.a |
\( 13^{2} \cdot 17 \) |
\( - 13^{2} \cdot 17^{2} \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
2.40.3, 3.40.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.011773\) |
\(16.836345\) |
\(0.396427\) |
$[828,36777,8302203,6251648]$ |
$[207,253,-6665,-360916,48841]$ |
$[380059617807/48841,2244044979/48841,-285588585/48841]$ |
$y^2 + (x^3 + x + 1)y = 2x^4 + 2x^2 + x$ |
| 2900.a.290000.1 |
2900.a |
\( 2^{2} \cdot 5^{2} \cdot 29 \) |
\( 2^{4} \cdot 5^{4} \cdot 29 \) |
$1$ |
$2$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$8$ |
$2$ |
2.90.3, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(0.146114\) |
\(8.037577\) |
\(0.391469\) |
$[10824,6384,22368156,1160000]$ |
$[5412,1219342,366049600,123566380559,290000]$ |
$[290180989287807552/18125,12080333233372536/18125,924267161664/25]$ |
$y^2 + (x^3 + x)y = -4x^4 + 17x^2 - 29$ |
| 2907.a.8721.1 |
2907.a |
\( 3^{2} \cdot 17 \cdot 19 \) |
\( 3^{3} \cdot 17 \cdot 19 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.004462\) |
\(20.693505\) |
\(0.276976\) |
$[4,-791,-252731,1116288]$ |
$[1,33,3501,603,8721]$ |
$[1/8721,11/2907,389/969]$ |
$y^2 + (x^3 + x + 1)y = -x^4 + 2x^3 - 3x^2$ |
| 2966.a.5932.1 |
2966.a |
\( 2 \cdot 1483 \) |
\( - 2^{2} \cdot 1483 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.034715\) |
\(22.798908\) |
\(0.395734\) |
$[416,1600,217415,-23728]$ |
$[208,1536,12081,38388,-5932]$ |
$[-97332232192/1483,-3455582208/1483,-130668096/1483]$ |
$y^2 + (x + 1)y = x^5 - x^4 - 2x^3 + x^2 + x$ |
| 3016.a.6032.1 |
3016.a |
\( 2^{3} \cdot 13 \cdot 29 \) |
\( - 2^{4} \cdot 13 \cdot 29 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$0$ |
2.10.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.006821\) |
\(24.436732\) |
\(0.333347\) |
$[56,469,9745,754]$ |
$[56,-182,-3392,-55769,6032]$ |
$[34420736/377,-153664/29,-664832/377]$ |
$y^2 + x^3y = -x^4 + 2x^2 - 2x + 1$ |
| 3021.a.172197.1 |
3021.a |
\( 3 \cdot 19 \cdot 53 \) |
\( - 3^{2} \cdot 19^{2} \cdot 53 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.026053\) |
\(13.989211\) |
\(0.364467\) |
$[556,-83543,-3468021,22041216]$ |
$[139,4286,-80020,-7373144,172197]$ |
$[51888844699/172197,11510563034/172197,-1546066420/172197]$ |
$y^2 + (x^3 + 1)y = -x^5 + x^4 - 4x^2 + 2$ |
