| 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 |
| 295.a.295.2 |
295.a |
\( 5 \cdot 59 \) |
\( - 5 \cdot 59 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,7$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.597073\) |
\(0.149268\) |
$[198804,305807001,18482629056189,-37760]$ |
$[49701,90182600,203402032096,494095763610824,-295]$ |
$[-303267334973269931148501/295,-2214359494206283568520/59,-502441543825401014496/295]$ |
$y^2 + (x^2 + x + 1)y = x^5 - 40x^3 + 22x^2 + 389x - 608$ |
| 336.a.172032.1 |
336.a |
\( 2^{4} \cdot 3 \cdot 7 \) |
\( - 2^{13} \cdot 3 \cdot 7 \) |
$0$ |
$2$ |
$\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.720.5 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(0.356066\) |
\(0.178033\) |
$[16916,151117825,232872423961,-21504]$ |
$[16916,-88822256,277597802496,-798387183476800,-172032]$ |
$[-1352659309173012149/168,419870026410625699/168,-461744933079368]$ |
$y^2 + (x^3 + x)y = -x^6 + 15x^4 - 75x^2 - 56$ |
| 523.a.523.2 |
523.a |
\( 523 \) |
\( -523 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.992796\) |
\(0.248199\) |
$[332400,10084860,1107044456391,-2092]$ |
$[166200,1149254190,10581558955401,109467476288772525,-523]$ |
$[-126810465636208320000000000/523,-5276053055713522320000000/523,-292288477352026798440000/523]$ |
$y^2 + xy = x^5 - 31x^4 - 110x^3 + 21x^2 - x$ |
| 644.a.659456.1 |
644.a |
\( 2^{2} \cdot 7 \cdot 23 \) |
\( 2^{12} \cdot 7 \cdot 23 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.90.3, 3.720.5 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(0.872985\) |
\(0.218246\) |
$[161796,1070662305,46065265919409,84410368]$ |
$[40449,23560804,14638854160,9253881697856,659456]$ |
$[108277681088425330677249/659456,389810454818831018649/164864,9297727292338785/256]$ |
$y^2 + (x^2 + x)y = -3x^6 - 13x^5 + 4x^4 + 51x^3 + 4x^2 - 13x - 3$ |
| 708.a.181248.1 |
708.a |
\( 2^{2} \cdot 3 \cdot 59 \) |
\( - 2^{10} \cdot 3 \cdot 59 \) |
$0$ |
$3$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,5$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.15.1 |
✓ |
✓ |
$4$ |
\( 1 \) |
\(1.000000\) |
\(0.325344\) |
\(0.325344\) |
$[234100,3468879025,202585466081177,-23199744]$ |
$[58525,-1820975,60952909,62829762150,-181248]$ |
$[-686605237334059580078125/181248,365029741228054296875/181248,-208774418179643125/181248]$ |
$y^2 + (x^3 + 1)y = -x^6 - 4x^5 + 9x^4 + 48x^3 - 41x^2 - 98x - 36$ |
| 784.b.25088.1 |
784.b |
\( 2^{4} \cdot 7^{2} \) |
\( - 2^{9} \cdot 7^{2} \) |
$0$ |
$2$ |
$\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.45.1, 3.720.5 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(0.626117\) |
\(0.313058\) |
$[2740,15382525,36170522453,3136]$ |
$[2740,-9942200,-24298750736,-41356479464160,25088]$ |
$[301635777856250/49,-399451653071875/49,-712598832131225/98]$ |
$y^2 + (x^2 + 1)y = -x^6 - 3x^5 + 7x^4 + 2x^3 - 49x^2 + 41x - 9$ |
| 810.a.196830.1 |
810.a |
\( 2 \cdot 3^{4} \cdot 5 \) |
\( - 2 \cdot 3^{9} \cdot 5 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1, 3.640.4 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(0.328982\) |
\(0.328982\) |
$[103200,92148840,2874875039973,-3240]$ |
$[154800,860236740,5905731060081,43549979813677800,-196830]$ |
$[-451609936896000000000,-16212110811776000000,-2156977131869584000/3]$ |
$y^2 + (x + 1)y = x^5 + 15x^4 + 20x^3 - 297x^2 + 94x - 8$ |
| 880.a.225280.1 |
880.a |
\( 2^{4} \cdot 5 \cdot 11 \) |
\( - 2^{12} \cdot 5 \cdot 11 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1, 3.640.4 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(1.515082\) |
\(0.378770\) |
$[2342,111952,73574536,-880]$ |
$[4684,615622,103120196,26006137795,-225280]$ |
$[-2201833501574851/220,-494259267301121/1760,-35350660170809/3520]$ |
$y^2 = x^5 + 13x^4 + 55x^3 + 76x^2 - 44$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.008698\) |
\(21.575863\) |
\(0.187677\) |
$[300,2601,306603,-815616]$ |
$[75,126,-1024,-23169,-6372]$ |
$[-87890625/236,-984375/118,160000/177]$ |
$y^2 + (x^3 + 1)y = x^5 - x^4 + x^2 - x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.035633\) |
\(21.235034\) |
\(0.189165\) |
$[155924,161593,8379938029,137856]$ |
$[38981,63306532,137068427976,333836849266358,1077]$ |
$[90004636142290020118901/1077,3749794358746968581012/1077,69425997674312689112/359]$ |
$y^2 + (x^3 + 1)y = 5x^5 + 34x^4 + 80x^3 - x^2 - 90x + 32$ |
| 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 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(0.712625\) |
\(0.356313\) |
$[14220,9418737,54280328031,17664]$ |
$[14220,2146192,-16790479872,-60841690970176,141312]$ |
$[189267815942240625/46,2008843709918625/46,-24026098775400]$ |
$y^2 + (x^3 + x)y = -x^6 - 3x^4 + 29x^2 - 46$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.026504\) |
\(7.396287\) |
\(0.196028\) |
$[5004,191097,289856403,18320000]$ |
$[1251,57246,3273124,204393402,143125]$ |
$[3063984390631251/143125,112077149104746/143125,5122442333124/143125]$ |
$y^2 + (x^3 + x^2 + x)y = 2x^4 + 4x^3 + 9x^2 + 10x + 9$ |
| 1216.a.19456.1 |
1216.a |
\( 2^{6} \cdot 19 \) |
\( - 2^{10} \cdot 19 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1, 3.80.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(1.625809\) |
\(0.406452\) |
$[3996,347595,394636194,-2432]$ |
$[3996,433604,54136720,7079476076,-19456]$ |
$[-995009990004999/19,-108076122094599/76,-3376781293545/76]$ |
$y^2 + x^2y = 4x^5 + 3x^4 - 11x^3 - 6x^2 + 6x - 1$ |
| 1270.a.325120.1 |
1270.a |
\( 2 \cdot 5 \cdot 127 \) |
\( 2^{9} \cdot 5 \cdot 127 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1, 3.80.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(1.894604\) |
\(0.473651\) |
$[239204,126763297,10436094933809,41615360]$ |
$[59801,143724846,437833820176,1381517230655315,325120]$ |
$[764790054928595680699001/325120,15368348330455841308623/162560,97860226229056869361/20320]$ |
$y^2 + (x^2 + x)y = x^5 + 17x^4 + 76x^3 + 14x^2 - 32x + 3$ |
| 1309.a.9163.2 |
1309.a |
\( 7 \cdot 11 \cdot 17 \) |
\( - 7^{2} \cdot 11 \cdot 17 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(0.846601\) |
\(0.423301\) |
$[1740928,18364336,10627907866359,-36652]$ |
$[870464,31568088248,1526311891463681,83013839664381477120,-9163]$ |
$[-10199009421268235327400574976/187,-424917527486779411910361088/187,-23602001682171372468506624/187]$ |
$y^2 + x^2y = -x^6 + 20x^5 - 128x^4 + 248x^3 + 32x^2 + x$ |
| 1312.a.2624.1 |
1312.a |
\( 2^{5} \cdot 41 \) |
\( - 2^{6} \cdot 41 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
2.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.028941\) |
\(16.518821\) |
\(0.239039\) |
$[112,91,1912,328]$ |
$[112,462,3440,42959,2624]$ |
$[275365888/41,10141824/41,674240/41]$ |
$y^2 + (x + 1)y = x^6 + 2x^5 + 3x^4 + 2x^3 + x^2$ |
| 1328.a.1328.1 |
1328.a |
\( 2^{4} \cdot 83 \) |
\( - 2^{4} \cdot 83 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(2.234905\) |
\(0.558726\) |
$[424,348664,-49372844,-5312]$ |
$[212,-56238,8930000,-317388161,-1328]$ |
$[-26764511552/83,33490178904/83,-25084370000/83]$ |
$y^2 + x^2y = x^5 - 3x^4 - 9x^3 - 5x^2 - 4x - 5$ |
| 1338.a.2676.1 |
1338.a |
\( 2 \cdot 3 \cdot 223 \) |
\( - 2^{2} \cdot 3 \cdot 223 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.029284\) |
\(15.069119\) |
\(0.220645\) |
$[716,985,119011,342528]$ |
$[179,1294,13664,192855,2676]$ |
$[183765996899/2676,3710764333/1338,109452056/669]$ |
$y^2 + (x^3 + x^2 + x)y = x^4 + x^3 + 2x^2 + x + 1$ |
| 1415.a.1415.1 |
1415.a |
\( 5 \cdot 283 \) |
\( - 5 \cdot 283 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.034409\) |
\(26.497058\) |
\(0.227936\) |
$[212,697,-48083,-181120]$ |
$[53,88,1440,17144,-1415]$ |
$[-418195493/1415,-13101176/1415,-808992/283]$ |
$y^2 + (x^2 + x + 1)y = x^5 - 3x^4 + x^3 - x$ |
| 1445.a.122825.1 |
1445.a |
\( 5 \cdot 17^{2} \) |
\( - 5^{2} \cdot 17^{3} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.90.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.034949\) |
\(6.593927\) |
\(0.230449\) |
$[20108,89641,589975531,15721600]$ |
$[5027,1049212,291086176,90611096452,122825]$ |
$[3210291184050373907/122825,133287648084859796/122825,7355959869342304/122825]$ |
$y^2 + (x^3 + x^2 + x)y = 3x^4 + 4x^3 + 18x^2 + 10x + 29$ |
| 1490.a.1490.1 |
1490.a |
\( 2 \cdot 5 \cdot 149 \) |
\( - 2 \cdot 5 \cdot 149 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.038412\) |
\(24.373454\) |
\(0.234059\) |
$[1108,2617,932621,-190720]$ |
$[277,3088,44636,707107,-1490]$ |
$[-1630793025157/1490,-32816072552/745,-1712437822/745]$ |
$y^2 + (x^3 + 1)y = x^5 - 4x^3 - 2x^2 + 2x$ |
| 1595.a.231275.1 |
1595.a |
\( 5 \cdot 11 \cdot 29 \) |
\( 5^{2} \cdot 11 \cdot 29^{2} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.027213\) |
\(10.105207\) |
\(0.274996\) |
$[432,22212,2142441,-925100]$ |
$[216,-1758,7399,-373095,-231275]$ |
$[-470184984576/231275,17716589568/231275,-345207744/231275]$ |
$y^2 + (x^3 + x)y = x^4 - x^3 + 2x^2 - 4x + 1$ |
| 1655.a.1655.1 |
1655.a |
\( 5 \cdot 331 \) |
\( - 5 \cdot 331 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.036902\) |
\(26.848074\) |
\(0.247686\) |
$[76,1417,134171,211840]$ |
$[19,-44,-1536,-7780,1655]$ |
$[2476099/1655,-301796/1655,-554496/1655]$ |
$y^2 + (x^3 + x^2 + x)y = x^3 - x$ |
| 1655.a.206875.1 |
1655.a |
\( 5 \cdot 331 \) |
\( - 5^{4} \cdot 331 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.036902\) |
\(6.712019\) |
\(0.247686\) |
$[11444,-79223,-306097691,-26480000]$ |
$[2861,344356,55836816,10292018960,-206875]$ |
$[-191685511916770301/206875,-8064198843467636/206875,-457042262577936/206875]$ |
$y^2 + (x^3 + 1)y = x^5 - x^4 - 7x^3 + 2x^2 + 14x - 10$ |
| 1664.a.3328.1 |
1664.a |
\( 2^{7} \cdot 13 \) |
\( - 2^{8} \cdot 13 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.020704\) |
\(27.242879\) |
\(0.282012\) |
$[276,810,65178,-416]$ |
$[276,2634,32132,482619,-3328]$ |
$[-6256125396/13,-432646353/26,-38245113/52]$ |
$y^2 + xy = x^6 - 2x^5 - x^4 + 3x^3 - x$ |
| 1689.a.1689.1 |
1689.a |
\( 3 \cdot 563 \) |
\( 3 \cdot 563 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.055530\) |
\(18.027326\) |
\(0.250263\) |
$[44,601,-24221,-216192]$ |
$[11,-20,416,1044,-1689]$ |
$[-161051/1689,26620/1689,-50336/1689]$ |
$y^2 + (x^2 + x + 1)y = x^5 + 2x^4 + 2x^3 + x^2$ |
| 1689.a.45603.1 |
1689.a |
\( 3 \cdot 563 \) |
\( - 3^{4} \cdot 563 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.055530\) |
\(9.013663\) |
\(0.250263\) |
$[34900,-37799,-434488675,-5837184]$ |
$[8725,3173476,1539708400,840751466856,-45603]$ |
$[-50562341569814453125/45603,-2107810313223812500/45603,-117211264267750000/45603]$ |
$y^2 + (x^2 + x + 1)y = x^5 - 6x^4 + 21x^3 + 15x^2 + 3x$ |
| 1696.a.217088.1 |
1696.a |
\( 2^{5} \cdot 53 \) |
\( - 2^{12} \cdot 53 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(1.270310\) |
\(0.635155\) |
$[3746,232693,328269020,848]$ |
$[7492,1718238,-69556676,-868365110309,217088]$ |
$[23050953088040593/212,5645035221351423/1696,-61003448054801/3392]$ |
$y^2 + (x^2 + 1)y = x^5 - 24x^4 - 28x^3 - 22x^2 - 7x - 1$ |
| 1702.a.39146.1 |
1702.a |
\( 2 \cdot 23 \cdot 37 \) |
\( 2 \cdot 23^{2} \cdot 37 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.036855\) |
\(15.535887\) |
\(0.286284\) |
$[7656,14184,36303939,156584]$ |
$[3828,608202,128326985,30331506444,39146]$ |
$[410988481022237184/19573,17058217029682752/19573,940225127082120/19573]$ |
$y^2 + (x + 1)y = x^5 - 13x^3 + 14x^2 + 22x - 30$ |
| 1738.a.137302.1 |
1738.a |
\( 2 \cdot 11 \cdot 79 \) |
\( - 2 \cdot 11 \cdot 79^{2} \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(0.974167\) |
\(0.487083\) |
$[15560,2578060,42581573889,549208]$ |
$[7780,2092340,-2712635321,-6370547368245,137302]$ |
$[14251743233518400000/68651,492652910653840000/68651,-7463248898346200/6241]$ |
$y^2 + xy = x^5 - 5x^3 - 66x^2 - 101x - 41$ |
| 1888.a.483328.2 |
1888.a |
\( 2^{5} \cdot 59 \) |
\( - 2^{13} \cdot 59 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(2.440736\) |
\(0.610184\) |
$[5152,10096,15976476,-1888]$ |
$[10304,4396928,2495856896,1596083404800,-483328]$ |
$[-14178794445340672/59,-587187714584576/59,-32347553300608/59]$ |
$y^2 = x^5 + 8x^4 + 8x^3 - 31x^2 + 20x - 4$ |
| 1899.a.5697.1 |
1899.a |
\( 3^{2} \cdot 211 \) |
\( 3^{3} \cdot 211 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.027932\) |
\(19.045771\) |
\(0.265996\) |
$[108,-2727,-18909,-729216]$ |
$[27,144,-544,-8856,-5697]$ |
$[-531441/211,-104976/211,14688/211]$ |
$y^2 + (x^3 + 1)y = -x^5 + x^4 - 3x + 2$ |
| 1929.a.1929.1 |
1929.a |
\( 3 \cdot 643 \) |
\( 3 \cdot 643 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.079463\) |
\(14.021063\) |
\(0.278540\) |
$[244,2665,300021,246912]$ |
$[61,44,-1760,-27324,1929]$ |
$[844596301/1929,9987164/1929,-6548960/1929]$ |
$y^2 + (x^2 + x + 1)y = x^5 - x^4 + x^3 - x^2$ |
| 1935.a.52245.2 |
1935.a |
\( 3^{2} \cdot 5 \cdot 43 \) |
\( - 3^{5} \cdot 5 \cdot 43 \) |
$0$ |
$3$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1 |
✓ |
✓ |
$4$ |
\( 2 \) |
\(1.000000\) |
\(0.234547\) |
\(0.469095\) |
$[307168,3207396712,267640995335223,-208980]$ |
$[153584,448269092,1453877009505,5586766946327864,-52245]$ |
$[-85453503231099874048999424/52245,-1623965199773111994400768/52245,-762091475690810672384/1161]$ |
$y^2 + xy = x^5 - 2x^4 - 82x^3 - 20x^2 + 927x - 1134$ |
| 1985.a.1985.1 |
1985.a |
\( 5 \cdot 397 \) |
\( - 5 \cdot 397 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.041851\) |
\(25.967882\) |
\(0.271696\) |
$[428,1705,359371,254080]$ |
$[107,406,-44,-42386,1985]$ |
$[14025517307/1985,497367458/1985,-503756/1985]$ |
$y^2 + (x^3 + 1)y = x^5 + x^4 - x$ |
| 2007.a.6021.1 |
2007.a |
\( 3^{2} \cdot 223 \) |
\( - 3^{3} \cdot 223 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.037139\) |
\(15.293007\) |
\(0.283981\) |
$[588,6777,1216467,770688]$ |
$[147,618,1988,-22422,6021]$ |
$[2542277241/223,72707082/223,4773188/669]$ |
$y^2 + (x^2 + x + 1)y = x^6 + x^4$ |
| 2020.a.646400.1 |
2020.a |
\( 2^{2} \cdot 5 \cdot 101 \) |
\( - 2^{8} \cdot 5^{2} \cdot 101 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(0.023673\) |
\(7.797718\) |
\(0.276890\) |
$[394,1648,195485,2525]$ |
$[788,21478,704476,23455651,646400]$ |
$[1186837123028/2525,82103660647/5050,6835002271/10100]$ |
$y^2 + x^3y = 2x^4 - x^3 + 5x^2 - 4x + 4$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.025629\) |
\(25.585662\) |
\(0.327866\) |
$[328,2488,259883,-16432]$ |
$[164,706,225,-115384,-4108]$ |
$[-29659187456/1027,-778531616/1027,-1512900/1027]$ |
$y^2 + (x + 1)y = x^5 + 2x^4 - x^3 - 2x^2$ |
| 2056.a.4112.1 |
2056.a |
\( 2^{3} \cdot 257 \) |
\( 2^{4} \cdot 257 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.039062\) |
\(16.785274\) |
\(0.327836\) |
$[16,52,-3812,-16448]$ |
$[8,-6,444,879,-4112]$ |
$[-2048/257,192/257,-1776/257]$ |
$y^2 + (x^3 + x)y = x^3 + x^2 + x$ |
| 2061.a.6183.1 |
2061.a |
\( 3^{2} \cdot 229 \) |
\( - 3^{3} \cdot 229 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.033357\) |
\(17.335371\) |
\(0.289124\) |
$[108,-4455,-78525,791424]$ |
$[27,216,-256,-13392,6183]$ |
$[531441/229,157464/229,-6912/229]$ |
$y^2 + (x^3 + 1)y = -x^4 - x$ |
| 2075.a.10375.1 |
2075.a |
\( 5^{2} \cdot 83 \) |
\( - 5^{3} \cdot 83 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.037752\) |
\(15.293009\) |
\(0.288670\) |
$[148,-6215,-372115,-1328000]$ |
$[37,316,2624,-692,-10375]$ |
$[-69343957/10375,-16006348/10375,-3592256/10375]$ |
$y^2 + (x^3 + 1)y = -2x^4 + x^2 - x$ |
| 2085.a.6255.1 |
2085.a |
\( 3 \cdot 5 \cdot 139 \) |
\( - 3^{2} \cdot 5 \cdot 139 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.028935\) |
\(20.000293\) |
\(0.289359\) |
$[564,-2967,-773067,-800640]$ |
$[141,952,12384,209960,-6255]$ |
$[-6192315189/695,-296518488/695,-27356256/695]$ |
$y^2 + (x^2 + x + 1)y = -x^6 + 2x^4 - x^2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.014693\) |
\(22.539432\) |
\(0.331172\) |
$[392,2200,166747,50256]$ |
$[196,1234,18865,543696,12564]$ |
$[72313663744/3141,2322861856/3141,181179460/3141]$ |
$y^2 + (x + 1)y = x^5 - 2x^4 - x^3 + 2x^2$ |
| 2127.a.6381.1 |
2127.a |
\( 3 \cdot 709 \) |
\( 3^{2} \cdot 709 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.048802\) |
\(13.721894\) |
\(0.334827\) |
$[2616,-1068,-963273,25524]$ |
$[1308,71464,5222473,430972847,6381]$ |
$[425398751050752/709,17769206871552/709,992771227408/709]$ |
$y^2 + (x^2 + 1)y = 3x^5 - 6x^4 + 4x^2 + 2x$ |
| 2165.a.2165.1 |
2165.a |
\( 5 \cdot 433 \) |
\( - 5 \cdot 433 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.061819\) |
\(18.315548\) |
\(0.283063\) |
$[2100,-3687,-2637987,-277120]$ |
$[525,11638,349196,11971214,-2165]$ |
$[-7976759765625/433,-336810993750/433,-19249429500/433]$ |
$y^2 + (x^3 + 1)y = x^5 - 3x^3 + x^2 + 3x - 2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.015455\) |
\(18.315548\) |
\(0.283063\) |
$[468,451353,-38126979,-34640000]$ |
$[117,-18236,1144456,-49662586,-270625]$ |
$[-21924480357/270625,29207014668/270625,-15666458184/270625]$ |
$y^2 + (x^2 + x + 1)y = x^5 + 6x^4 - 4x^3 + x$ |
| 2173.a.89093.1 |
2173.a |
\( 41 \cdot 53 \) |
\( 41^{2} \cdot 53 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.072534\) |
\(8.214958\) |
\(0.297933\) |
$[340,114841,25395389,11403904]$ |
$[85,-4484,-238312,-10090694,89093]$ |
$[4437053125/89093,-2753736500/89093,-1721804200/89093]$ |
$y^2 + (x^3 + x^2 + x)y = x^4 + 3x^3 + 3x^2 + 6x + 1$ |
| 2178.b.287496.1 |
2178.b |
\( 2 \cdot 3^{2} \cdot 11^{2} \) |
\( - 2^{3} \cdot 3^{3} \cdot 11^{3} \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.1, 3.720.5 |
|
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(2.382791\) |
\(0.595698\) |
$[8284,1201825,3762835279,36799488]$ |
$[2071,128634,-2892384,-5634208305,287496]$ |
$[38097852361039351/287496,17312195022539/4356,-1423961612/33]$ |
$y^2 + (x^2 + x)y = -x^6 - 2x^5 + 3x^4 - 8x^2 + 9x - 3$ |
