| 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 |
| 360.a.6480.1 |
360.a |
\( 2^{3} \cdot 3^{2} \cdot 5 \) |
\( 2^{4} \cdot 3^{4} \cdot 5 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/8\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$4$ |
2.360.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(24.163379\) |
\(0.188776\) |
$[2360,11992,9047820,25920]$ |
$[1180,56018,3453120,234166319,6480]$ |
$[28596971960000/81,1150492082200/81,6677950400/9]$ |
$y^2 + (x^3 + x)y = -3x^4 + 7x^2 - 5$ |
| 600.a.18000.1 |
600.a |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 5^{3} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$6$ |
$4$ |
2.360.2, 3.640.2 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(18.934319\) |
\(0.262977\) |
$[1376,23824,11410044,72000]$ |
$[688,15752,244900,-19908576,18000]$ |
$[9634345320448/1125,320612931584/1125,289804864/45]$ |
$y^2 + xy = 10x^5 - 18x^4 + 8x^3 + x^2 - x$ |
| 600.b.450000.1 |
600.b |
\( 2^{3} \cdot 3 \cdot 5^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 5^{5} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/8\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$4$ |
2.360.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{5} \) |
\(1.000000\) |
\(8.316291\) |
\(0.259884\) |
$[18072,38904,233095932,1800000]$ |
$[9036,3395570,1698206400,953774351375,450000]$ |
$[418329622965299904/3125,3479436045234936/625,38515932506304/125]$ |
$y^2 + (x^3 + x)y = -5x^4 + 25x^2 - 45$ |
| 630.a.34020.1 |
630.a |
\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
\( 2^{2} \cdot 3^{5} \cdot 5 \cdot 7 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$4$ |
2.360.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(19.470889\) |
\(0.304233\) |
$[24100,969793,7474503265,4354560]$ |
$[6025,1472118,470090880,166291536519,34020]$ |
$[1587871127345703125/6804,10732293030978125/1134,13543327580000/27]$ |
$y^2 + (x^2 + x)y = 3x^5 + 10x^4 - 23x^2 - 6x + 15$ |
| 816.a.39168.1 |
816.a |
\( 2^{4} \cdot 3 \cdot 17 \) |
\( 2^{8} \cdot 3^{2} \cdot 17 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/6\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$4$ |
2.360.2, 3.80.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(22.166697\) |
\(0.307871\) |
$[436,3373,434667,4896]$ |
$[436,5672,77824,439920,39168]$ |
$[61544958196/153,1836351122/153,57789184/153]$ |
$y^2 + (x^2 + 1)y = 3x^5 - 4x^3 - x^2 + x$ |
| 1584.a.684288.1 |
1584.a |
\( 2^{4} \cdot 3^{2} \cdot 11 \) |
\( 2^{8} \cdot 3^{5} \cdot 11 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$4$ |
2.360.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(4.753791\) |
\(0.594224\) |
$[7444,76621,183223627,85536]$ |
$[7444,2257800,897608448,396034111728,684288]$ |
$[89287745446261204/2673,1212671977685150/891,1962567037712/27]$ |
$y^2 + (x^3 + x)y = -x^6 + 6x^4 - 17x^2 + 11$ |
| 2169.a.175689.1 |
2169.a |
\( 3^{2} \cdot 241 \) |
\( 3^{6} \cdot 241 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q\) |
|
$N(\mathrm{SU}(2)\times\mathrm{SU}(2))$ |
|
✓ |
|
$C_2$ |
$C_2^2$ |
$4$ |
$4$ |
2.360.2, 3.90.2 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(10.183530\) |
\(0.636471\) |
$[2860,62145,64270095,92544]$ |
$[2145,168405,12629605,-317435325,175689]$ |
$[186865965446875/723,20518794993125/2169,26790746125/81]$ |
$y^2 + (x^2 + x)y = x^5 - 9x^4 + 22x^3 - 14x^2 - x$ |
| 2457.b.199017.1 |
2457.b |
\( 3^{3} \cdot 7 \cdot 13 \) |
\( 3^{7} \cdot 7 \cdot 13 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q\) |
|
$N(\mathrm{SU}(2)\times\mathrm{SU}(2))$ |
|
✓ |
|
$C_2$ |
$C_2^2$ |
$4$ |
$4$ |
2.360.2, 3.90.2 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(9.926544\) |
\(0.620409\) |
$[3308,70369,83658591,104832]$ |
$[2481,230085,22164597,512814483,199017]$ |
$[386836591312907/819,14459801319895/819,2056574503/3]$ |
$y^2 + (x^2 + x)y = -x^5 + 4x^4 + x^3 - 13x^2 - 9x$ |
| 2560.a.5120.1 |
2560.a |
\( 2^{9} \cdot 5 \) |
\( 2^{10} \cdot 5 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q\) |
|
$N(\mathrm{SU}(2)\times\mathrm{SU}(2))$ |
|
✓ |
|
$C_2$ |
$C_2^2$ |
$4$ |
$4$ |
2.360.2, 3.45.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(21.001976\) |
\(0.656312\) |
$[80,112,3020,20]$ |
$[160,768,1280,-96256,5120]$ |
$[20480000,614400,6400]$ |
$y^2 = x^5 - x^4 - 2x^3 + x^2 + x$ |
| 2560.a.819200.1 |
2560.a |
\( 2^{9} \cdot 5 \) |
\( 2^{15} \cdot 5^{2} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q\) |
|
$N(\mathrm{SU}(2)\times\mathrm{SU}(2))$ |
|
✓ |
|
$C_2$ |
$C_2^2$ |
$4$ |
$4$ |
2.360.2, 3.45.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(10.500988\) |
\(0.656312\) |
$[484,853,144121,100]$ |
$[1936,147072,13491200,1122197504,819200]$ |
$[829997587232/25,32568377424/25,61726456]$ |
$y^2 = 2x^5 - 7x^4 + 2x^3 + 7x^2 + 2x$ |
| 2600.a.338000.1 |
2600.a |
\( 2^{3} \cdot 5^{2} \cdot 13 \) |
\( 2^{4} \cdot 5^{3} \cdot 13^{2} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$4$ |
2.360.2 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(6.475715\) |
\(0.809464\) |
$[3608,166936,209750684,1352000]$ |
$[1804,107778,4226816,-997730305,338000]$ |
$[1194160449744064/21125,39547563972312/21125,859738601216/21125]$ |
$y^2 + xy = 10x^5 + 8x^4 - 5x^3 - 3x^2 + x$ |
| 2745.a.502335.1 |
2745.a |
\( 3^{2} \cdot 5 \cdot 61 \) |
\( - 3^{3} \cdot 5 \cdot 61^{2} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$4$ |
2.360.2 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(11.100418\) |
\(0.693776\) |
$[260,-34487,-4132395,-64298880]$ |
$[65,1613,32085,-129061,-502335]$ |
$[-232058125/100467,-88594025/100467,-3012425/11163]$ |
$y^2 + (x^2 + x)y = 3x^5 + 7x^4 + 5x^3 - x$ |
| 3417.a.686817.1 |
3417.a |
\( 3 \cdot 17 \cdot 67 \) |
\( 3^{2} \cdot 17 \cdot 67^{2} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$4$ |
2.360.2 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(11.580296\) |
\(0.723769\) |
$[1348,46057,19365765,87912576]$ |
$[337,2813,-731,-2039829,686817]$ |
$[4346598285457/686817,107661254189/686817,-4883467/40401]$ |
$y^2 + (x^2 + x)y = 3x^5 - 9x^4 + 6x^3 - x$ |
| 3591.a.226233.1 |
3591.a |
\( 3^{3} \cdot 7 \cdot 19 \) |
\( 3^{5} \cdot 7^{2} \cdot 19 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$4$ |
2.360.2 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(6.643806\) |
\(0.830476\) |
$[1964,59393,40017455,119168]$ |
$[1473,68133,1504741,-606405549,226233]$ |
$[28536943843451/931,2688318580181/2793,7403356429/513]$ |
$y^2 + (x^2 + x)y = 3x^5 + 3x^4 - 6x^3 - 4x^2 + 3x$ |
| 3978.a.930852.1 |
3978.a |
\( 2 \cdot 3^{2} \cdot 13 \cdot 17 \) |
\( 2^{2} \cdot 3^{4} \cdot 13^{2} \cdot 17 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$4$ |
2.360.2 |
✓ |
✓ |
$1$ |
\( 2^{4} \) |
\(1.000000\) |
\(12.005528\) |
\(0.750346\) |
$[5444,262801,507052857,119149056]$ |
$[1361,66230,2932992,-98652697,930852]$ |
$[4669717691462801/930852,83483209094315/465426,150912296512/25857]$ |
$y^2 + (x^2 + x)y = x^5 + 3x^4 - 3x^3 - 8x^2 + 6x$ |
| 4096.b.65536.1 |
4096.b |
\( 2^{12} \) |
\( - 2^{16} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\mathsf{CM})\) |
\(\mathsf{CM}\) |
✓ |
$J(C_2)$ |
|
✓ |
|
$C_4$ |
$GL(2,3)$ |
$4$ |
$4$ |
2.360.2, 3.6480.22 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(12.689987\) |
\(0.793124\) |
$[20,-20,-40,8]$ |
$[80,480,-1280,-83200,65536]$ |
$[50000,3750,-125]$ |
$y^2 = x^5 - x$ |
| 4352.b.278528.1 |
4352.b |
\( 2^{8} \cdot 17 \) |
\( 2^{14} \cdot 17 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q\) |
|
$N(\mathrm{SU}(2)\times\mathrm{SU}(2))$ |
|
✓ |
|
$C_2$ |
$C_2^2$ |
$4$ |
$4$ |
2.360.2, 3.45.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(12.931176\) |
\(0.808199\) |
$[136,301,14773,34]$ |
$[544,9120,17408,-18426112,278528]$ |
$[171051008,5271360,18496]$ |
$y^2 = 2x^5 - x^4 - 4x^3 + x^2 + 2x$ |
| 4608.c.27648.1 |
4608.c |
\( 2^{9} \cdot 3^{2} \) |
\( - 2^{10} \cdot 3^{3} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_4)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$4$ |
$4$ |
2.360.2, 3.540.5 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(13.756159\) |
\(0.859760\) |
$[24,-72,-180,108]$ |
$[48,288,-1024,-33024,27648]$ |
$[9216,1152,-256/3]$ |
$y^2 = x^5 - x^4 + x^2 - x$ |
| 4950.a.742500.1 |
4950.a |
\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 11 \) |
\( 2^{2} \cdot 3^{3} \cdot 5^{4} \cdot 11 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$4$ |
2.360.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{4} \) |
\(1.000000\) |
\(13.551501\) |
\(0.846969\) |
$[60740,861841,17199817017,95040000]$ |
$[15185,9571766,8017726464,7532617999271,742500]$ |
$[1291796084758794785/1188,134059147400774599/2970,62247853298432/25]$ |
$y^2 + (x^2 + x)y = 15x^5 - 22x^3 - 5x^2 + 8x + 3$ |
| 5655.b.491985.1 |
5655.b |
\( 3 \cdot 5 \cdot 13 \cdot 29 \) |
\( 3^{2} \cdot 5 \cdot 13 \cdot 29^{2} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$4$ |
2.360.2 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(16.062150\) |
\(1.003884\) |
$[2340,104793,77140845,62974080]$ |
$[585,9893,101565,-9613981,491985]$ |
$[117117950625/841,3385631925/841,59415525/841]$ |
$y^2 + (x^2 + x)y = x^5 + 2x^4 - 4x^3 - 3x^2 + 3x$ |
| 6105.a.201465.1 |
6105.a |
\( 3 \cdot 5 \cdot 11 \cdot 37 \) |
\( 3^{2} \cdot 5 \cdot 11^{2} \cdot 37 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$4$ |
2.360.2 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(16.499239\) |
\(1.031202\) |
$[7300,339913,789994005,25787520]$ |
$[1825,124613,10278085,807276339,201465]$ |
$[4048967955078125/40293,151489298190625/40293,6846489370625/40293]$ |
$y^2 + (x^2 + x)y = x^5 - 8x^3 - 4x^2 + 14x + 11$ |
| 6270.a.188100.1 |
6270.a |
\( 2 \cdot 3 \cdot 5 \cdot 11 \cdot 19 \) |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 11 \cdot 19 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$4$ |
2.360.2 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(7.864568\) |
\(0.983071\) |
$[7780,369313,1001245425,24076800]$ |
$[1945,142238,11440000,504787839,188100]$ |
$[1113417440118625/7524,20931697497055/3762,39343460000/171]$ |
$y^2 + (x^2 + x)y = -x^5 + 4x^4 - 11x^2 - 6x$ |
| 6615.b.416745.1 |
6615.b |
\( 3^{3} \cdot 5 \cdot 7^{2} \) |
\( 3^{5} \cdot 5 \cdot 7^{3} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$4$ |
2.360.2 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(6.636255\) |
\(0.829532\) |
$[5220,347193,554170365,53343360]$ |
$[1305,56493,2691805,80336619,416745]$ |
$[3115130754375/343,103335583275/343,11319040025/1029]$ |
$y^2 + (x^2 + x)y = x^5 - 7x^3 + 10x - 5$ |
| 6825.a.716625.1 |
6825.a |
\( 3 \cdot 5^{2} \cdot 7 \cdot 13 \) |
\( 3^{2} \cdot 5^{3} \cdot 7^{2} \cdot 13 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$4$ |
2.360.2 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(8.548168\) |
\(1.068521\) |
$[2212,130585,86250765,91728000]$ |
$[553,7301,29341,-9269757,716625]$ |
$[1055430344857/14625,25197744173/14625,14085937/1125]$ |
$y^2 + (x^2 + x)y = x^5 - 2x^4 - 5x^3 + x^2 + 3x$ |
| 7680.a.46080.1 |
7680.a |
\( 2^{9} \cdot 3 \cdot 5 \) |
\( 2^{10} \cdot 3^{2} \cdot 5 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$4$ |
2.360.2 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(14.167858\) |
\(0.885491\) |
$[200,472,32580,180]$ |
$[400,5408,56320,-1679616,46080]$ |
$[2000000000/9,67600000/9,1760000/9]$ |
$y^2 = x^5 - 3x^4 + 5x^2 - x - 2$ |
| 7680.b.46080.1 |
7680.b |
\( 2^{9} \cdot 3 \cdot 5 \) |
\( 2^{10} \cdot 3^{2} \cdot 5 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$4$ |
2.360.2 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(17.497219\) |
\(1.093576\) |
$[200,472,32580,180]$ |
$[400,5408,56320,-1679616,46080]$ |
$[2000000000/9,67600000/9,1760000/9]$ |
$y^2 = x^5 + 3x^4 - 5x^2 - x + 2$ |
| 8190.a.982800.1 |
8190.a |
\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \) |
\( 2^{4} \cdot 3^{3} \cdot 5^{2} \cdot 7 \cdot 13 \) |
$1$ |
$4$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$4$ |
2.360.2 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.499493\) |
\(14.095125\) |
\(0.880053\) |
$[17892,1459521,8200886049,125798400]$ |
$[4473,772842,168822784,39464888967,982800]$ |
$[9473984867119437/5200,182976624000513/2600,85921868928/25]$ |
$y^2 + (x^2 + x)y = x^5 - 7x^4 + 6x^3 + 17x^2 + 3x$ |
| 8192.a.32768.1 |
8192.a |
\( 2^{13} \) |
\( 2^{15} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_4)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$4$ |
$4$ |
2.360.2, 3.270.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(16.855414\) |
\(1.053463\) |
$[67,82,1930,4]$ |
$[268,2118,-124,-1129789,32768]$ |
$[1350125107/32,318508017/256,-139159/512]$ |
$y^2 = x^5 - 3x^3 + 2x$ |
| 8192.b.131072.1 |
8192.b |
\( 2^{13} \) |
\( 2^{17} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_2)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$4$ |
$4$ |
2.360.2, 3.540.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(15.683046\) |
\(0.980190\) |
$[64,76,1552,16]$ |
$[256,1920,8192,-397312,131072]$ |
$[8388608,245760,4096]$ |
$y^2 = x^5 - 3x^4 + 6x^2 - 4x$ |
| 12800.c.128000.1 |
12800.c |
\( 2^{9} \cdot 5^{2} \) |
\( 2^{10} \cdot 5^{3} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_4)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$4$ |
$4$ |
2.360.2, 3.270.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(15.952863\) |
\(0.997054\) |
$[104,280,9140,500]$ |
$[208,1056,-1024,-332032,128000]$ |
$[380204032/125,9280128/125,-43264/125]$ |
$y^2 = x^5 - 3x^4 + 3x^2 - x$ |
| 15360.h.184320.1 |
15360.h |
\( 2^{10} \cdot 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{2} \cdot 5 \) |
$1$ |
$4$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$4$ |
2.360.2, 3.270.2 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.516278\) |
\(17.101360\) |
\(1.103633\) |
$[390,852,105720,720]$ |
$[780,23078,838980,30452579,184320]$ |
$[6265569375/4,1901338725/32,177234525/64]$ |
$y^2 = 2x^5 - x^4 - 5x^3 + 3x + 1$ |
| 15360.i.184320.1 |
15360.i |
\( 2^{10} \cdot 3 \cdot 5 \) |
\( 2^{12} \cdot 3^{2} \cdot 5 \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$4$ |
2.360.2, 3.270.2 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(10.695870\) |
\(1.336984\) |
$[390,852,105720,720]$ |
$[780,23078,838980,30452579,184320]$ |
$[6265569375/4,1901338725/32,177234525/64]$ |
$y^2 = 2x^5 + x^4 - 5x^3 + 3x - 1$ |
| 20480.h.409600.1 |
20480.h |
\( 2^{12} \cdot 5 \) |
\( - 2^{14} \cdot 5^{2} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$4$ |
2.360.2 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(11.077305\) |
\(1.384663\) |
$[5,-62,50,50]$ |
$[20,678,-6500,-147421,409600]$ |
$[125/16,1695/128,-1625/256]$ |
$y^2 = x^5 - 2x^4 + x^3 + 2x^2 - 2x$ |
| 20480.i.409600.1 |
20480.i |
\( 2^{12} \cdot 5 \) |
\( - 2^{14} \cdot 5^{2} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$4$ |
2.360.2 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(9.806212\) |
\(1.225777\) |
$[5,-62,50,50]$ |
$[20,678,-6500,-147421,409600]$ |
$[125/16,1695/128,-1625/256]$ |
$y^2 = x^5 + 2x^4 + x^3 - 2x^2 - 2x$ |
| 24576.a.294912.1 |
24576.a |
\( 2^{13} \cdot 3 \) |
\( 2^{15} \cdot 3^{2} \) |
$1$ |
$4$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$4$ |
2.360.2 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.648107\) |
\(16.092064\) |
\(1.303672\) |
$[163,262,13830,36]$ |
$[652,14918,360964,3200451,294912]$ |
$[115063617043/288,32303041873/2304,2397613129/4608]$ |
$y^2 = x^5 - 3x^4 - x^3 + 5x^2 + 2x$ |
| 24576.b.294912.1 |
24576.b |
\( 2^{13} \cdot 3 \) |
\( 2^{15} \cdot 3^{2} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$4$ |
2.360.2 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(10.476834\) |
\(1.309604\) |
$[163,262,13830,36]$ |
$[652,14918,360964,3200451,294912]$ |
$[115063617043/288,32303041873/2304,2397613129/4608]$ |
$y^2 = x^5 + 3x^4 - x^3 - 5x^2 + 2x$ |
| 25600.f.512000.1 |
25600.f |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{3} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathsf{RM}\) |
✓ |
$J(E_1)$ |
|
✓ |
|
$C_2$ |
$C_2^2$ |
$4$ |
$4$ |
2.360.2, 3.1080.4 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(11.501498\) |
\(1.437687\) |
$[566,2164,432824,2000]$ |
$[1132,47622,2094500,25779779,512000]$ |
$[1815232161643/500,539680767657/4000,335492821/64]$ |
$y^2 = 2x^5 - 5x^4 - x^3 + 5x^2 + 2x$ |
| 36864.e.442368.1 |
36864.e |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{3} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$4$ |
2.360.2 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(11.143802\) |
\(1.392975\) |
$[99,198,6138,54]$ |
$[396,4422,26884,-2227005,442368]$ |
$[352218537/16,79456707/128,2439723/256]$ |
$y^2 = x^5 + 3x^4 - x^3 - 9x^2 - 6x$ |
| 36864.f.442368.1 |
36864.f |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{3} \) |
$1$ |
$4$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$4$ |
2.360.2 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.865926\) |
\(15.925274\) |
\(1.723764\) |
$[99,198,6138,54]$ |
$[396,4422,26884,-2227005,442368]$ |
$[352218537/16,79456707/128,2439723/256]$ |
$y^2 = x^5 - 3x^4 - x^3 + 9x^2 - 6x$ |
| 73728.d.884736.1 |
73728.d |
\( 2^{13} \cdot 3^{2} \) |
\( 2^{15} \cdot 3^{3} \) |
$0$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_4)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$4$ |
$4$ |
2.360.2, 3.270.1 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(11.166308\) |
\(1.395789\) |
$[195,630,44910,108]$ |
$[780,18630,-380,-86843325,884736]$ |
$[10442615625/32,2558131875/256,-401375/1536]$ |
$y^2 = 2x^5 - 5x^3 + 3x$ |
