| 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 |
| 15104.a.15104.1 |
15104.a |
\( 2^{8} \cdot 59 \) |
\( 2^{8} \cdot 59 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.059415\) |
\(15.582130\) |
\(0.925815\) |
$[96,666,14922,-1888]$ |
$[96,-60,624,14076,-15104]$ |
$[-31850496/59,207360/59,-22464/59]$ |
$y^2 + (x^3 + x)y = x^4 - x^3 + 2x^2 - x$ |
| 15104.b.241664.1 |
15104.b |
\( 2^{8} \cdot 59 \) |
\( - 2^{12} \cdot 59 \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.356425\) |
\(12.164392\) |
\(1.083925\) |
$[32,-224,-796,944]$ |
$[64,768,-4352,-217088,241664]$ |
$[262144/59,49152/59,-4352/59]$ |
$y^2 = x^5 + x^4 - 2x^3 + x^2 - x$ |
| 15104.b.483328.1 |
15104.b |
\( 2^{8} \cdot 59 \) |
\( - 2^{13} \cdot 59 \) |
$1$ |
$2$ |
$\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.356425\) |
\(12.164392\) |
\(1.083925\) |
$[5152,10096,15976476,-1888]$ |
$[10304,4396928,2495856896,1596083404800,-483328]$ |
$[-14178794445340672/59,-587187714584576/59,-32347553300608/59]$ |
$y^2 = x^5 - 8x^4 + 8x^3 + 31x^2 + 20x + 4$ |
| 15104.c.966656.1 |
15104.c |
\( 2^{8} \cdot 59 \) |
\( - 2^{14} \cdot 59 \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$3$ |
2.120.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(5.109262\) |
\(1.277316\) |
$[280,760,60604,-3776]$ |
$[560,11040,290816,10243840,-966656]$ |
$[-3361400000/59,-118335000/59,-5566400/59]$ |
$y^2 = x^5 + 3x^4 - 5x^2 + x$ |
| 15104.d.966656.1 |
15104.d |
\( 2^{8} \cdot 59 \) |
\( 2^{14} \cdot 59 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 13 \) |
\(0.006540\) |
\(15.612919\) |
\(1.327460\) |
$[24,6834,-49026,120832]$ |
$[24,-4532,73984,-4690852,966656]$ |
$[486/59,-30591/472,2601/59]$ |
$y^2 + (x^3 + x)y = -x^4 - 3x^3 + 2x^2 + 3x + 1$ |
