| 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 |
| 26384.a.422144.1 |
26384.a |
\( 2^{4} \cdot 17 \cdot 97 \) |
\( 2^{8} \cdot 17 \cdot 97 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(0.020396\) |
\(13.895515\) |
\(1.417032\) |
$[112,-452,-38388,1649]$ |
$[224,3296,224000,9828096,422144]$ |
$[2202927104/1649,144707584/1649,43904000/1649]$ |
$y^2 = x^5 + x^4 + 2x^3 + 7x^2 + 5x + 1$ |
| 26384.b.422144.1 |
26384.b |
\( 2^{4} \cdot 17 \cdot 97 \) |
\( 2^{8} \cdot 17 \cdot 97 \) |
$0$ |
$0$ |
$\Z/3\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(3.970347\) |
\(1.323449\) |
$[66,708,10950,-1649]$ |
$[132,-1162,-3316,-446989,-422144]$ |
$[-156541572/1649,20879397/3298,902781/6596]$ |
$y^2 = x^5 - 3x^3 - 5x^2 - 3x - 1$ |
| 26384.c.422144.1 |
26384.c |
\( 2^{4} \cdot 17 \cdot 97 \) |
\( 2^{8} \cdot 17 \cdot 97 \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$7$ |
$1$ |
2.6.1, 3.80.1 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(0.086363\) |
\(15.978186\) |
\(1.379923\) |
$[202,688,53546,-1649]$ |
$[404,4966,-22244,-8411933,-422144]$ |
$[-42040402004/1649,-2558237383/3298,56727761/6596]$ |
$y^2 = x^6 - 2x^4 - x^3 + x^2 + 2x + 1$ |
| 26384.d.422144.1 |
26384.d |
\( 2^{4} \cdot 17 \cdot 97 \) |
\( 2^{8} \cdot 17 \cdot 97 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$9$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(0.017174\) |
\(11.654543\) |
\(1.000796\) |
$[24,180,1224,-1649]$ |
$[48,-384,-2048,-61440,-422144]$ |
$[-995328/1649,165888/1649,18432/1649]$ |
$y^2 = x^5 - x^4 + x^2 - x + 1$ |
