| 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 |
| 5547.a.5547.1 |
5547.a |
\( 3 \cdot 43^{2} \) |
\( 3 \cdot 43^{2} \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.021445\) |
\(25.434606\) |
\(0.545445\) |
$[1188,14577,4818537,710016]$ |
$[297,3068,43828,901073,5547]$ |
$[\frac{770301940419}{1849},\frac{26791895988}{1849},\frac{1288674684}{1849}]$ |
$y^2 + (x^3 + x + 1)y = -2x^4 + 4x^2 + x - 1$ |
| 5547.b.16641.1 |
5547.b |
\( 3 \cdot 43^{2} \) |
\( 3^{2} \cdot 43^{2} \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$14$ |
$0$ |
2.30.2, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.006279\) |
\(24.460380\) |
\(0.307178\) |
$[520,6292,896816,66564]$ |
$[260,1768,16776,308984,16641]$ |
$[\frac{1188137600000}{16641},\frac{31074368000}{16641},\frac{126006400}{1849}]$ |
$y^2 + y = x^6 - 3x^5 + x^4 + 3x^3 - x^2 - x$ |
| 5547.c.715563.1 |
5547.c |
\( 3 \cdot 43^{2} \) |
\( - 3^{2} \cdot 43^{3} \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2$ |
$C_2$ |
$5$ |
$3$ |
2.120.3, 3.80.4 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.188450\) |
\(11.733230\) |
\(0.552780\) |
$[344,-14972,-2380065,-2862252]$ |
$[172,3728,157009,3276891,-715563]$ |
$[-\frac{1893376}{9},-\frac{238592}{9},-\frac{2512144}{387}]$ |
$y^2 + (x + 1)y = 3x^5 - 5x^4 + x^3$ |
