| 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 |
| 2457.a.95823.1 |
2457.a |
\( 3^{3} \cdot 7 \cdot 13 \) |
\( - 3^{4} \cdot 7 \cdot 13^{2} \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$2$ |
2.180.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.066494\) |
\(18.983107\) |
\(0.315567\) |
$[1932,57897,45198315,12265344]$ |
$[483,7308,-43264,-18575844,95823]$ |
$[46360978629/169,1452301788/169,-947968/9]$ |
$y^2 + (x^3 + 1)y = x^5 - x^4 - 3x^3 + 6x^2 - 6x + 2$ |
| 2457.a.154791.1 |
2457.a |
\( 3^{3} \cdot 7 \cdot 13 \) |
\( - 3^{5} \cdot 7^{2} \cdot 13 \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$2$ |
2.180.3 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.033247\) |
\(18.983107\) |
\(0.315567\) |
$[780,63657,23411115,19813248]$ |
$[195,-1068,-164320,-8295756,154791]$ |
$[89253125/49,-7520500/147,-53404000/1323]$ |
$y^2 + (x^3 + 1)y = x^5 - 3x^3 - x^2 + 2$ |
| 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 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(9.926544\) |
\(0.620409\) |
$[3308,70369,83658591,104832]$ |
$[2481,230085,22164597,512814483,199017]$ |
$[386836591312907/819,14459801319895/819,2056574503/3]$ |
$y^2 + (x^2 + x)y = -x^5 + 4x^4 + x^3 - 13x^2 - 9x$ |
