| 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 |
| 7200.a.14400.1 |
7200.a |
\( 2^{5} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.180.5, 3.270.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(19.538372\) |
\(0.610574\) |
$[4640,936979,1146878196,1800]$ |
$[4640,272414,16904448,1056812831,14400]$ |
$[1344218660864000/9,17008396917760/9,25274028032]$ |
$y^2 + xy = x^6 - 8x^4 + 16x^2 - 1$ |
| 7200.b.14400.1 |
7200.b |
\( 2^{5} \cdot 3^{2} \cdot 5^{2} \) |
\( - 2^{6} \cdot 3^{2} \cdot 5^{2} \) |
$1$ |
$2$ |
$\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.90.5, 3.270.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.035720\) |
\(4.453530\) |
\(0.576576\) |
$[4640,936979,1146878196,1800]$ |
$[4640,272414,16904448,1056812831,14400]$ |
$[1344218660864000/9,17008396917760/9,25274028032]$ |
$y^2 + xy = x^6 + 8x^4 + 16x^2 + 1$ |
| 7200.c.43200.1 |
7200.c |
\( 2^{5} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{6} \cdot 3^{3} \cdot 5^{2} \) |
$1$ |
$2$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.90.5, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(0.445811\) |
\(9.374250\) |
\(0.696523\) |
$[4360,4024,5725876,172800]$ |
$[2180,197346,23751936,3208444191,43200]$ |
$[30772479098000/27,425947988390/9,7838798656/3]$ |
$y^2 + (x^3 + x)y = -3x^4 + 9x^2 - 12$ |
| 7200.d.345600.1 |
7200.d |
\( 2^{5} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{9} \cdot 3^{3} \cdot 5^{2} \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$0$ |
2.20.3 |
✓ |
✓ |
$1$ |
\( 2^{3} \cdot 3 \) |
\(0.001910\) |
\(17.244566\) |
\(0.790323\) |
$[148,1945,58045,43200]$ |
$[148,-384,9216,304128,345600]$ |
$[138687914/675,-810448/225,43808/75]$ |
$y^2 + y = x^6 - 2x^4 - x^3 + 4x^2 - 2x$ |
