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 |
2304.a.13824.2 |
2304.a |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{9} \cdot 3^{3} \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$0$ |
2.90.6 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.099203\) |
\(11.872466\) |
\(0.294447\) |
$[186,54,2664,54]$ |
$[372,5622,115100,2802579,13824]$ |
$[515324718,83742501/4,27652775/24]$ |
$y^2 + (x^3 + x^2 + x + 1)y = x^4 + x^3 + 3x^2 + x + 2$ |
2304.a.13824.1 |
2304.a |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{9} \cdot 3^{3} \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$10$ |
$2$ |
2.180.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.049602\) |
\(23.744931\) |
\(0.294447\) |
$[102,234,7128,54]$ |
$[204,1110,4324,-87501,13824]$ |
$[25557426,2726715/4,312409/24]$ |
$y^2 + y = 2x^5 + 3x^4 - x^3 - 2x^2$ |
2304.b.147456.1 |
2304.b |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{14} \cdot 3^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathrm{M}_2(\Q)\) |
|
$E_1$ |
|
|
|
$D_4$ |
$D_4$ |
$0$ |
$0$ |
2.180.7, 3.2160.25 |
|
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(5.683509\) |
\(0.710439\) |
$[152,109,5469,18]$ |
$[608,14240,405504,10942208,147456]$ |
$[5071050752/9,195344320/9,1016576]$ |
$y^2 = -x^6 - 2x^4 - 2x^2 - 1$ |
2304.c.294912.1 |
2304.c |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{15} \cdot 3^{2} \) |
$0$ |
$1$ |
$\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.5, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(5.052371\) |
\(0.631546\) |
$[784,9991,2278962,36]$ |
$[3136,303200,34578432,4126930688,294912]$ |
$[9256148959232/9,285369414400/9,1153094656]$ |
$y^2 + x^3y = 4x^4 + 17x^2 + 8$ |
2304.d.294912.1 |
2304.d |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{15} \cdot 3^{2} \) |
$0$ |
$2$ |
$\Z/2\Z\oplus\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.180.7, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(17.270712\) |
\(0.539710\) |
$[784,9991,2278962,36]$ |
$[3136,303200,34578432,4126930688,294912]$ |
$[9256148959232/9,285369414400/9,1153094656]$ |
$y^2 + x^3y = -4x^4 + 17x^2 - 8$ |