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 |
576.b.147456.1 |
576.b |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{14} \cdot 3^{2} \) |
$0$ |
$2$ |
$\Z/4\Z\oplus\Z/4\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathrm{M}_2(\Q)\) |
|
$E_1$ |
|
|
|
$D_4$ |
$D_4$ |
$4$ |
$0$ |
2.180.7, 3.2160.25 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(1.000000\) |
\(9.301119\) |
\(0.290660\) |
$[152,109,5469,18]$ |
$[608,14240,405504,10942208,147456]$ |
$[5071050752/9,195344320/9,1016576]$ |
$y^2 = x^6 + 2x^4 + 2x^2 + 1$ |
1152.a.147456.1 |
1152.a |
\( 2^{7} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{2} \) |
$0$ |
$1$ |
$\Z/8\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$4$ |
$2$ |
2.180.5, 3.1080.10 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(1.000000\) |
\(7.270694\) |
\(0.454418\) |
$[152,109,5469,18]$ |
$[608,14240,405504,10942208,147456]$ |
$[5071050752/9,195344320/9,1016576]$ |
$y^2 = x^6 - 2x^4 + 2x^2 - 1$ |
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 |
|
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(5.683509\) |
\(0.710439\) |
$[152,109,5469,18]$ |
$[608,14240,405504,10942208,147456]$ |
$[5071050752/9,195344320/9,1016576]$ |
$y^2 = -x^6 - 2x^4 - 2x^2 - 1$ |
4608.a.4608.1 |
4608.a |
\( 2^{9} \cdot 3^{2} \) |
\( - 2^{9} \cdot 3^{2} \) |
$0$ |
$1$ |
$\Z/4\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$2$ |
$0$ |
2.90.5, 3.1080.10 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(13.153769\) |
\(0.822111\) |
$[152,109,5469,18]$ |
$[304,3560,50688,683888,4608]$ |
$[5071050752/9,195344320/9,1016576]$ |
$y^2 + x^3y = x^4 + 2x^2 + 2$ |
4608.b.4608.1 |
4608.b |
\( 2^{9} \cdot 3^{2} \) |
\( 2^{9} \cdot 3^{2} \) |
$0$ |
$1$ |
$\Z/4\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$2$ |
$0$ |
2.90.5, 3.1080.10 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(10.282314\) |
\(0.642645\) |
$[152,109,5469,18]$ |
$[304,3560,50688,683888,4608]$ |
$[5071050752/9,195344320/9,1016576]$ |
$y^2 + x^3y = -x^4 + 2x^2 - 2$ |