| 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 |
| 3584.a.3584.1 |
3584.a |
\( 2^{9} \cdot 7 \) |
\( 2^{9} \cdot 7 \) |
$0$ |
$1$ |
$\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q\) |
|
$N(\mathrm{SU}(2)\times\mathrm{SU}(2))$ |
|
✓ |
|
$C_2$ |
$C_2^2$ |
$2$ |
$0$ |
2.45.1, 3.45.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(12.033318\) |
\(0.752082\) |
$[8,349,3355,14]$ |
$[16,-920,-19712,-290448,3584]$ |
$[\frac{2048}{7},-\frac{7360}{7},-1408]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -x^5 - 3x^2 + 3x - 1$ |
| 3584.b.229376.1 |
3584.b |
\( 2^{9} \cdot 7 \) |
\( - 2^{15} \cdot 7 \) |
$1$ |
$2$ |
$\Z/4\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.90.1, 3.270.2 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.059980\) |
\(17.689513\) |
\(0.530508\) |
$[420,3963,638988,28]$ |
$[1680,75328,-5648384,-3790898176,229376]$ |
$[58344300000,1557171000,-69501600]$ |
$y^2 + (x^3 + x^2 + x + 1)y = -6x^4 + 34x^2 - 68x + 40$ |
| 3584.c.458752.1 |
3584.c |
\( 2^{9} \cdot 7 \) |
\( 2^{16} \cdot 7 \) |
$0$ |
$2$ |
$\Z/4\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.2160.9 |
|
|
$2$ |
\( 2 \) |
\(1.000000\) |
\(3.475514\) |
\(0.868879\) |
$[828,16635,5308452,56]$ |
$[3312,279616,-54648832,-64795509760,458752]$ |
$[\frac{6080953884912}{7},\frac{155007628668}{7},-1306723104]$ |
$y^2 + x^3y = x^6 - 4x^5 - 13x^4 - 22x^3 - 21x^2 - 12x - 4$ |
