| 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 |
| 800.a.409600.1 |
800.a |
\( 2^{5} \cdot 5^{2} \) |
\( - 2^{14} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/24\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$2$ |
2.90.3, 3.2160.21 |
✓ |
✓ |
$1$ |
\( 2^{2} \cdot 3 \) |
\(1.000000\) |
\(16.770151\) |
\(0.349378\) |
$[120,309,14889,50]$ |
$[480,6304,-151552,-28121344,409600]$ |
$[62208000,1702080,-85248]$ |
$y^2 = x^6 - 2x^2 + 1$ |
| 1600.a.409600.1 |
1600.a |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.2, 3.2160.21 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(5.702147\) |
\(0.475179\) |
$[120,309,14889,50]$ |
$[480,6304,-151552,-28121344,409600]$ |
$[62208000,1702080,-85248]$ |
$y^2 = x^6 - 2x^2 - 1$ |
| 3200.d.409600.1 |
3200.d |
\( 2^{7} \cdot 5^{2} \) |
\( 2^{14} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.2, 3.1080.9 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(6.751598\) |
\(0.843950\) |
$[120,309,14889,50]$ |
$[480,6304,-151552,-28121344,409600]$ |
$[62208000,1702080,-85248]$ |
$y^2 = x^6 + 2x^4 - 1$ |
| 6400.c.12800.1 |
6400.c |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{9} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.45.1, 3.2160.21 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(8.064054\) |
\(0.672005\) |
$[120,309,14889,50]$ |
$[240,1576,-18944,-1757584,12800]$ |
$[62208000,1702080,-85248]$ |
$y^2 + x^3y = -2x^2 - 2$ |
| 6400.e.12800.1 |
6400.e |
\( 2^{8} \cdot 5^{2} \) |
\( - 2^{9} \cdot 5^{2} \) |
$1$ |
$2$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.45.1, 3.2160.21 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.361103\) |
\(23.716575\) |
\(0.713677\) |
$[120,309,14889,50]$ |
$[240,1576,-18944,-1757584,12800]$ |
$[62208000,1702080,-85248]$ |
$y^2 + x^3y = -2x^2 + 2$ |
| 6400.h.409600.1 |
6400.h |
\( 2^{8} \cdot 5^{2} \) |
\( - 2^{14} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.90.3, 3.1080.9 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(4.591325\) |
\(1.147831\) |
$[120,309,14889,50]$ |
$[480,6304,-151552,-28121344,409600]$ |
$[62208000,1702080,-85248]$ |
$y^2 = -x^6 + 2x^2 - 1$ |
| 12800.a.12800.1 |
12800.a |
\( 2^{9} \cdot 5^{2} \) |
\( - 2^{9} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.45.1, 3.1080.9 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(23.716575\) |
\(1.482286\) |
$[120,309,14889,50]$ |
$[240,1576,-18944,-1757584,12800]$ |
$[62208000,1702080,-85248]$ |
$y^2 + x^3y = -x^4 + 2$ |
| 12800.b.12800.1 |
12800.b |
\( 2^{9} \cdot 5^{2} \) |
\( 2^{9} \cdot 5^{2} \) |
$1$ |
$2$ |
$\Z/4\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.45.1, 3.1080.9 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.653748\) |
\(9.548202\) |
\(0.986895\) |
$[120,309,14889,50]$ |
$[240,1576,-18944,-1757584,12800]$ |
$[62208000,1702080,-85248]$ |
$y^2 + x^3y = x^4 - 2$ |
