| 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 |
| 102400.a.102400.1 |
102400.a |
\( 2^{12} \cdot 5^{2} \) |
\( - 2^{12} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\mathsf{RM}\) |
\(\Q\) |
|
$N(\mathrm{SU}(2)\times\mathrm{SU}(2))$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.90.3, 3.36.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(7.701023\) |
\(1.925256\) |
$[18,-36,2160,400]$ |
$[36,150,-16212,-151533,102400]$ |
$[59049/100,2187/32,-328293/1600]$ |
$y^2 = x^5 + x^4 - x^3 - x^2 - x - 1$ |
| 102400.b.102400.1 |
102400.b |
\( 2^{12} \cdot 5^{2} \) |
\( - 2^{12} \cdot 5^{2} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_2)$ |
|
✓ |
|
$C_2$ |
$D_4$ |
$4$ |
$2$ |
2.90.3, 3.540.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.797280\) |
\(12.084061\) |
\(2.408596\) |
$[34,-116,-424,400]$ |
$[68,502,-2100,-98701,102400]$ |
$[1419857/100,1233163/800,-6069/64]$ |
$y^2 = x^5 - x^3 - x$ |
| 102400.c.102400.1 |
102400.c |
\( 2^{12} \cdot 5^{2} \) |
\( - 2^{12} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$2$ |
2.90.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(8.574530\) |
\(2.143632\) |
$[50,-284,-2432,400]$ |
$[100,1174,-1428,-380269,102400]$ |
$[390625/4,366875/32,-8925/64]$ |
$y^2 = x^5 + x^4 + x^3 + x^2 - x - 1$ |
| 102400.d.102400.1 |
102400.d |
\( 2^{12} \cdot 5^{2} \) |
\( - 2^{12} \cdot 5^{2} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.90.3 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.533017\) |
\(14.587978\) |
\(1.943909\) |
$[50,-284,-2432,400]$ |
$[100,1174,-1428,-380269,102400]$ |
$[390625/4,366875/32,-8925/64]$ |
$y^2 = x^5 - x^4 + x^3 - x^2 - x + 1$ |
| 102400.e.102400.1 |
102400.e |
\( 2^{12} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_4$ |
$2$ |
$2$ |
2.180.5, 3.1080.10 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(8.209049\) |
\(2.052262\) |
$[94,244,7096,400]$ |
$[188,822,-1100,-220621,102400]$ |
$[229345007/100,42671253/800,-24299/64]$ |
$y^2 = x^5 + 3x^3 + x$ |
| 102400.f.102400.1 |
102400.f |
\( 2^{12} \cdot 5^{2} \) |
\( - 2^{12} \cdot 5^{2} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\mathsf{RM}\) |
\(\Q\) |
|
$N(\mathrm{SU}(2)\times\mathrm{SU}(2))$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.90.3, 3.36.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.562662\) |
\(16.506692\) |
\(2.321922\) |
$[18,-36,2160,400]$ |
$[36,150,-16212,-151533,102400]$ |
$[59049/100,2187/32,-328293/1600]$ |
$y^2 = x^5 - x^4 - x^3 + x^2 - x + 1$ |
