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 |
8450.a.8450.1 |
8450.a |
\( 2 \cdot 5^{2} \cdot 13^{2} \) |
\( 2 \cdot 5^{2} \cdot 13^{2} \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,13$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.096036\) |
\(6.226282\) |
\(0.597950\) |
$[5688,483444,1033020495,33800]$ |
$[2844,256440,2121617,-14931898713,8450]$ |
$[93028916891930112/4225,589894768164096/845,8580175579656/4225]$ |
$y^2 + (x + 1)y = x^5 + x^4 - 9x^3 - 5x^2 + 21x$ |
8450.b.67600.1 |
8450.b |
\( 2 \cdot 5^{2} \cdot 13^{2} \) |
\( - 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
$1$ |
$2$ |
$\Z/8\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$2$ |
2.90.3, 3.90.1 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.751028\) |
\(16.845250\) |
\(0.790704\) |
$[540,129,595071,8652800]$ |
$[135,754,-2368,-222049,67600]$ |
$[1793613375/2704,2854035/104,-107892/169]$ |
$y^2 + (x^2 + x)y = x^5 + 4x^4 + 5x^3 + 4x^2 + x$ |
8450.c.84500.1 |
8450.c |
\( 2 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{2} \cdot 5^{3} \cdot 13^{2} \) |
$2$ |
$3$ |
$\Z/6\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$14$ |
$0$ |
2.180.4, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(0.109881\) |
\(20.369950\) |
\(0.373047\) |
$[1972,60889,35769757,10816000]$ |
$[493,7590,128000,1373975,84500]$ |
$[29122898485693/84500,90945776163/8450,62220544/169]$ |
$y^2 + (x^3 + 1)y = -5x^4 + 10x^3 - 5x^2$ |