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 |
67203.a.67203.1 |
67203.a |
\( 3^{3} \cdot 19 \cdot 131 \) |
\( 3^{3} \cdot 19 \cdot 131 \) |
$1$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
|
✓ |
✓ |
$4$ |
\( 1 \) |
\(0.161475\) |
\(4.677551\) |
\(3.021224\) |
$[51780,24849,425950713,8601984]$ |
$[12945,6981174,5019179296,4059121392111,67203]$ |
$[13463144580390271875/2489,560881173463697250/2489,93453228627565600/7467]$ |
$y^2 + (x^3 + x + 1)y = -2x^6 - 6x^5 + 14x^3 - x^2 - 13x + 5$ |
67203.b.604827.1 |
67203.b |
\( 3^{3} \cdot 19 \cdot 131 \) |
\( - 3^{5} \cdot 19 \cdot 131 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.066187\) |
\(16.855442\) |
\(1.115608\) |
$[1080,36180,11353815,-2419308]$ |
$[540,6120,7465,-8355825,-604827]$ |
$[-188956800000/2489,-3965760000/2489,-8958000/2489]$ |
$y^2 + xy = 3x^5 - 5x^3 + x^2 + x$ |
67203.c.604827.1 |
67203.c |
\( 3^{3} \cdot 19 \cdot 131 \) |
\( 3^{5} \cdot 19 \cdot 131 \) |
$3$ |
$3$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$18$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 3 \) |
\(0.016859\) |
\(13.556935\) |
\(0.685653\) |
$[1116,27657,9938475,-77417856]$ |
$[279,2091,1547,-985167,-604827]$ |
$[-6956883693/2489,-186878943/2489,-1486667/7467]$ |
$y^2 + (x^3 + x + 1)y = -x^4 - x^2 + 2$ |