| 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 |
| 6081.a.6081.1 |
6081.a |
\( 3 \cdot 2027 \) |
\( - 3 \cdot 2027 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.237855\) |
\(10.408774\) |
\(0.618943\) |
$[28840,-556316,-5352895937,-24324]$ |
$[14420,8756736,7164213793,6656884380341,-6081]$ |
$[-623485419736323200000/6081,-8752190927097856000/2027,-1489700824946765200/6081]$ |
$y^2 + (x^3 + x^2)y = -7x^4 - 3x^3 + 57x^2 - 49x - 33$ |
| 6081.a.164187.1 |
6081.a |
\( 3 \cdot 2027 \) |
\( - 3^{4} \cdot 2027 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.059464\) |
\(10.408774\) |
\(0.618943\) |
$[80,-2276,-1383,656748]$ |
$[40,446,-3913,-88859,164187]$ |
$[102400000/164187,28544000/164187,-6260800/164187]$ |
$y^2 + (x + 1)y = -x^5 - 2x^4 + x^2 + x$ |
| 6081.b.164187.1 |
6081.b |
\( 3 \cdot 2027 \) |
\( 3^{4} \cdot 2027 \) |
$2$ |
$2$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$16$ |
$0$ |
|
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.003504\) |
\(20.379079\) |
\(0.285654\) |
$[804,62697,11560485,21015936]$ |
$[201,-929,4093,-10087,164187]$ |
$[4050375321/2027,-279408827/6081,18373477/18243]$ |
$y^2 + (x^3 + x^2 + 1)y = -2x^4 - 5x^3 + 5x + 2$ |
