| 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 |
| 14848.a.14848.1 |
14848.a |
\( 2^{9} \cdot 29 \) |
\( 2^{9} \cdot 29 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.101698\) |
\(10.111061\) |
\(1.028275\) |
$[248,34,7188,1856]$ |
$[248,2540,30480,276860,14848]$ |
$[\frac{1832265664}{29},\frac{75669140}{29},\frac{3661410}{29}]$ |
$y^2 + (x + 1)y = -x^6 + 2x^5 - 2x^3$ |
| 14848.b.14848.1 |
14848.b |
\( 2^{9} \cdot 29 \) |
\( - 2^{9} \cdot 29 \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.468905\) |
\(8.123456\) |
\(0.952281\) |
$[144,-243,-14355,-58]$ |
$[288,4104,105536,3387888,-14848]$ |
$[-\frac{3869835264}{29},-\frac{191476224}{29},-\frac{17096832}{29}]$ |
$y^2 + x^3y = x^5 - 2x^3 - 2$ |
| 14848.c.14848.1 |
14848.c |
\( 2^{9} \cdot 29 \) |
\( - 2^{9} \cdot 29 \) |
$0$ |
$1$ |
$\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.15.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(22.340410\) |
\(1.396276\) |
$[136,397,10491,-58]$ |
$[272,2024,51968,2509680,-14848]$ |
$[-\frac{2907867136}{29},-\frac{79551296}{29},-258944]$ |
$y^2 + x^3y = x^5 - 4x^3 - 2x^2 + 4x + 2$ |
| 14848.d.59392.1 |
14848.d |
\( 2^{9} \cdot 29 \) |
\( 2^{11} \cdot 29 \) |
$1$ |
$1$ |
$\mathsf{trivial}$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$5$ |
$1$ |
2.6.1 |
✓ |
✓ |
$1$ |
\( 5 \) |
\(0.026427\) |
\(9.060001\) |
\(1.197124\) |
$[160,142,17416,7424]$ |
$[160,972,-1792,-307876,59392]$ |
$[\frac{51200000}{29},\frac{1944000}{29},-\frac{22400}{29}]$ |
$y^2 + (x^3 + x^2)y = -2x^3 - 4x^2 - 4x - 2$ |
| 14848.e.950272.1 |
14848.e |
\( 2^{9} \cdot 29 \) |
\( - 2^{15} \cdot 29 \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(3.045869\) |
\(0.761467\) |
$[276,909,35055,-116]$ |
$[1104,41088,4093952,707874816,-950272]$ |
$[-\frac{50049003168}{29},-\frac{1687222224}{29},-\frac{152275824}{29}]$ |
$y^2 = 2x^5 + x^4 - 6x^3 - x^2 + 4x - 2$ |
| 14848.f.950272.1 |
14848.f |
\( 2^{9} \cdot 29 \) |
\( - 2^{15} \cdot 29 \) |
$0$ |
$1$ |
$\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$1$ |
$1$ |
2.60.1 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(13.441730\) |
\(1.680216\) |
$[276,909,35055,-116]$ |
$[1104,41088,4093952,707874816,-950272]$ |
$[-\frac{50049003168}{29},-\frac{1687222224}{29},-\frac{152275824}{29}]$ |
$y^2 = 2x^5 - x^4 - 6x^3 + x^2 + 4x + 2$ |
