| 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 |
| 18225.a.18225.1 |
18225.a |
\( 3^{6} \cdot 5^{2} \) |
\( - 3^{6} \cdot 5^{2} \) |
$1$ |
$1$ |
$\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_6)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$4$ |
$0$ |
2.20.3, 3.2880.4 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(0.687921\) |
\(16.468178\) |
\(1.258756\) |
$[196,1305,73965,9600]$ |
$[147,411,-401,-56967,18225]$ |
$[282475249/75,16117913/225,-962801/2025]$ |
$y^2 + (x^3 + 1)y = 1$ |
| 18225.b.54675.1 |
18225.b |
\( 3^{6} \cdot 5^{2} \) |
\( - 3^{7} \cdot 5^{2} \) |
$1$ |
$2$ |
$\Z/4\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$6$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.365966\) |
\(20.922845\) |
\(0.957132\) |
$[120,504,16809,-900]$ |
$[180,594,873,-48924,-54675]$ |
$[-3456000,-63360,-1552/3]$ |
$y^2 + xy = x^5 + x^4 - 3x^3 + x$ |
| 18225.b.492075.1 |
18225.b |
\( 3^{6} \cdot 5^{2} \) |
\( - 3^{9} \cdot 5^{2} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$4$ |
$2$ |
2.30.3 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.365966\) |
\(5.230711\) |
\(0.957132\) |
$[96600,-2736,-87972519,-8100]$ |
$[144900,874837854,7042510419057,63779622232508496,-492075]$ |
$[-129810740161200000000,-5408806213598480000,-8113285003216733200/27]$ |
$y^2 + (x^2 + 1)y = 3x^5 + 23x^4 + 84x^3 - 75x^2 + 20x - 2$ |
| 18225.c.54675.1 |
18225.c |
\( 3^{6} \cdot 5^{2} \) |
\( 3^{7} \cdot 5^{2} \) |
$0$ |
$1$ |
$\Z/3\Z$ |
\(\mathsf{RM}\) |
\(\mathsf{RM}\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$0$ |
$0$ |
2.15.2, 3.720.4 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(6.799615\) |
\(1.511025\) |
$[9900,-339471,-832044249,28800]$ |
$[7425,2424411,997014609,381266193726,54675]$ |
$[412756098046875,18151262105625,1005323064075]$ |
$y^2 + (x^3 + x + 1)y = x^6 - 11x^4 + 5x^3 + 23x^2 - 23x + 1$ |
| 18225.c.164025.1 |
18225.c |
\( 3^{6} \cdot 5^{2} \) |
\( 3^{8} \cdot 5^{2} \) |
$0$ |
$0$ |
$\Z/3\Z$ |
\(\mathsf{RM}\) |
\(\mathsf{RM}\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
✓ |
✓ |
$C_2$ |
$C_2$ |
$2$ |
$0$ |
2.120.2, 3.720.4 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(13.599229\) |
\(1.511025\) |
$[596,21969,3352809,-86400]$ |
$[447,87,-27625,-3088986,-164025]$ |
$[-73439775749/675,-95930521/2025,24532105/729]$ |
$y^2 + (x^3 + x + 1)y = x^6 + 4x^4 + x^3 + 2x^2 + x$ |
