| 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 |
| 864.a.442368.1 |
864.a |
\( 2^{5} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{3} \) |
$0$ |
$1$ |
$\Z/12\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$2$ |
2.90.3, 3.720.4 |
✓ |
✓ |
$1$ |
\( 2 \cdot 3 \) |
\(1.000000\) |
\(9.071483\) |
\(0.377978\) |
$[552,45,7083,54]$ |
$[2208,202656,24809472,3427464960,442368]$ |
$[118634674176,4931431104,273421056]$ |
$y^2 = x^6 - 4x^4 + 6x^2 - 3$ |
| 1728.b.442368.1 |
1728.b |
\( 2^{6} \cdot 3^{3} \) |
\( - 2^{14} \cdot 3^{3} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.90.4, 3.720.4 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(7.091187\) |
\(0.590932\) |
$[552,45,7083,54]$ |
$[2208,202656,24809472,3427464960,442368]$ |
$[118634674176,4931431104,273421056]$ |
$y^2 = x^6 + 4x^4 + 6x^2 + 3$ |
| 3456.d.442368.1 |
3456.d |
\( 2^{7} \cdot 3^{3} \) |
\( - 2^{14} \cdot 3^{3} \) |
$0$ |
$1$ |
$\Z/4\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.90.4, 3.360.2 |
|
✓ |
$1$ |
\( 2 \) |
\(1.000000\) |
\(5.237423\) |
\(0.654678\) |
$[552,45,7083,54]$ |
$[2208,202656,24809472,3427464960,442368]$ |
$[118634674176,4931431104,273421056]$ |
$y^2 = -x^6 - 4x^4 - 6x^2 - 3$ |
| 6912.a.13824.1 |
6912.a |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{9} \cdot 3^{3} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.45.1, 3.720.4 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(12.829014\) |
\(1.069085\) |
$[552,45,7083,54]$ |
$[1104,50664,3101184,214216560,13824]$ |
$[118634674176,4931431104,273421056]$ |
$y^2 + x^3y = -2x^4 + 6x^2 - 6$ |
| 6912.c.13824.1 |
6912.c |
\( 2^{8} \cdot 3^{3} \) |
\( - 2^{9} \cdot 3^{3} \) |
$0$ |
$1$ |
$\Z/6\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.45.1, 3.720.4 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(10.028453\) |
\(0.835704\) |
$[552,45,7083,54]$ |
$[1104,50664,3101184,214216560,13824]$ |
$[118634674176,4931431104,273421056]$ |
$y^2 + x^3y = 2x^4 + 6x^2 + 6$ |
| 6912.e.442368.1 |
6912.e |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{3} \) |
$0$ |
$1$ |
$\Z/2\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$2$ |
2.90.3, 3.360.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(4.094099\) |
\(1.023525\) |
$[552,45,7083,54]$ |
$[2208,202656,24809472,3427464960,442368]$ |
$[118634674176,4931431104,273421056]$ |
$y^2 = -x^6 + 4x^4 - 6x^2 + 3$ |
| 13824.a.13824.1 |
13824.a |
\( 2^{9} \cdot 3^{3} \) |
\( 2^{9} \cdot 3^{3} \) |
$1$ |
$2$ |
$\Z/4\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.45.1, 3.360.2 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.306469\) |
\(12.829014\) |
\(1.047545\) |
$[552,45,7083,54]$ |
$[1104,50664,3101184,214216560,13824]$ |
$[118634674176,4931431104,273421056]$ |
$y^2 + y = 2x^6 - 4x^4 + 3x^2 - 1$ |
| 13824.b.13824.1 |
13824.b |
\( 2^{9} \cdot 3^{3} \) |
\( - 2^{9} \cdot 3^{3} \) |
$0$ |
$2$ |
$\Z/4\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$0$ |
$0$ |
2.45.1, 3.360.2 |
|
|
$2$ |
\( 1 \) |
\(1.000000\) |
\(7.406835\) |
\(0.925854\) |
$[552,45,7083,54]$ |
$[1104,50664,3101184,214216560,13824]$ |
$[118634674176,4931431104,273421056]$ |
$y^2 + y = -2x^6 - 4x^4 - 3x^2 - 1$ |
