| 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 |
| 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.b.13824.1 |
6912.b |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{9} \cdot 3^{3} \) |
$1$ |
$2$ |
$\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2,3$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$3$ |
$1$ |
2.60.1, 3.80.2 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(0.170431\) |
\(8.435547\) |
\(0.718838\) |
$[54,126,2232,54]$ |
$[108,150,-2876,-83277,13824]$ |
$[1062882,54675/4,-19413/8]$ |
$y^2 + x^3y = x^5 - 7x^3 - 17x^2 - 18x - 8$ |
| 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.d.41472.1 |
6912.d |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{9} \cdot 3^{4} \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$2$ |
2.180.3 |
✓ |
✓ |
$1$ |
\( 2^{2} \) |
\(0.118365\) |
\(16.509596\) |
\(0.488541\) |
$[486,378,61200,162]$ |
$[972,38358,1962724,109107891,41472]$ |
$[20920706406,3397502313/4,357706449/8]$ |
$y^2 + y = 6x^5 - 3x^4 - 7x^3 - x^2 + x$ |
| 6912.d.124416.1 |
6912.d |
\( 2^{8} \cdot 3^{3} \) |
\( - 2^{9} \cdot 3^{5} \) |
$1$ |
$3$ |
$\Z/2\Z\oplus\Z/2\Z$ |
\(\Q\) |
\(\Q\) |
|
$\mathrm{USp}(4)$ |
$2$ |
✓ |
✓ |
$C_2$ |
$C_2$ |
$8$ |
$2$ |
2.180.3 |
✓ |
✓ |
$1$ |
\( 2^{3} \) |
\(0.059183\) |
\(16.509596\) |
\(0.488541\) |
$[90,18,3600,486]$ |
$[180,1302,-9700,-860301,124416]$ |
$[1518750,244125/4,-60625/24]$ |
$y^2 + y = 2x^5 + x^4 - x^3 + x^2 - x$ |
| 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 |
✓ |
✓ |
$1$ |
\( 1 \) |
\(1.000000\) |
\(4.094099\) |
\(1.023525\) |
$[552,45,7083,54]$ |
$[2208,202656,24809472,3427464960,442368]$ |
$[118634674176,4931431104,273421056]$ |
$y^2 = -x^6 + 4x^4 - 6x^2 + 3$ |
| 6912.f.884736.2 |
6912.f |
\( 2^{8} \cdot 3^{3} \) |
\( - 2^{15} \cdot 3^{3} \) |
$1$ |
$2$ |
$\Z/4\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.45.1, 3.270.2 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.002365\) |
\(6.076164\) |
\(0.761317\) |
$[1080,333,119313,108]$ |
$[4320,774048,184098816,49039144704,884736]$ |
$[1700611200000,70535124000,3883334400]$ |
$y^2 = x^6 + 5x^4 + 9x^2 + 6$ |
| 6912.f.884736.1 |
6912.f |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{15} \cdot 3^{3} \) |
$1$ |
$2$ |
$\Z/4\Z$ |
\(\mathsf{CM} \times \Q\) |
\(\Q \times \Q\) |
✓ |
$N(\mathrm{U}(1)\times\mathrm{SU}(2))$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$4$ |
$0$ |
2.45.1, 3.270.2 |
✓ |
✓ |
$1$ |
\( 2 \) |
\(1.002365\) |
\(6.076164\) |
\(0.761317\) |
$[1080,333,119313,108]$ |
$[4320,774048,184098816,49039144704,884736]$ |
$[1700611200000,70535124000,3883334400]$ |
$y^2 = -x^6 + 5x^4 - 9x^2 + 6$ |
