| 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 |
| 676.b.17576.1 |
676.b |
\( 2^{2} \cdot 13^{2} \) |
\( - 2^{3} \cdot 13^{3} \) |
$0$ |
$0$ |
$\Z/3\Z\oplus\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\mathrm{M}_2(\Q)\) |
|
$E_1$ |
|
|
|
$D_6$ |
$D_6$ |
$0$ |
$0$ |
2.120.4, 3.17280.1 |
|
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(7.177121\) |
\(0.265819\) |
$[1244,1249,129167,2249728]$ |
$[311,3978,72332,1667692,17576]$ |
$[\frac{2909390022551}{17576},\frac{4602275343}{676},\frac{10349147}{26}]$ |
$y^2 + (x^2 + x)y = -x^6 + 3x^5 - 6x^4 + 6x^3 - 6x^2 + 3x - 1$ |
| 2916.a.5832.1 |
2916.a |
\( 2^{2} \cdot 3^{6} \) |
\( 2^{3} \cdot 3^{6} \) |
$0$ |
$0$ |
$\Z/3\Z\oplus\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_6$ |
$4$ |
$0$ |
2.60.2, 3.17280.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(19.520681\) |
\(0.722988\) |
$[4,369,1257,-3072]$ |
$[3,-138,-356,-5028,-5832]$ |
$[-\frac{1}{24},\frac{23}{36},\frac{89}{162}]$ |
$y^2 + (x^3 + 1)y = x^3$ |
| 2916.b.11664.1 |
2916.b |
\( 2^{2} \cdot 3^{6} \) |
\( - 2^{4} \cdot 3^{6} \) |
$0$ |
$0$ |
$\Z/3\Z\oplus\Z/3\Z$ |
\(\mathrm{M}_2(\mathsf{CM})\) |
\(\Q \times \Q\) |
✓ |
$D_{3,2}$ |
|
|
|
$C_2^2$ |
$C_3:D_4$ |
$4$ |
$0$ |
2.60.2, 3.17280.1 |
✓ |
✓ |
$1$ |
\( 3 \) |
\(1.000000\) |
\(17.695032\) |
\(0.655372\) |
$[40,45,555,6]$ |
$[120,330,-320,-36825,11664]$ |
$[\frac{6400000}{3},\frac{440000}{9},-\frac{32000}{81}]$ |
$y^2 + y = x^6$ |
| 4900.a.98000.1 |
4900.a |
\( 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( - 2^{4} \cdot 5^{3} \cdot 7^{2} \) |
$0$ |
$0$ |
$\Z/3\Z\oplus\Z/3\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$2$ |
$0$ |
2.60.2, 3.5760.3 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(8.504322\) |
\(0.944925\) |
$[1112,1549,528677,12250]$ |
$[1112,50490,3032000,205585975,98000]$ |
$[\frac{106268353943552}{6125},\frac{867820181184}{1225},\frac{1874600704}{49}]$ |
$y^2 + y = x^6 + 4x^4 + 4x^2 + 1$ |
| 26244.c.157464.1 |
26244.c |
\( 2^{2} \cdot 3^{8} \) |
\( 2^{3} \cdot 3^{9} \) |
$0$ |
$0$ |
$\Z/3\Z\oplus\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q \times \Q\) |
✓ |
$J(E_1)$ |
|
|
|
$C_2^2$ |
$D_6$ |
$4$ |
$0$ |
2.60.2, 3.5760.3 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(14.148765\) |
\(1.572085\) |
$[60,945,2295,82944]$ |
$[45,-270,3780,24300,157464]$ |
$[\frac{9375}{8},-\frac{625}{4},\frac{875}{18}]$ |
$y^2 + (x^3 + 1)y = 2x^3$ |
| 26244.d.314928.1 |
26244.d |
\( 2^{2} \cdot 3^{8} \) |
\( 2^{4} \cdot 3^{9} \) |
$1$ |
$1$ |
$\Z/3\Z\oplus\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_3)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$6$ |
$0$ |
2.20.3, 3.5760.3 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(0.985565\) |
\(12.739642\) |
\(1.395083\) |
$[24,189,1107,-162]$ |
$[72,-918,-3024,-265113,-314928]$ |
$[-6144,1088,\frac{448}{9}]$ |
$y^2 + y = x^6 - 2x^3$ |
| 26244.e.472392.1 |
26244.e |
\( 2^{2} \cdot 3^{8} \) |
\( - 2^{3} \cdot 3^{10} \) |
$0$ |
$0$ |
$\Z/3\Z\oplus\Z/3\Z$ |
\(\mathrm{M}_2(\Q)\) |
\(\Q\) |
|
$J(E_3)$ |
|
✓ |
|
$C_2$ |
$D_6$ |
$4$ |
$0$ |
2.20.3, 3.5760.3 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(1.000000\) |
\(12.048083\) |
\(1.338676\) |
$[356,3969,419553,248832]$ |
$[267,1482,-2884,-741588,472392]$ |
$[\frac{5584059449}{1944},\frac{174127343}{2916},-\frac{5711041}{13122}]$ |
$y^2 + (x^3 + 1)y = 2$ |
| 52488.a.629856.1 |
52488.a |
\( 2^{3} \cdot 3^{8} \) |
\( - 2^{5} \cdot 3^{9} \) |
$1$ |
$1$ |
$\Z/3\Z\oplus\Z/3\Z$ |
\(\Q \times \Q\) |
\(\Q \times \Q\) |
✓ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)$ |
|
|
|
$C_2^2$ |
$C_2^2$ |
$6$ |
$0$ |
2.15.2, 3.5760.3 |
✓ |
✓ |
$1$ |
\( 3^{2} \) |
\(0.611870\) |
\(16.925754\) |
\(1.150706\) |
$[264,15984,2059452,10368]$ |
$[396,-17442,-3397248,-412383393,629856]$ |
$[15460896,-1719652,-\frac{7612352}{9}]$ |
$y^2 + (x^3 + x)y = x^4 - 7x^2 + 6$ |
