Atkin-Lehner |
2- 3- 11+ |
Signs for the Atkin-Lehner involutions |
Class |
69696fj |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
368640 |
Modular degree for the optimal curve |
Δ |
15452252209152 = 216 · 311 · 113 |
Discriminant |
Eigenvalues |
2- 3- -4 -4 11+ 6 6 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-33132,-2313520] |
[a1,a2,a3,a4,a6] |
Generators |
[-107:81:1] |
Generators of the group modulo torsion |
j |
63253004/243 |
j-invariant |
L |
4.3997830034903 |
L(r)(E,1)/r! |
Ω |
0.3539468013886 |
Real period |
R |
1.5538292005406 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000014 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69696bg1 17424n1 23232cs1 69696fi1 |
Quadratic twists by: -4 8 -3 -11 |