Atkin-Lehner |
2+ 3+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
69312d |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
486400 |
Modular degree for the optimal curve |
Δ |
15860745721233408 = 214 · 3 · 199 |
Discriminant |
Eigenvalues |
2+ 3+ 2 -4 -2 0 -2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-64017,1488657] |
[a1,a2,a3,a4,a6] |
Generators |
[-429:42704:27] |
Generators of the group modulo torsion |
j |
5488/3 |
j-invariant |
L |
4.3757190249746 |
L(r)(E,1)/r! |
Ω |
0.3414340513297 |
Real period |
R |
6.407853885063 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000829 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69312da1 8664l1 69312bf1 |
Quadratic twists by: -4 8 -19 |