Atkin-Lehner |
2+ 11+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
31768a |
Isogeny class |
Conductor |
31768 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
76608 |
Modular degree for the optimal curve |
Δ |
32880178047376 = 24 · 112 · 198 |
Discriminant |
Eigenvalues |
2+ 1 3 -4 11+ 1 1 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-16004,-734167] |
[a1,a2,a3,a4,a6] |
Generators |
[-64:179:1] |
Generators of the group modulo torsion |
j |
1668352/121 |
j-invariant |
L |
6.8763686625977 |
L(r)(E,1)/r! |
Ω |
0.42640601563772 |
Real period |
R |
4.0315851620395 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
63536e1 31768f1 |
Quadratic twists by: -4 -19 |