Atkin-Lehner |
2- 3+ 13+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
69966v |
Isogeny class |
Conductor |
69966 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
387072 |
Modular degree for the optimal curve |
Δ |
7272145505933568 = 28 · 39 · 137 · 23 |
Discriminant |
Eigenvalues |
2- 3+ 0 0 -4 13+ -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-52760,2232091] |
[a1,a2,a3,a4,a6] |
Generators |
[257:2237:1] |
Generators of the group modulo torsion |
j |
170953875/76544 |
j-invariant |
L |
9.2532806932154 |
L(r)(E,1)/r! |
Ω |
0.37595108229153 |
Real period |
R |
1.5383119521471 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000246 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69966a1 5382a1 |
Quadratic twists by: -3 13 |