Atkin-Lehner |
2+ 5+ 13+ 67- |
Signs for the Atkin-Lehner involutions |
Class |
8710b |
Isogeny class |
Conductor |
8710 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
55296 |
Modular degree for the optimal curve |
Δ |
-37409165148160000 = -1 · 236 · 54 · 13 · 67 |
Discriminant |
Eigenvalues |
2+ 0 5+ 0 4 13+ 2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-76040,-12298944] |
[a1,a2,a3,a4,a6] |
j |
-48624287362698592089/37409165148160000 |
j-invariant |
L |
1.252127596844 |
L(r)(E,1)/r! |
Ω |
0.13912528853822 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
9 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69680m1 78390by1 43550s1 113230r1 |
Quadratic twists by: -4 -3 5 13 |