Atkin-Lehner |
3- 7+ 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
117117bf |
Isogeny class |
Conductor |
117117 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
101376 |
Modular degree for the optimal curve |
Δ |
-940100384223 = -1 · 38 · 72 · 113 · 133 |
Discriminant |
Eigenvalues |
-1 3- 0 7+ 11- 13- -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,2425,7310] |
[a1,a2,a3,a4,a6] |
Generators |
[6:-152:1] [30:1007:8] |
Generators of the group modulo torsion |
j |
985074875/586971 |
j-invariant |
L |
7.5235101726848 |
L(r)(E,1)/r! |
Ω |
0.53920912949836 |
Real period |
R |
1.162738438301 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999998509 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
39039s1 117117bk1 |
Quadratic twists by: -3 13 |