Atkin-Lehner |
2- 3+ 13+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
117624bi |
Isogeny class |
Conductor |
117624 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
946176 |
Modular degree for the optimal curve |
Δ |
5539741277617872 = 24 · 38 · 137 · 292 |
Discriminant |
Eigenvalues |
2- 3+ -2 -4 -6 13+ 2 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-133059,18379620] |
[a1,a2,a3,a4,a6] |
Generators |
[-339:4941:1] [-212:6084:1] |
Generators of the group modulo torsion |
j |
3373491693568/71731413 |
j-invariant |
L |
7.0762246176826 |
L(r)(E,1)/r! |
Ω |
0.42793229041411 |
Real period |
R |
2.0669813820886 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000001468 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
9048d1 |
Quadratic twists by: 13 |