Atkin-Lehner |
2+ 3- 13- 47- |
Signs for the Atkin-Lehner involutions |
Class |
117312bm |
Isogeny class |
Conductor |
117312 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
34560 |
Modular degree for the optimal curve |
Δ |
13725504 = 26 · 33 · 132 · 47 |
Discriminant |
Eigenvalues |
2+ 3- -3 -1 -5 13- -2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-137,-639] |
[a1,a2,a3,a4,a6] |
Generators |
[-8:3:1] [16:39:1] |
Generators of the group modulo torsion |
j |
4475809792/214461 |
j-invariant |
L |
11.13265606717 |
L(r)(E,1)/r! |
Ω |
1.3987620091968 |
Real period |
R |
1.3264891846966 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.000000000376 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117312cg1 1833b1 |
Quadratic twists by: -4 8 |