Atkin-Lehner |
2- 3- 13+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
117312cu |
Isogeny class |
Conductor |
117312 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
156672 |
Modular degree for the optimal curve |
Δ |
-934111346688 = -1 · 221 · 36 · 13 · 47 |
Discriminant |
Eigenvalues |
2- 3- 0 -2 6 13+ 3 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-3713,-99969] |
[a1,a2,a3,a4,a6] |
j |
-21601086625/3563352 |
j-invariant |
L |
3.6366433155356 |
L(r)(E,1)/r! |
Ω |
0.3030535440666 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117312b1 29328m1 |
Quadratic twists by: -4 8 |