Atkin-Lehner |
2+ 3- 7- 31- |
Signs for the Atkin-Lehner involutions |
Class |
31248x |
Isogeny class |
Conductor |
31248 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
221184 |
Modular degree for the optimal curve |
Δ |
52077884802048 = 210 · 314 · 73 · 31 |
Discriminant |
Eigenvalues |
2+ 3- 4 7- 6 -6 6 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-33843,-2371070] |
[a1,a2,a3,a4,a6] |
j |
5742523604164/69763113 |
j-invariant |
L |
4.2270035446964 |
L(r)(E,1)/r! |
Ω |
0.35225029539108 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
15624t1 124992hb1 10416n1 |
Quadratic twists by: -4 8 -3 |