Atkin-Lehner |
2+ 3- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
69192g |
Isogeny class |
Conductor |
69192 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
172800 |
Modular degree for the optimal curve |
Δ |
172351183104 = 28 · 36 · 314 |
Discriminant |
Eigenvalues |
2+ 3- -3 -1 -1 7 5 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-37479,2792666] |
[a1,a2,a3,a4,a6] |
j |
33781072 |
j-invariant |
L |
1.8933767928823 |
L(r)(E,1)/r! |
Ω |
0.94668839868169 |
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 |
7688e1 69192x1 |
Quadratic twists by: -3 -31 |