Atkin-Lehner |
2- 3+ 7+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
85176bg |
Isogeny class |
Conductor |
85176 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1290240 |
Modular degree for the optimal curve |
Δ |
120871715314896 = 24 · 33 · 73 · 138 |
Discriminant |
Eigenvalues |
2- 3+ 2 7+ -2 13+ 6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-9796254,-11801526035] |
[a1,a2,a3,a4,a6] |
j |
49860882714802176/57967 |
j-invariant |
L |
2.7307662367938 |
L(r)(E,1)/r! |
Ω |
0.08533644473432 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
16 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
85176c1 6552c1 |
Quadratic twists by: -3 13 |