Atkin-Lehner |
2+ 7+ 13+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
99008f |
Isogeny class |
Conductor |
99008 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
172032 |
Modular degree for the optimal curve |
Δ |
-1386134870848 = -1 · 26 · 78 · 13 · 172 |
Discriminant |
Eigenvalues |
2+ 2 0 7+ 4 13+ 17- 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-13588,-607770] |
[a1,a2,a3,a4,a6] |
j |
-4335531180616000/21658357357 |
j-invariant |
L |
3.536455681725 |
L(r)(E,1)/r! |
Ω |
0.22102848573997 |
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 |
99008bc1 49504n2 |
Quadratic twists by: -4 8 |