Atkin-Lehner |
3- 13+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
8619j |
Isogeny class |
Conductor |
8619 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
10752 |
Modular degree for the optimal curve |
Δ |
1123261202817 = 34 · 138 · 17 |
Discriminant |
Eigenvalues |
1 3- 0 2 2 13+ 17- 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-5581,-152605] |
[a1,a2,a3,a4,a6] |
Generators |
[-35:29:1] |
Generators of the group modulo torsion |
j |
3981876625/232713 |
j-invariant |
L |
6.5666267050729 |
L(r)(E,1)/r! |
Ω |
0.5543875327639 |
Real period |
R |
2.9612077820072 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
25857f1 663c1 |
Quadratic twists by: -3 13 |