Atkin-Lehner |
3- 13+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
8619k |
Isogeny class |
Conductor |
8619 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
11856 |
Modular degree for the optimal curve |
Δ |
-41602266771 = -1 · 3 · 138 · 17 |
Discriminant |
Eigenvalues |
2 3- -3 -2 4 13+ 17- 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-732,12185] |
[a1,a2,a3,a4,a6] |
Generators |
[4762:116159:8] |
Generators of the group modulo torsion |
j |
-53248/51 |
j-invariant |
L |
8.1336955372799 |
L(r)(E,1)/r! |
Ω |
1.0437782189569 |
Real period |
R |
7.7925515109984 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
25857o1 8619l1 |
Quadratic twists by: -3 13 |