Atkin-Lehner |
3- 11+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
32307h |
Isogeny class |
Conductor |
32307 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
6912 |
Modular degree for the optimal curve |
Δ |
-9595179 = -1 · 34 · 113 · 89 |
Discriminant |
Eigenvalues |
-2 3- -1 0 11+ 1 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,4,-148] |
[a1,a2,a3,a4,a6] |
Generators |
[7:16:1] |
Generators of the group modulo torsion |
j |
4096/7209 |
j-invariant |
L |
3.2914095860891 |
L(r)(E,1)/r! |
Ω |
1.0688603733254 |
Real period |
R |
0.38492043350911 |
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 |
96921m1 32307g1 |
Quadratic twists by: -3 -11 |