Atkin-Lehner |
3- 11- 13- 53+ |
Signs for the Atkin-Lehner involutions |
Class |
68211f |
Isogeny class |
Conductor |
68211 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
15360 |
Modular degree for the optimal curve |
Δ |
-292829823 = -1 · 36 · 11 · 13 · 532 |
Discriminant |
Eigenvalues |
1 3- 0 0 11- 13- -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-132,1043] |
[a1,a2,a3,a4,a6] |
Generators |
[-2:37:1] [2:27:1] |
Generators of the group modulo torsion |
j |
-350402625/401687 |
j-invariant |
L |
12.622151141132 |
L(r)(E,1)/r! |
Ω |
1.5681931594561 |
Real period |
R |
4.0244248819232 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999829 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
7579c1 |
Quadratic twists by: -3 |