Atkin-Lehner |
2- 5+ 13+ 67- |
Signs for the Atkin-Lehner involutions |
Class |
69680q |
Isogeny class |
Conductor |
69680 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
115200 |
Modular degree for the optimal curve |
Δ |
19901304800000 = 28 · 55 · 135 · 67 |
Discriminant |
Eigenvalues |
2- 0 5+ -1 0 13+ -6 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-10703,368202] |
[a1,a2,a3,a4,a6] |
Generators |
[322:409:8] |
Generators of the group modulo torsion |
j |
529663837936464/77739471875 |
j-invariant |
L |
3.7552654494631 |
L(r)(E,1)/r! |
Ω |
0.6567155522278 |
Real period |
R |
5.7182526533162 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001232 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
17420a1 |
Quadratic twists by: -4 |