Atkin-Lehner |
3- 11+ 19+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
69597b |
Isogeny class |
Conductor |
69597 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
267264 |
Modular degree for the optimal curve |
Δ |
75639626525133 = 310 · 113 · 19 · 373 |
Discriminant |
Eigenvalues |
2 3- 2 0 11+ -6 3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-11289,-195057] |
[a1,a2,a3,a4,a6] |
Generators |
[2658:45765:8] |
Generators of the group modulo torsion |
j |
218254196518912/103758061077 |
j-invariant |
L |
14.370205752523 |
L(r)(E,1)/r! |
Ω |
0.48533430546241 |
Real period |
R |
4.9348135193908 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000028 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
23199g1 |
Quadratic twists by: -3 |