Atkin-Lehner |
2- 3+ 31- 47- |
Signs for the Atkin-Lehner involutions |
Class |
69936t |
Isogeny class |
Conductor |
69936 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
118272 |
Modular degree for the optimal curve |
Δ |
-5240526946416 = -1 · 24 · 314 · 31 · 472 |
Discriminant |
Eigenvalues |
2- 3+ -3 -3 -2 -4 -2 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,3478,75651] |
[a1,a2,a3,a4,a6] |
Generators |
[-15:141:1] [161:2187:1] |
Generators of the group modulo torsion |
j |
290715098300672/327532934151 |
j-invariant |
L |
6.1774489028719 |
L(r)(E,1)/r! |
Ω |
0.50905643474024 |
Real period |
R |
3.0337740971947 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999529 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
17484c1 |
Quadratic twists by: -4 |