Atkin-Lehner |
2+ 3- 31+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
69936g |
Isogeny class |
Conductor |
69936 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
28416 |
Modular degree for the optimal curve |
Δ |
34688256 = 28 · 3 · 312 · 47 |
Discriminant |
Eigenvalues |
2+ 3- -1 -3 3 -4 -6 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-721,7211] |
[a1,a2,a3,a4,a6] |
Generators |
[-2:93:1] |
Generators of the group modulo torsion |
j |
162140591104/135501 |
j-invariant |
L |
5.9970379824868 |
L(r)(E,1)/r! |
Ω |
2.0519223731393 |
Real period |
R |
1.461321846631 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999992801 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34968a1 |
Quadratic twists by: -4 |