Atkin-Lehner |
2- 3- 31- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
69936ba |
Isogeny class |
Conductor |
69936 |
Conductor |
∏ cp |
28 |
Product of Tamagawa factors cp |
deg |
72576 |
Modular degree for the optimal curve |
Δ |
25287738624 = 28 · 37 · 312 · 47 |
Discriminant |
Eigenvalues |
2- 3- -3 -3 -3 0 6 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-757,2159] |
[a1,a2,a3,a4,a6] |
Generators |
[-25:78:1] [-22:93:1] |
Generators of the group modulo torsion |
j |
187648442368/98780229 |
j-invariant |
L |
9.4693274890099 |
L(r)(E,1)/r! |
Ω |
1.0472277579374 |
Real period |
R |
0.32293860137186 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999957 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
17484a1 |
Quadratic twists by: -4 |