Atkin-Lehner |
2+ 5+ 13- 67+ |
Signs for the Atkin-Lehner involutions |
Class |
69680c |
Isogeny class |
Conductor |
69680 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
53760 |
Modular degree for the optimal curve |
Δ |
753658880 = 210 · 5 · 133 · 67 |
Discriminant |
Eigenvalues |
2+ -2 5+ 1 -6 13- -4 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-3216,69124] |
[a1,a2,a3,a4,a6] |
Generators |
[-64:130:1] [27:52:1] |
Generators of the group modulo torsion |
j |
3593411145796/735995 |
j-invariant |
L |
6.7381039722053 |
L(r)(E,1)/r! |
Ω |
1.5539371787246 |
Real period |
R |
0.72269158886929 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000048 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34840h1 |
Quadratic twists by: -4 |