Atkin-Lehner |
2+ 13+ 103- |
Signs for the Atkin-Lehner involutions |
Class |
85696p |
Isogeny class |
Conductor |
85696 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
552960 |
Modular degree for the optimal curve |
Δ |
11232346112 = 223 · 13 · 103 |
Discriminant |
Eigenvalues |
2+ 2 0 -1 -3 13+ -3 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1999713,1089094625] |
[a1,a2,a3,a4,a6] |
Generators |
[809:384:1] [10448:1058583:1] |
Generators of the group modulo torsion |
j |
3373548958002561625/42848 |
j-invariant |
L |
14.382005915885 |
L(r)(E,1)/r! |
Ω |
0.64652918592119 |
Real period |
R |
5.5612361473053 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999829 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
85696bp1 2678h1 |
Quadratic twists by: -4 8 |