Atkin-Lehner |
2+ 7+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
40768c |
Isogeny class |
Conductor |
40768 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
27648 |
Modular degree for the optimal curve |
Δ |
415507456 = 210 · 74 · 132 |
Discriminant |
Eigenvalues |
2+ -1 3 7+ -3 13+ 3 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-2809,58241] |
[a1,a2,a3,a4,a6] |
Generators |
[40:91:1] |
Generators of the group modulo torsion |
j |
997335808/169 |
j-invariant |
L |
5.1370197761281 |
L(r)(E,1)/r! |
Ω |
1.6271791449824 |
Real period |
R |
0.52616822513249 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
40768by1 2548c1 40768bk1 |
Quadratic twists by: -4 8 -7 |