Atkin-Lehner |
3- 7+ 17+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
117453o |
Isogeny class |
Conductor |
117453 |
Conductor |
∏ cp |
84 |
Product of Tamagawa factors cp |
deg |
4708704 |
Modular degree for the optimal curve |
Δ |
-8048717079640587 = -1 · 37 · 78 · 172 · 472 |
Discriminant |
Eigenvalues |
-2 3- 0 7+ -4 3 17+ -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-10574118,13231183970] |
[a1,a2,a3,a4,a6] |
Generators |
[-3732:27001:1] [2025:-11246:1] |
Generators of the group modulo torsion |
j |
-22681506174111232000/1396182987 |
j-invariant |
L |
7.3467604304833 |
L(r)(E,1)/r! |
Ω |
0.31327887165726 |
Real period |
R |
0.27918076071897 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999988311 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117453n1 |
Quadratic twists by: -7 |