Atkin-Lehner |
2+ 3- 5- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
67680l |
Isogeny class |
Conductor |
67680 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1208320 |
Modular degree for the optimal curve |
Δ |
-277352311159664640 = -1 · 212 · 310 · 5 · 475 |
Discriminant |
Eigenvalues |
2+ 3- 5- -4 6 1 -2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-634152,196018544] |
[a1,a2,a3,a4,a6] |
Generators |
[-380:19548:1] |
Generators of the group modulo torsion |
j |
-9445312588271104/92884727835 |
j-invariant |
L |
5.9394406894469 |
L(r)(E,1)/r! |
Ω |
0.31046121063049 |
Real period |
R |
4.7827558530888 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000416 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
67680be1 22560o1 |
Quadratic twists by: -4 -3 |