Atkin-Lehner |
5+ 7+ 13+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
117845a |
Isogeny class |
Conductor |
117845 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
2428608 |
Modular degree for the optimal curve |
Δ |
3384850196533203125 = 513 · 78 · 13 · 37 |
Discriminant |
Eigenvalues |
1 0 5+ 7+ 4 13+ -3 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-2651840,1660450175] |
[a1,a2,a3,a4,a6] |
Generators |
[122309797296673750:30634224366908033:134611328125000] |
Generators of the group modulo torsion |
j |
357751477145368089/587158203125 |
j-invariant |
L |
6.9470410018892 |
L(r)(E,1)/r! |
Ω |
0.25080824907008 |
Real period |
R |
27.698614489941 |
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 |
117845l1 |
Quadratic twists by: -7 |