Atkin-Lehner |
2+ 3+ 5- 7- 11- 17- |
Signs for the Atkin-Lehner involutions |
Class |
117810r |
Isogeny class |
Conductor |
117810 |
Conductor |
∏ cp |
432 |
Product of Tamagawa factors cp |
deg |
5308416 |
Modular degree for the optimal curve |
Δ |
553687396416000000 = 212 · 33 · 56 · 72 · 113 · 173 |
Discriminant |
Eigenvalues |
2+ 3+ 5- 7- 11- -4 17- 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-20034309,34520132565] |
[a1,a2,a3,a4,a6] |
Generators |
[20718:-6789:8] |
Generators of the group modulo torsion |
j |
32936925972917687507274123/20506940608000000 |
j-invariant |
L |
5.3378887764573 |
L(r)(E,1)/r! |
Ω |
0.24074234358553 |
Real period |
R |
1.8477184259212 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000012642 |
(Analytic) order of Ш |
t |
6 |
Number of elements in the torsion subgroup |
Twists |
117810cl3 |
Quadratic twists by: -3 |