Atkin-Lehner |
3+ 5+ 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
117975n |
Isogeny class |
Conductor |
117975 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
656640 |
Modular degree for the optimal curve |
Δ |
8163639580078125 = 312 · 510 · 112 · 13 |
Discriminant |
Eigenvalues |
0 3+ 5+ 2 11- 13- 3 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-73333,6311568] |
[a1,a2,a3,a4,a6] |
Generators |
[-102:3566:1] |
Generators of the group modulo torsion |
j |
36909875200/6908733 |
j-invariant |
L |
4.6001480782173 |
L(r)(E,1)/r! |
Ω |
0.3939939878058 |
Real period |
R |
5.8378405273621 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999998676518 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117975cl1 117975g1 |
Quadratic twists by: 5 -11 |