Atkin-Lehner |
3- 5- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
117975cl |
Isogeny class |
Conductor |
117975 |
Conductor |
∏ cp |
36 |
Product of Tamagawa factors cp |
deg |
131328 |
Modular degree for the optimal curve |
Δ |
522472933125 = 312 · 54 · 112 · 13 |
Discriminant |
Eigenvalues |
0 3- 5- -2 11- 13+ -3 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-2933,49319] |
[a1,a2,a3,a4,a6] |
Generators |
[43:-68:1] [-17:307:1] |
Generators of the group modulo torsion |
j |
36909875200/6908733 |
j-invariant |
L |
11.150718733676 |
L(r)(E,1)/r! |
Ω |
0.88099733945999 |
Real period |
R |
0.35158129675162 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000145 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117975n1 117975cp1 |
Quadratic twists by: 5 -11 |