Atkin-Lehner |
3- 7- 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
117117bl |
Isogeny class |
Conductor |
117117 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
248832 |
Modular degree for the optimal curve |
Δ |
-18654388615863 = -1 · 38 · 76 · 11 · 133 |
Discriminant |
Eigenvalues |
-1 3- -2 7- 11+ 13- 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-13136,618882] |
[a1,a2,a3,a4,a6] |
Generators |
[-770:8319:8] [-42:1067:1] |
Generators of the group modulo torsion |
j |
-156503678869/11647251 |
j-invariant |
L |
7.0864176467323 |
L(r)(E,1)/r! |
Ω |
0.6755393697257 |
Real period |
R |
0.87416785805622 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000484 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
39039o1 117117bc1 |
Quadratic twists by: -3 13 |