Atkin-Lehner |
2- 31+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
117242g |
Isogeny class |
Conductor |
117242 |
Conductor |
∏ cp |
144 |
Product of Tamagawa factors cp |
deg |
9999360 |
Modular degree for the optimal curve |
Δ |
5.3244299370915E+22 |
Discriminant |
Eigenvalues |
2- 1 3 -1 -3 -1 -3 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-19502554,31234267492] |
[a1,a2,a3,a4,a6] |
Generators |
[16213068:1053484762:12167] |
Generators of the group modulo torsion |
j |
961843977602977/62428020736 |
j-invariant |
L |
14.837510035908 |
L(r)(E,1)/r! |
Ω |
0.11012332511421 |
Real period |
R |
8.4209623781026 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999946722 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
117242k1 |
Quadratic twists by: -31 |