Atkin-Lehner |
2- 31+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
117242h |
Isogeny class |
Conductor |
117242 |
Conductor |
∏ cp |
60 |
Product of Tamagawa factors cp |
deg |
2976000 |
Modular degree for the optimal curve |
Δ |
3249774131525592064 = 210 · 318 · 612 |
Discriminant |
Eigenvalues |
2- -1 -3 -1 3 -7 5 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-1121507,-449305983] |
[a1,a2,a3,a4,a6] |
Generators |
[-561:2202:1] |
Generators of the group modulo torsion |
j |
182909453233/3810304 |
j-invariant |
L |
4.4610901537391 |
L(r)(E,1)/r! |
Ω |
0.14689235133365 |
Real period |
R |
0.50616320260782 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999425281 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117242i1 |
Quadratic twists by: -31 |