Atkin-Lehner |
2- 5- 7+ 11- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
117040bz |
Isogeny class |
Conductor |
117040 |
Conductor |
∏ cp |
192 |
Product of Tamagawa factors cp |
deg |
1179648 |
Modular degree for the optimal curve |
Δ |
1982657600000000 = 212 · 58 · 72 · 113 · 19 |
Discriminant |
Eigenvalues |
2- 0 5- 7+ 11- -6 -6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-416387,103395266] |
[a1,a2,a3,a4,a6] |
Generators |
[-623:11000:1] [-73:11550:1] |
Generators of the group modulo torsion |
j |
1949194826613160281/484047265625 |
j-invariant |
L |
11.456419634616 |
L(r)(E,1)/r! |
Ω |
0.4549178346078 |
Real period |
R |
0.52465608254353 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000002932 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
7315f1 |
Quadratic twists by: -4 |