Atkin-Lehner |
11- 13- 71+ |
Signs for the Atkin-Lehner involutions |
Class |
111683c |
Isogeny class |
Conductor |
111683 |
Conductor |
∏ cp |
3 |
Product of Tamagawa factors cp |
deg |
79920 |
Modular degree for the optimal curve |
Δ |
13513643 = 114 · 13 · 71 |
Discriminant |
Eigenvalues |
1 -2 0 2 11- 13- 6 -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-6416,-198321] |
[a1,a2,a3,a4,a6] |
Generators |
[-15897:7832:343] |
Generators of the group modulo torsion |
j |
1994567463625/923 |
j-invariant |
L |
5.1829923095915 |
L(r)(E,1)/r! |
Ω |
0.53344738046502 |
Real period |
R |
3.2386776336569 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000019403 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
111683a1 |
Quadratic twists by: -11 |