Atkin-Lehner |
2- 7+ 11- 19- |
Signs for the Atkin-Lehner involutions |
Class |
111188j |
Isogeny class |
Conductor |
111188 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
34560 |
Modular degree for the optimal curve |
Δ |
34245904 = 24 · 72 · 112 · 192 |
Discriminant |
Eigenvalues |
2- -1 -3 7+ 11- -7 -5 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-82,-31] |
[a1,a2,a3,a4,a6] |
Generators |
[-8:7:1] [-2:11:1] |
Generators of the group modulo torsion |
j |
10686208/5929 |
j-invariant |
L |
6.6132554026694 |
L(r)(E,1)/r! |
Ω |
1.6986649953522 |
Real period |
R |
0.32443396327384 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000003129 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
111188d1 |
Quadratic twists by: -19 |