Atkin-Lehner |
2+ 7+ 71- |
Signs for the Atkin-Lehner involutions |
Class |
111328c |
Isogeny class |
Conductor |
111328 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
131712 |
Modular degree for the optimal curve |
Δ |
1676496367616 = 212 · 78 · 71 |
Discriminant |
Eigenvalues |
2+ -2 -1 7+ 0 0 -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-3201,-32369] |
[a1,a2,a3,a4,a6] |
Generators |
[-33:196:1] [-22:167:1] |
Generators of the group modulo torsion |
j |
153664/71 |
j-invariant |
L |
7.6450149885707 |
L(r)(E,1)/r! |
Ω |
0.66341601698487 |
Real period |
R |
0.96030931710305 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000002432 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
111328u1 111328r1 |
Quadratic twists by: -4 -7 |