Atkin-Lehner |
2+ 3- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
89232r |
Isogeny class |
Conductor |
89232 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
11520 |
Modular degree for the optimal curve |
Δ |
11421696 = 211 · 3 · 11 · 132 |
Discriminant |
Eigenvalues |
2+ 3- -1 0 11- 13+ 5 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-56,-12] |
[a1,a2,a3,a4,a6] |
Generators |
[-6:12:1] |
Generators of the group modulo torsion |
j |
57122/33 |
j-invariant |
L |
8.380454266131 |
L(r)(E,1)/r! |
Ω |
1.9248646350692 |
Real period |
R |
1.0884472224998 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000003836 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
44616a1 89232m1 |
Quadratic twists by: -4 13 |