Atkin-Lehner |
2+ 3- 11- 43+ |
Signs for the Atkin-Lehner involutions |
Class |
68112n |
Isogeny class |
Conductor |
68112 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
36864 |
Modular degree for the optimal curve |
Δ |
54072822672 = 24 · 310 · 113 · 43 |
Discriminant |
Eigenvalues |
2+ 3- 0 -3 11- -2 2 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1335,15077] |
[a1,a2,a3,a4,a6] |
Generators |
[4:99:1] |
Generators of the group modulo torsion |
j |
22559008000/4635873 |
j-invariant |
L |
5.503484055759 |
L(r)(E,1)/r! |
Ω |
1.0599521437087 |
Real period |
R |
0.86536675080761 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000015 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34056f1 22704b1 |
Quadratic twists by: -4 -3 |