Atkin-Lehner |
2- 3- 31- |
Signs for the Atkin-Lehner involutions |
Class |
69192bi |
Isogeny class |
Conductor |
69192 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
184320 |
Modular degree for the optimal curve |
Δ |
-320907130990704 = -1 · 24 · 36 · 317 |
Discriminant |
Eigenvalues |
2- 3- -1 -3 -2 2 -6 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-2883,863939] |
[a1,a2,a3,a4,a6] |
Generators |
[-83:729:1] [-31:961:1] |
Generators of the group modulo torsion |
j |
-256/31 |
j-invariant |
L |
9.0097726417746 |
L(r)(E,1)/r! |
Ω |
0.44524566030354 |
Real period |
R |
1.2647193230966 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000002 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7688c1 2232j1 |
Quadratic twists by: -3 -31 |