Atkin-Lehner |
2- 3- 31- |
Signs for the Atkin-Lehner involutions |
Class |
69192bh |
Isogeny class |
Conductor |
69192 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
2232000 |
Modular degree for the optimal curve |
Δ |
6.1184923771802E+20 |
Discriminant |
Eigenvalues |
2- 3- -1 3 -5 -1 3 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-2770563,-1316940946] |
[a1,a2,a3,a4,a6] |
j |
3844 |
j-invariant |
L |
2.1469545646111 |
L(r)(E,1)/r! |
Ω |
0.11927525482953 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
9 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7688b1 69192bd1 |
Quadratic twists by: -3 -31 |