Atkin-Lehner |
2+ 3- 61- |
Signs for the Atkin-Lehner involutions |
Class |
11712o |
Isogeny class |
Conductor |
11712 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1536 |
Modular degree for the optimal curve |
Δ |
5059584 = 210 · 34 · 61 |
Discriminant |
Eigenvalues |
2+ 3- -2 2 -2 2 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-69,171] |
[a1,a2,a3,a4,a6] |
Generators |
[-9:12:1] |
Generators of the group modulo torsion |
j |
35995648/4941 |
j-invariant |
L |
5.1348461940629 |
L(r)(E,1)/r! |
Ω |
2.3333036324009 |
Real period |
R |
1.100338190615 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
11712bb1 732a1 35136x1 |
Quadratic twists by: -4 8 -3 |