Atkin-Lehner |
3- 5+ 31- 59- |
Signs for the Atkin-Lehner involutions |
Class |
82305f |
Isogeny class |
Conductor |
82305 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
39936 |
Modular degree for the optimal curve |
Δ |
15500089125 = 37 · 53 · 312 · 59 |
Discriminant |
Eigenvalues |
0 3- 5+ -2 -3 3 -3 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-678,3208] |
[a1,a2,a3,a4,a6] |
Generators |
[-28:15:1] [-2:67:1] |
Generators of the group modulo torsion |
j |
47280848896/21262125 |
j-invariant |
L |
7.7233812248448 |
L(r)(E,1)/r! |
Ω |
1.1156602756535 |
Real period |
R |
1.7306749629964 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999996274 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
27435d1 |
Quadratic twists by: -3 |