Atkin-Lehner |
2- 3- 7- 41+ |
Signs for the Atkin-Lehner involutions |
Class |
82656bj |
Isogeny class |
Conductor |
82656 |
Conductor |
∏ cp |
56 |
Product of Tamagawa factors cp |
deg |
430080 |
Modular degree for the optimal curve |
Δ |
-302467605221376 = -1 · 212 · 37 · 77 · 41 |
Discriminant |
Eigenvalues |
2- 3- -3 7- -2 -1 -2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-134364,18975584] |
[a1,a2,a3,a4,a6] |
Generators |
[-410:2268:1] [206:196:1] |
Generators of the group modulo torsion |
j |
-89843157911872/101295789 |
j-invariant |
L |
9.3683340902669 |
L(r)(E,1)/r! |
Ω |
0.54353192512591 |
Real period |
R |
0.3077863000229 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.000000000027 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
82656j1 27552e1 |
Quadratic twists by: -4 -3 |