Atkin-Lehner |
3+ 7- 11+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
82467a |
Isogeny class |
Conductor |
82467 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1327104 |
Modular degree for the optimal curve |
Δ |
6164455892597982441 = 39 · 712 · 113 · 17 |
Discriminant |
Eigenvalues |
-1 3+ 2 7- 11+ -4 17+ 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-472394,36830728] |
[a1,a2,a3,a4,a6] |
j |
5034501056619/2662043923 |
j-invariant |
L |
0.41857747327525 |
L(r)(E,1)/r! |
Ω |
0.20928875583646 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82467e1 11781a1 |
Quadratic twists by: -3 -7 |