Atkin-Lehner |
3- 11+ 83- |
Signs for the Atkin-Lehner involutions |
Class |
8217f |
Isogeny class |
Conductor |
8217 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
11520 |
Modular degree for the optimal curve |
Δ |
180478524897 = 39 · 113 · 832 |
Discriminant |
Eigenvalues |
1 3- -4 0 11+ 0 -2 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-6489,201784] |
[a1,a2,a3,a4,a6] |
Generators |
[56:80:1] |
Generators of the group modulo torsion |
j |
41454067728529/247569993 |
j-invariant |
L |
3.4945374585713 |
L(r)(E,1)/r! |
Ω |
1.0182987832879 |
Real period |
R |
1.7158703888893 |
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 |
2739f1 90387o1 |
Quadratic twists by: -3 -11 |