Atkin-Lehner |
2- 3+ 17- 67+ |
Signs for the Atkin-Lehner involutions |
Class |
82008k |
Isogeny class |
Conductor |
82008 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
186624 |
Modular degree for the optimal curve |
Δ |
206107869579264 = 211 · 39 · 17 · 673 |
Discriminant |
Eigenvalues |
2- 3+ 1 1 3 -1 17- 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-36747,2621862] |
[a1,a2,a3,a4,a6] |
Generators |
[39624:251613:512] |
Generators of the group modulo torsion |
j |
136134479574/5112971 |
j-invariant |
L |
8.1477567361385 |
L(r)(E,1)/r! |
Ω |
0.55892390632931 |
Real period |
R |
7.2887889048842 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002311 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
82008a1 |
Quadratic twists by: -3 |