Atkin-Lehner |
2+ 41+ |
Signs for the Atkin-Lehner involutions |
Class |
82a |
Isogeny class |
Conductor |
82 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
4 |
Modular degree for the optimal curve |
Δ |
164 = 22 · 41 |
Discriminant |
Eigenvalues |
2+ -2 -2 -4 -2 4 -2 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-2,0] |
[a1,a2,a3,a4,a6] |
Generators |
[-1:1:1] |
Generators of the group modulo torsion |
j |
389017/164 |
j-invariant |
L |
0.58300155947061 |
L(r)(E,1)/r! |
Ω |
5.1889950403716 |
Real period |
R |
0.22470692491888 |
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 |
656c1 2624b1 738i1 2050e1 |
Quadratic twists by: -4 8 -3 5 |