Atkin-Lehner |
2+ 3- 5+ 11- 83+ |
Signs for the Atkin-Lehner involutions |
Class |
82170p |
Isogeny class |
Conductor |
82170 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
50688 |
Modular degree for the optimal curve |
Δ |
-1497548250 = -1 · 2 · 38 · 53 · 11 · 83 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 2 11- 1 -7 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-900,10786] |
[a1,a2,a3,a4,a6] |
Generators |
[17:5:1] |
Generators of the group modulo torsion |
j |
-110661134401/2054250 |
j-invariant |
L |
4.5910968545747 |
L(r)(E,1)/r! |
Ω |
1.51147915115 |
Real period |
R |
1.5187430312063 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999985389 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
27390s1 |
Quadratic twists by: -3 |