Atkin-Lehner |
2- 3+ 5- 11- 83+ |
Signs for the Atkin-Lehner involutions |
Class |
82170bl |
Isogeny class |
Conductor |
82170 |
Conductor |
∏ cp |
54 |
Product of Tamagawa factors cp |
deg |
54720 |
Modular degree for the optimal curve |
Δ |
-2982771000 = -1 · 23 · 33 · 53 · 113 · 83 |
Discriminant |
Eigenvalues |
2- 3+ 5- -1 11- 5 -6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,358,209] |
[a1,a2,a3,a4,a6] |
j |
188428167837/110473000 |
j-invariant |
L |
5.1860289374613 |
L(r)(E,1)/r! |
Ω |
0.86433815769558 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
82170b2 |
Quadratic twists by: -3 |