Atkin-Lehner |
2- 3+ 5- 11- 83- |
Signs for the Atkin-Lehner involutions |
Class |
82170bm |
Isogeny class |
Conductor |
82170 |
Conductor |
∏ cp |
102 |
Product of Tamagawa factors cp |
deg |
342720 |
Modular degree for the optimal curve |
Δ |
-294429966336000 = -1 · 217 · 39 · 53 · 11 · 83 |
Discriminant |
Eigenvalues |
2- 3+ 5- 1 11- -3 -2 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-51572,4595671] |
[a1,a2,a3,a4,a6] |
Generators |
[181:989:1] |
Generators of the group modulo torsion |
j |
-770666439108987/14958592000 |
j-invariant |
L |
11.560168852887 |
L(r)(E,1)/r! |
Ω |
0.54715020498463 |
Real period |
R |
0.20713688430851 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000003928 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
82170a1 |
Quadratic twists by: -3 |