Atkin-Lehner |
2- 3- 5+ 11+ 83+ |
Signs for the Atkin-Lehner involutions |
Class |
82170bn |
Isogeny class |
Conductor |
82170 |
Conductor |
∏ cp |
52 |
Product of Tamagawa factors cp |
deg |
399360 |
Modular degree for the optimal curve |
Δ |
165616856064000 = 213 · 311 · 53 · 11 · 83 |
Discriminant |
Eigenvalues |
2- 3- 5+ 2 11+ -1 2 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-99158,12026981] |
[a1,a2,a3,a4,a6] |
Generators |
[153:-725:1] |
Generators of the group modulo torsion |
j |
147902444959927321/227183616000 |
j-invariant |
L |
10.431171550172 |
L(r)(E,1)/r! |
Ω |
0.57319415259434 |
Real period |
R |
0.34996772376458 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001462 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
27390j1 |
Quadratic twists by: -3 |