Atkin-Lehner |
2+ 3- 5+ 11+ 83+ |
Signs for the Atkin-Lehner involutions |
Class |
82170g |
Isogeny class |
Conductor |
82170 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
59904 |
Modular degree for the optimal curve |
Δ |
-41598562500 = -1 · 22 · 36 · 56 · 11 · 83 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 1 11+ -3 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,45,9801] |
[a1,a2,a3,a4,a6] |
Generators |
[-18:63:1] [-17:71:1] |
Generators of the group modulo torsion |
j |
13651919/57062500 |
j-invariant |
L |
7.9224663258175 |
L(r)(E,1)/r! |
Ω |
0.90002045757006 |
Real period |
R |
1.1003175343233 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000133 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
9130k1 |
Quadratic twists by: -3 |