Atkin-Lehner |
2- 3+ 5- 37+ |
Signs for the Atkin-Lehner involutions |
Class |
82140f |
Isogeny class |
Conductor |
82140 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
3677184 |
Modular degree for the optimal curve |
Δ |
6228480458696130000 = 24 · 38 · 54 · 377 |
Discriminant |
Eigenvalues |
2- 3+ 5- 4 -4 -2 -2 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-10515745,-13121214218] |
[a1,a2,a3,a4,a6] |
Generators |
[333447316031296:-19180362291401745:59501707264] |
Generators of the group modulo torsion |
j |
3132662187311104/151723125 |
j-invariant |
L |
6.1851401050269 |
L(r)(E,1)/r! |
Ω |
0.08383797921471 |
Real period |
R |
18.443729684676 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002012 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
2220b1 |
Quadratic twists by: 37 |