Atkin-Lehner |
3- 11- 47- |
Signs for the Atkin-Lehner involutions |
Class |
51183i |
Isogeny class |
Conductor |
51183 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
61440 |
Modular degree for the optimal curve |
Δ |
-4916618557983 = -1 · 310 · 116 · 47 |
Discriminant |
Eigenvalues |
-1 3- -2 0 11- 2 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-2201,114392] |
[a1,a2,a3,a4,a6] |
Generators |
[-60:196:1] [18:274:1] |
Generators of the group modulo torsion |
j |
-912673/3807 |
j-invariant |
L |
5.8969392466414 |
L(r)(E,1)/r! |
Ω |
0.67018363509406 |
Real period |
R |
4.3994951068982 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000004 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
17061c1 423c1 |
Quadratic twists by: -3 -11 |