Atkin-Lehner |
2- 17- 47- |
Signs for the Atkin-Lehner involutions |
Class |
51136n |
Isogeny class |
Conductor |
51136 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
36864 |
Modular degree for the optimal curve |
Δ |
-53619982336 = -1 · 226 · 17 · 47 |
Discriminant |
Eigenvalues |
2- 0 -2 4 -4 2 17- 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,724,-8240] |
[a1,a2,a3,a4,a6] |
j |
160103007/204544 |
j-invariant |
L |
2.3961223694413 |
L(r)(E,1)/r! |
Ω |
0.59903059245332 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
51136c1 12784e1 |
Quadratic twists by: -4 8 |