Atkin-Lehner |
2- 3- 31+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
69936z |
Isogeny class |
Conductor |
69936 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
155520 |
Modular degree for the optimal curve |
Δ |
82499862528 = 221 · 33 · 31 · 47 |
Discriminant |
Eigenvalues |
2- 3- 2 0 -4 6 -3 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-65912,-6535212] |
[a1,a2,a3,a4,a6] |
j |
7731501112194553/20141568 |
j-invariant |
L |
3.5755198810344 |
L(r)(E,1)/r! |
Ω |
0.29795998999355 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8742c1 |
Quadratic twists by: -4 |