Atkin-Lehner |
2- 3- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
13536x |
Isogeny class |
Conductor |
13536 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
7680 |
Modular degree for the optimal curve |
Δ |
-129484536768 = -1 · 26 · 316 · 47 |
Discriminant |
Eigenvalues |
2- 3- 0 0 0 -2 -2 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-165,-17332] |
[a1,a2,a3,a4,a6] |
Generators |
[197:2756:1] |
Generators of the group modulo torsion |
j |
-10648000/2775303 |
j-invariant |
L |
4.6717157323768 |
L(r)(E,1)/r! |
Ω |
0.46542190907087 |
Real period |
R |
5.0187965385032 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
13536k1 27072i2 4512c1 |
Quadratic twists by: -4 8 -3 |