Atkin-Lehner |
2- 3- 13- 53- |
Signs for the Atkin-Lehner involutions |
Class |
33072x |
Isogeny class |
Conductor |
33072 |
Conductor |
∏ cp |
36 |
Product of Tamagawa factors cp |
deg |
27648 |
Modular degree for the optimal curve |
Δ |
71982894672 = 24 · 36 · 133 · 532 |
Discriminant |
Eigenvalues |
2- 3- -2 2 4 13- -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-1209,-10170] |
[a1,a2,a3,a4,a6] |
Generators |
[-18:78:1] |
Generators of the group modulo torsion |
j |
12224801062912/4498930917 |
j-invariant |
L |
6.8225547276896 |
L(r)(E,1)/r! |
Ω |
0.83462634428846 |
Real period |
R |
0.90826468826138 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
8268c1 99216bm1 |
Quadratic twists by: -4 -3 |