Atkin-Lehner |
2+ 3- 11- 19- |
Signs for the Atkin-Lehner involutions |
Class |
120384bw |
Isogeny class |
Conductor |
120384 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
294912 |
Modular degree for the optimal curve |
Δ |
23005740662784 = 224 · 38 · 11 · 19 |
Discriminant |
Eigenvalues |
2+ 3- -2 -2 11- 2 -6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-21036,-1151440] |
[a1,a2,a3,a4,a6] |
Generators |
[-92:72:1] [1586:12573:8] |
Generators of the group modulo torsion |
j |
5386984777/120384 |
j-invariant |
L |
10.186336278287 |
L(r)(E,1)/r! |
Ω |
0.39696251363685 |
Real period |
R |
12.830350383922 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999998049 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
120384cr1 3762n1 40128e1 |
Quadratic twists by: -4 8 -3 |