Atkin-Lehner |
2- 3- 7- 13- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
111384ck |
Isogeny class |
Conductor |
111384 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
64512 |
Modular degree for the optimal curve |
Δ |
9148413456 = 24 · 37 · 7 · 133 · 17 |
Discriminant |
Eigenvalues |
2- 3- -1 7- 0 13- 17+ -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-2343,-43409] |
[a1,a2,a3,a4,a6] |
Generators |
[-27:13:1] |
Generators of the group modulo torsion |
j |
121953162496/784329 |
j-invariant |
L |
6.3018231732192 |
L(r)(E,1)/r! |
Ω |
0.68647504806938 |
Real period |
R |
0.76499784432982 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999983668 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
37128p1 |
Quadratic twists by: -3 |