Atkin-Lehner |
2+ 3- 13- 61- |
Signs for the Atkin-Lehner involutions |
Class |
19032j |
Isogeny class |
Conductor |
19032 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
21504 |
Modular degree for the optimal curve |
Δ |
87658004304 = 24 · 312 · 132 · 61 |
Discriminant |
Eigenvalues |
2+ 3- -2 -4 -4 13- -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-3679,83486] |
[a1,a2,a3,a4,a6] |
Generators |
[-70:54:1] [-43:405:1] |
Generators of the group modulo torsion |
j |
344279476959232/5478625269 |
j-invariant |
L |
7.0652175734265 |
L(r)(E,1)/r! |
Ω |
1.0777635353001 |
Real period |
R |
2.1851477131486 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999981 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
38064g1 57096t1 |
Quadratic twists by: -4 -3 |