Atkin-Lehner |
3- 7- 19+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
12369j |
Isogeny class |
Conductor |
12369 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
Δ |
84838971 = 3 · 7 · 194 · 31 |
Discriminant |
Eigenvalues |
1 3- 2 7- 4 2 2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-3480,-79289] |
[a1,a2,a3,a4,a6] |
j |
4658885483793913/84838971 |
j-invariant |
L |
4.9729049215322 |
L(r)(E,1)/r! |
Ω |
0.62161311519152 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
16 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
37107n4 86583k4 |
Quadratic twists by: -3 -7 |