Atkin-Lehner |
3- 19+ 71+ |
Signs for the Atkin-Lehner involutions |
Class |
4047a |
Isogeny class |
Conductor |
4047 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
4272 |
Modular degree for the optimal curve |
Δ |
-13621364271 = -1 · 312 · 192 · 71 |
Discriminant |
Eigenvalues |
-1 3- -2 -4 4 6 6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,291,-5256] |
[a1,a2,a3,a4,a6] |
j |
2724641702063/13621364271 |
j-invariant |
L |
0.94805749056202 |
L(r)(E,1)/r! |
Ω |
0.63203832704135 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
64752k1 12141f1 101175b1 76893d1 |
Quadratic twists by: -4 -3 5 -19 |