Atkin-Lehner |
2- 13- 43+ |
Signs for the Atkin-Lehner involutions |
Class |
4472b |
Isogeny class |
Conductor |
4472 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
192 |
Modular degree for the optimal curve |
Δ |
-116272 = -1 · 24 · 132 · 43 |
Discriminant |
Eigenvalues |
2- 0 0 2 0 13- 2 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,10,-11] |
[a1,a2,a3,a4,a6] |
Generators |
[10:33:1] |
Generators of the group modulo torsion |
j |
6912000/7267 |
j-invariant |
L |
3.8145222177728 |
L(r)(E,1)/r! |
Ω |
1.8003019775885 |
Real period |
R |
2.1188235447491 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
8944c1 35776c1 40248m1 111800e1 |
Quadratic twists by: -4 8 -3 5 |