Atkin-Lehner |
5+ 7+ 13+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
21385b |
Isogeny class |
Conductor |
21385 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
1189027385 = 5 · 72 · 133 · 472 |
Discriminant |
Eigenvalues |
1 -2 5+ 7+ -2 13+ 4 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-339,-1759] |
[a1,a2,a3,a4,a6] |
j |
4290223486249/1189027385 |
j-invariant |
L |
1.1362868963123 |
L(r)(E,1)/r! |
Ω |
1.1362868963123 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
106925p1 |
Quadratic twists by: 5 |