Atkin-Lehner |
2+ 7+ 29+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
12586a |
Isogeny class |
Conductor |
12586 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
6720 |
Modular degree for the optimal curve |
Δ |
-5232553984 = -1 · 212 · 72 · 292 · 31 |
Discriminant |
Eigenvalues |
2+ 0 2 7+ 2 0 8 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,394,1652] |
[a1,a2,a3,a4,a6] |
j |
6754484400327/5232553984 |
j-invariant |
L |
1.7461365342732 |
L(r)(E,1)/r! |
Ω |
0.87306826713661 |
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 |
100688y1 113274bm1 88102b1 |
Quadratic twists by: -4 -3 -7 |