Atkin-Lehner |
2+ 3- 13+ 67+ |
Signs for the Atkin-Lehner involutions |
Class |
15678d |
Isogeny class |
Conductor |
15678 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
269568 |
Modular degree for the optimal curve |
Δ |
-3449890168069423104 = -1 · 218 · 319 · 132 · 67 |
Discriminant |
Eigenvalues |
2+ 3- 3 -1 -2 13+ 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-23013,89379477] |
[a1,a2,a3,a4,a6] |
j |
-1848955724169553/4732359626981376 |
j-invariant |
L |
1.610335633242 |
L(r)(E,1)/r! |
Ω |
0.20129195415525 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
125424x1 5226f1 |
Quadratic twists by: -4 -3 |