Atkin-Lehner |
2+ 7- 19- |
Signs for the Atkin-Lehner involutions |
Class |
59584z |
Isogeny class |
Conductor |
59584 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
12096 |
Modular degree for the optimal curve |
Δ |
-143061184 = -1 · 26 · 76 · 19 |
Discriminant |
Eigenvalues |
2+ 0 -1 7- -3 -4 3 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-98,-686] |
[a1,a2,a3,a4,a6] |
Generators |
[177:2351:1] |
Generators of the group modulo torsion |
j |
-13824/19 |
j-invariant |
L |
3.7645902262986 |
L(r)(E,1)/r! |
Ω |
0.72230685547618 |
Real period |
R |
5.2118987905489 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999995674 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
59584p1 29792h1 1216a1 |
Quadratic twists by: -4 8 -7 |