Atkin-Lehner |
2+ 7+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
59584o |
Isogeny class |
Conductor |
59584 |
Conductor |
∏ cp |
18 |
Product of Tamagawa factors cp |
deg |
258048 |
Modular degree for the optimal curve |
Δ |
-647835976646656 = -1 · 214 · 78 · 193 |
Discriminant |
Eigenvalues |
2+ -2 1 7+ 3 -6 -2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-19665,1614031] |
[a1,a2,a3,a4,a6] |
Generators |
[-171:76:1] [114:-931:1] |
Generators of the group modulo torsion |
j |
-8904784/6859 |
j-invariant |
L |
7.7901096106791 |
L(r)(E,1)/r! |
Ω |
0.47032457038154 |
Real period |
R |
0.92018128440325 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999966 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
59584bq1 7448b1 59584t1 |
Quadratic twists by: -4 8 -7 |