Atkin-Lehner |
2- 3+ 7+ 13- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
111384bk |
Isogeny class |
Conductor |
111384 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
1437696 |
Modular degree for the optimal curve |
Δ |
1870479199352994048 = 28 · 39 · 7 · 133 · 176 |
Discriminant |
Eigenvalues |
2- 3+ 2 7+ -4 13- 17+ -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-315279,17691858] |
[a1,a2,a3,a4,a6] |
Generators |
[-441:8424:1] |
Generators of the group modulo torsion |
j |
687824414956656/371211673651 |
j-invariant |
L |
7.22643533659 |
L(r)(E,1)/r! |
Ω |
0.23015198724232 |
Real period |
R |
2.6165446343599 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999569857 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
111384c1 |
Quadratic twists by: -3 |