Atkin-Lehner |
2- 11+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
11968r |
Isogeny class |
Conductor |
11968 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
2048 |
Modular degree for the optimal curve |
Δ |
-52084736 = -1 · 214 · 11 · 172 |
Discriminant |
Eigenvalues |
2- -1 1 -2 11+ -2 17- -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-5,349] |
[a1,a2,a3,a4,a6] |
Generators |
[-4:17:1] |
Generators of the group modulo torsion |
j |
-1024/3179 |
j-invariant |
L |
3.355799296124 |
L(r)(E,1)/r! |
Ω |
1.6042376793571 |
Real period |
R |
1.0459171166796 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
11968j1 2992d1 107712ei1 |
Quadratic twists by: -4 8 -3 |