Atkin-Lehner |
2+ 11- 17- |
Signs for the Atkin-Lehner involutions |
Class |
11968j |
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 |
[210:323:27] |
Generators of the group modulo torsion |
j |
-1024/3179 |
j-invariant |
L |
6.0868570166939 |
L(r)(E,1)/r! |
Ω |
0.90593287471693 |
Real period |
R |
3.3594415141386 |
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 |
11968r1 1496e1 107712w1 |
Quadratic twists by: -4 8 -3 |