Atkin-Lehner |
2- 11- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
2068d |
Isogeny class |
Conductor |
2068 |
Conductor |
∏ cp |
9 |
Product of Tamagawa factors cp |
deg |
432 |
Modular degree for the optimal curve |
Δ |
-16014592 = -1 · 28 · 113 · 47 |
Discriminant |
Eigenvalues |
2- -2 0 -1 11- 5 -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,12,-188] |
[a1,a2,a3,a4,a6] |
Generators |
[16:66:1] |
Generators of the group modulo torsion |
j |
686000/62557 |
j-invariant |
L |
2.1788338408151 |
L(r)(E,1)/r! |
Ω |
1.0470221571459 |
Real period |
R |
2.0809815971368 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
8272j1 33088e1 18612d1 51700i1 |
Quadratic twists by: -4 8 -3 5 |