ON THE CURVE Y n = Xℓ(Xm + 1) OVER FINITE FIELDS II

Abstract. Let F be the finite field of order q2. In this paper we continue the study
in [20], [19], [18] of F-maximal curves defined by equations of type yn = xℓ(xm + 1).
For example new results are obtained via certain subcovers of the nonsingular model of
vN = ut2
− u where q = tα,  ≥ 3 odd and N = (tα + 1)/(t + 1). We do observe that
the case  = 3 is closely related to the Giulietti-Korchm´aros curve.