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Let  F  be the finite field of order  q  2 . In this paper we continue the study in [ 24 ], [ 23 ], [ 22 ] of  F -maximal curves defined by equations of typey  n   =   x  ℓ    (    x  m   +  1   )   .${{y}^{n}}={{x}^{\ell }}\left( {{x}^{m}}+1 \right).$   New results are obtained via certain subcovers of the nonsingular model ofv  N   =   u    t  2−  u${{v}^{N}}={{u}^{{{t}^{2}}}}-u$   where  q  =  t α  ,  α  ≥ 3 is odd and  N  = ( t α   + 1)/( t  + 1). We observe that the case  α  = 3 is closely related to the Giulietti–Korchmáros curve.

The curve Y n = X ℓ ( X m + 1) over finite fields II