Let $\cal X$ be a projective, geometrically irreducible, non-singular, algebraic curve defined over a finite field Fq2 of order q2. If the number of Fq2-rational points of $\cal X$ satisfies the Hasse–Weil upper bound, then $\cal X$ is said to be Fq2-maximal. For a point P0 ∈ $\cal X$(Fq2), let π be the morphism arising from the linear series $\cal D$: = |(q + 1)P0|, and let N: = dim($\cal D$). It is known that N [ges ] 2 and that π is independent of P0 whenever $\cal X$ is Fq2-maximal.