The Hurwitz curve over a finite field and its Weierstrass points for the morphism of lines

For any smooth Hurwitz curve H n : X Y + Z = 0 over the finite field F p , an explicit description of its Weierstrass points for morphism lines is presented. As a consequence, bounds on number rational are obtained via Stöhr-Voloch Theory. Further, full automorphism group Aut ( ) as well genera all Galois subcovers with ≠ 3 r computed. Finally, question by F. Torres plane nonsingular maximal curves answered.