Isomorphism classes of picard curves over finite fields
In this paper we count the number of isomorphism classes of pointed Picard curves, i. e., nonsingular plane curves y(3) = f(x) of genus 3 with the fixed point at infinity, over finite fields of characteristic different from 3. In the process of doing this we also provide reduced forms of Picard curves that represent the isomorphism classes together with the number of such forms up to isomorphism. In addition to its own theoretical meaning, it has applications to cryptography.
isomorphism classes picard curve superelliptic curve algebraic function field