## Cryptology ePrint Archive: Report 2003/060

Isomorphism Classes of Picard Curves over Finite Fields

Jong Won Lee

Abstract: In this paper we determine the number of isomorphism classes of Picard curves, i.e., superelliptic curves $y^3=f(x)$ of genus three, over finite fields of characteristic different from $3$. In the process of doing this we also provide reduced forms of Picard curves together the number of such forms up to isomorphism. In addition to its own theoretical meaning it has applications to cryptography.

Category / Keywords: foundations / Picard curves, superelliptic curves, isomorphism classes, algebraic function field

Publication Info: preprint