Abstract
In this paper we count the number of isomorphism classes of pointed Picard curves, i.e., nonsingular plane curves y3=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.
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