Isomorphism Classes of Picard Curves over Finite Fields

In this paper we determine the number of isomorphism classes of Picard curves, i.e., superelliptic curves y3 = 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.

• Type: Journal
• Year: 2005
• Where: AAECC
• Authors: Jong Won Lee
• Keywords: AAECC 2005, Algorithms, Isomorphism Classes, Picard, Superelliptic Curves