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Paper 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.

Metadata
Available format(s)
PDF PS
Category
Foundations
Publication info
Published elsewhere. preprint
Keywords
Picard curvessuperelliptic curvesisomorphism classesalgebraic function field
Contact author(s)
lee @ exp-math uni-essen de
History
2003-04-07: received
Short URL
https://ia.cr/2003/060
License
Creative Commons Attribution
CC BY
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