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Isomorphism Classes of Picard Curves over Finite Fields
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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. |
BibTeX
@misc{eprint-2003-11777, title={Isomorphism Classes of Picard Curves over Finite Fields}, booktitle={IACR Eprint archive}, keywords={foundations / Picard curves, superelliptic curves, isomorphism classes, algebraic function field}, url={http://eprint.iacr.org/2003/060}, note={preprint lee@exp-math.uni-essen.de 12142 received 31 Mar 2003}, author={Jong Won Lee}, year=2003 }