Hyperelliptic curves of genus three over finite fields of even characteristic

Enric Nart, Daniel Sadornil

Research output: Contribution to journalArticleResearchpeer-review

8 Citations (Scopus)


In this paper we classify hyperelliptic curves of genus 3 defined over a finite field k of even characteristic. We consider rational models representing all k-isomorphy classes of curves with a given arithmetic structure for the ramification divisor and we find necessary and sufficient conditions for two models of the same type to be k-isomorphic. Also, we compute the automorphism group of each curve and an explicit formula for the total number of curves. © 2003 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)198-220
JournalFinite Fields and Their Applications
Publication statusPublished - 1 Jan 2004


  • Automorphism group
  • Hyperelliptic curves
  • Moduli spaces


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