ISOMORPHISM CLASSES OF HYPERELLIPTIC CURVES OF GENUS 2 OVER F2n

Abstract

L. H. Encinas, A. J. Menezes, and J. M. Masque in [2] proposed a classification of isomorphism classes of hyperelliptic curve of genus 2 over finite fields with characteristic different from 2 and 5. Y. Choie and D. Yun in [1] obtained for the number of isomorphic classes of hyperelliptic curves of genus 2 over Fq using direct counting method. In this paper we will classify the isomorphism classes of hyperelliptic curves of genus 2 over F2n for odd n, represented by an equation of the form y2 + a5y = x5 + a8x + a10(a5 6= 0).

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