Large Cyclic Subgroups of Jacobians of Hyperelliptic Curves

Abstract

In this paper we obtain conditions on the divisors of the group order of the Jacobian of a hyperelliptic genus 2 curve, generated by the complex multiplication method described by Weng (2003) and Gaudry (2005). Examples, where these conditions imply that the Jacobian has a large cyclic subgroup, are given.

arXiv comment8 pages, 1 figure