Welcome to the resource topic for 2016/328
Title:
Constructing genus 3 hyperelliptic Jacobians with CM
Authors: Jennifer Balakrishnan, Sorina Ionica, Kristin Lauter, Christelle Vincent
Abstract:Given a sextic CM field K, we give an explicit method for finding all genus 3 hyperelliptic curves defined over the complex whose Jacobians are simple and have complex multiplication by the maximal order of this field, via an approximation of their Rosenhain invariants. Building on the work of Weng, we give an algorithm which works in complete generality, for any CM sextic field K, and computes minimal polynomials of the Rosenhain invariants for any period matrix of the Jacobian. This algorithm can be used to generate genus 3 hyperelliptic curves over a finite field F_p with a given zeta function by finding roots of the Rosenhain minimal polynomials modulo p.
ePrint: https://eprint.iacr.org/2016/328
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