Modular polynomials for genus 2

2008/04/09 by Reinier Broker, Kristin Lauter, Broker, Reinier +1
Mathematics · #11Gxx #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11Gxx

paper · pdf · doi:10.48550/arxiv.0804.1565

arxiv created 2009/02/04 · arxiv updated 2009/12/01

Abstract

Modular polynomials are an important tool in many algorithms involving elliptic curves. In this article we investigate their generalization to the genus 2 case following pioneering work by Gaudry and Dupont. We prove various properties of these genus 2 modular polynomials and give an improved way to explicitly compute them.

Related

• The arithmetic of genus two curves
• The class of the d-elliptic locus in genus 2
• Computing the Charlap-Coley-Robbins modular polynomials
• Computing Modular Polynomials
• Computation of Hilbert class polynomials and modular polynomials from supersingular elliptic curves