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Computing with the analytic Jacobian of a genus 2 curve

  • Paul B. van Wamelen
Part of the Algorithms and Computation in Mathematics book series (AACIM, volume 19)

Abstract

We solve two genus 2 curve problems using Magma. First we give examples of how Magma can be used to find the equation of a genus 2 curve whose Jacobian has prescribed Complex Multiplication. We treat 2 fields, one easy and one harder. Secondly we show how Magma can be used to find, and ultimately prove existence of, rational isogenies between the Jacobians of two genus 2 curves.

Keywords

Riemann Surface Abelian Variety Endomorphism Ring Hyperelliptic Curve Ideal Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer 2006

Authors and Affiliations

  • Paul B. van Wamelen
    • 1
  1. 1.Department of MathematicsLouisiana State UniversityBaton RougeUSA

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