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)


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.


Riemann Surface Abelian Variety Endomorphism Ring Hyperelliptic Curve Ideal Class 
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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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