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Explicit Equations Of Non-Hyperelliptic Genus 3 Curves With Real Multiplication By Q(ζ7+ζ7-1), Dun Liang

LSU Doctoral Dissertations

This thesis is devoted to proving the following:

For all (u₁, u₂, u₃, u₄) in a Zariski dense open subset of C⁴ there is a genus 3 curve X(u₁, u₂, u₃, u₄) with the following properties:

1. X(u₁, u₂, u₃, u₄) is not hyperelliptic.
2. End(Jac((X(u₁, u₂, u₃, u₄))) ⊗Q contains the real cubic field Q(ζ₇+ζ₇^-1) where ζ₇ is …