Equations of Shimura curves of genus 2
Abstract
We present explicit models for Shimura curves XD and Atkin-Lehner quotients XD/wm of them of genus 2. We show that several equations conjectured by Kurihara are correct and compute for them the kernel of Ribet's isogeny J0(D)new --> JD between the new part of the Jacobian of the modular curve X0(D) and the Jacobian of XD.
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