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Equations of Shimura curves of genus 2

Josep Gonzalez·Victor Rotger
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Abstract

We present explicit models for Shimura curves X_D and Atkin-Lehner quotients X_D/w_m 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 J_0(D)^{new} --> J_D between the new part of the Jacobian of the modular curve X_0(D) and the Jacobian of X_D.

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Josep Gonzalez, Victor Rotger. 2003-12-23. Equations of Shimura curves of genus 2. https://arxiv.org/abs/math/0312434

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