Equations of Shimura curves of genus 2
classification
🧮 math.NT
math.AG
keywords
curvesequationsgenusjacobianshimurathematkin-lehnercompute
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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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