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Equations of Shimura curves of genus 2

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.

preprint2007arXivOpen access
Josep GonzalezVictor Rotger
math.AGmath.NT
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Josep GonzalezVictor Rotger

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