Equations of Shimura curves of genus 2

Details Equations of Shimura curves of genus 2 Equations of Shimura curves of genus 2

2003-12-23

arxiv.org/abs/math/0312434v2

International Mathematics Reserach Notices, 14 (2004)

Mathematics

Number Theory

Some misprints corrected in Table 4.1

Scientific paper

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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