  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.
