  We describe an algorithm that computes explicit models of hyperelliptic
Shimura curves attached to an indefnite quaternion algebra over Q and
Atkin-Lehner quotients of them. It exploits Cerednik-Drinfeld's non-archimedean
uniformisation of Shimura curves, a formula of Gross and Zagier for the
endomorphism ring of Heegner points over Artinian rings and the connection
between Ribet's bimodules and the specialization of Heegner points. As an
application, we provide a list of equations of Shimura curves and quotients of
them obtained by our algorithm that had been conjectured by Kurihara.
