Twists of Shimura Curves

Consider a Shimura curve $X_0^D(N)$ over the rational numbers. We determine criteria for the twist by an Atkin-Lehner involution to have points over a local field. As a corollary we give a new proof of the theorem of Jordan-Livn'e on ${\mathbf{Q}}_p$ points when $p\mid D$ and for the first time give criteria for ${\mathbf{Q}}_p$ points when $p\mid N$. We also give congruence conditions for roots modulo $p$ of Hilbert class polynomials.