  Consider a Shimura curve $X^D_0(N)$ 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.
