  Let $p$ and $q$ be two distinct prime numbers, and $X^{pq}/w_q$ be the
quotient of the Shimura curve of discriminant $pq$ by the Atkin-Lehner
involution $w_q$. We describe a way to verify in wide generality a criterion of
Parent and Yafaev to prove that if $p$ and $q$ satisfy some explicite
congruence conditions, known as the conditions of the non ramified case of Ogg,
and if $p$ is large enough compared to $q$, then the quotient $X^{pq}/w_q$ has
no rational point, except possibly special points.
