  Let $p$ and $q$ be two distinct odd primes, $p<q$ and $E_{p,q}:y^2=x^3-pqx$
be an elliptic curve. Fix a line $L_{a.b}:y=\frac{a}{b}x$ where $a\in
\mathbb{Z},b\in \mathbb{N}$ and $(a,b)=1$. We study sufficient conditions that
$p$ and $q$ must satisfy so that there are infinitely many elliptic curves
$E_{p,q}$ that intersect $L_{a,b}$.
