Sign of square free integer which makes elliptic curves rank $0$

Question

Let $E/\mathbb{Q}$ be an arbitrary elliptic curve.

It is known that there exists a square-free integer such that $rank(E_D/\mathbb{Q}) = 0$.

Is it known whether there exists a positive $D$ such that $rank(E_D/\mathbb{Q}) = 0$ and, similarly, a negative $D$ for which $rank(E_D/\mathbb{Q}) = 0$?