The parity conjecture for prime quadratic twists

Let $E^d$ denote the quadratic twist of the elliptic curve $E$ by $d$, let $\operatorname{rank}(E^d)$ be its Mordell–Weil rank, and let $w(E^d)$ be the root number of $E^d$. For $d\in\mathbf{Z}$ with $|d|$ prime, The parity conjecture.

$$(-1)^{\operatorname{rank}(E^d)}=w(E^d).$$

The parity conjecture predicts that the root number determines the parity of the rank in this family of quadratic twists; the supplied context gives no resolution of the assertion.