I'm a graduate student just checking to make sure that what he's researching isn't already known.

Let $\mathbb{F}$ be a number field, and let $E$ be an elliptic curve defined over $\mathbb{F}$. Is it already known that, for any integer $r\geq1$, there exists a finite-degree extension $\mathbb{K}$ of $\mathbb{F}$ so that $\textrm{rank}\left(E\left(\mathbb{K}\right)\right)\geq r$?