# Mordell-Weil Rank Growth of Elliptic Curves on Field Extensions

I am a graduate student checking to make sure his research is not already known.

Let $$mathbb {F}$$ to be a numeric field and let $$E$$ to be an elliptical curve defined on $$mathbb {F}$$. Do we already know that for all $$r geq1$$there is an extension of finite degree $$mathbb {K}$$ of $$mathbb {F}$$ so that $$textrm {rank} left (E left ( mathbb {K} right) right) geq r$$?