I will talk about a working paper on a Dirichlet theorem for rank 1 elliptic curves. I will focus on a theorem proving a relation between the homogeneous approximability of a number and its inhomogeneous approximability. This proof uses Kleinbock and Margulis' refinement of the celebrated Dani Correspondence between Diophantine approximation and flows on spaces of lattices, as well as a version of Schmidt's Game.