Let E, A be elliptic curves over a number field K. We say E,A are p-Selmer near-companion curves over K if the difference between p-Selmer ranks of E^\chi and A^\chi is bounded by some constant C(E,K) independent of the choice of \chi. Mazur and Rubin conjectured that if E and A are p-Selmer near companion over K, then there exists a G_K module isomorphism between E[p] and A[p]. In this talk, I will prove the conjecture holds for p=2. Speaker(s): Myungjun Yu (University of Michigan)