Local-global divisibility by 4 in elliptic curves defined over Q

Let E be an elliptic curve defined over Q. Let P is an element of epsilon(Q) and let q be a positive integer. Assume that for almost all valuations v is an element of Q, there exist points D(v) is an element of epsilon(Q(v)) such that P = qD(v). Is it possible to conclude that there exists a point D is an element of epsilon(Q) such that P = qD? A full answer to this question is known when q is a power of almost all primes p is an element of N, but some cases remain open when p is an element of S = {2, 3, 5, 7, 11, 13, 17, 19, 37, 43, 67, 163}. We now give a complete answer in the case when q = 4.