Non-divisible point on a two-parameter family of elliptic curves

Let n be a positive integer and t be a non-zero integer. We consider the two-parameter family of elliptic curves over Q given by epsilon(n)(t): y(2) = x(3) + tx(2) - n(2)(t + 3n(2))x + n(6). We prove a result of non-divisibility of the point (0, n(3)) is an element of epsilon(n)(t)(Q) whenever t is sufficiently large compared to n and t(2) + 3n(2)t + 9n(4) is squarefree. Our work extends to this family of elliptic curves a previous study of Duquesne mainly stated for n = 1 and t > 0.