Generators for the elliptic curve y2=x3−nx of rank at least three

Let E be an elliptic curve defined by y2=x3−nx with n a positive integer. In the previous work, Terai and the author gave several infinite families of n for which certain two points of infinite order can be in a system of generators for the Mordell-Weil group E(Q). In this paper, we extend this result to give those examples of infinite families of n for which the rank of E(Q) is greater than or equal to three and the generators for the rank three part of E(Q) can be explicitly described.