Generators for the elliptic curve y2~?=?x~3?nx II

摘要

Let E be an elliptic curve defined by y~2=x~3?nx with n a positive integer. In our previous work, we 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 and give those examples of infinite families of n for which the generators for rank three part of E(Q) can be explicitly described.