  We study an infinite family of Mordell curves (i.e. the elliptic curves in
the form y^2=x^3+n, n \in Z) over Q with three explicit integral points. We
show that the points are independent in certain cases. We describe how to
compute bounds of the canonical heights of the points. Using the result we show
that any pair in the three points can always be a part of a basis of the free
part of the Mordell--Weil group.
