ON ELLIPTIC CURVES OF RANK FOUR WITH THREE-DIVISION RATIONAL POINT

A universal family of elliptic curves of rank 4 with 3-division rational points is constructed. The base space is shown to be an elliptic K3 surface whose group of sections is of infinite order. Thus we obtain infinitely many such elliptic curves with mutually distinct j-invariants. 1. Introduction. In [5], we have reduced the problem of constructing elliptic curves of rank n (n ≥ 1) with generators to the problem of finding rational points on a certain variety Vn using the theory of twist. Moreover we have obtained all elliptic curves of at least rank n (1 ≤ n ≤ 7), by parametrizing all rationa