ON A CLASS OF ELLIPTIC-CURVES WITH RANK AT MOST 2

In this note we consider the elliptic curves y(2) = x(3) + px defined over Q for primes p satisfying p = 1 (mod 8), and review some of their properties. We then compute and list (in the supplement) their ranks, and give, when the rank is positive, the generators of the group of r ational points and Mordell-Weil lattice invariant tau for all primes p < 50000 of the form m(2) + 64n(2).