Hizuru Yamagishi
A unified method of construction of elliptic curves with high Mordell-Weil rank

By using the twist theory, we reduce the problem of constructing elliptic curves of rank n (n >= 1) with generators to the problem of finding rational points on a certain variety V_n. By parametrizing all rational points on V_n (1 <= n <= 7), we get all elliptic curves of at least rank n (n <= 7).