A unified method of construction of elliptic curves with high Mordell–Weil rank

Hizuru Yamagishi

Vol. 191 (1999), No. 1, 189–200

DOI: 10.2140/pjm.1999.191.189

Abstract

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).

Milestones

Received: 5 February 1998

Revised: 24 June 1998

Published: 1 November 1999