Vol. 3, No. 3, 2010

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Infinite family of elliptic curves of rank at least 4

Bartosz Naskręcki

Vol. 3 (2010), No. 3, 297–316
Abstract

We investigate -ranks of the elliptic curve Et: y2 + txy = x3 + tx2 x + 1, where t is a rational parameter. We prove that for infinitely many values of t the rank of Et() is at least 4.

Keywords
elliptic curves, Mordell–Weil group, ranks in families
Mathematical Subject Classification 2000
Primary: 11D25, 11G05
Milestones
Received: 30 January 2010
Revised: 25 August 2010
Accepted: 4 September 2010
Published: 16 October 2010

Proposed: Bjorn Poonen
Communicated by Bjorn Poonen
Authors
Bartosz Naskręcki
Faculty of Mathematics and Computer Science
Adam Mickiewicz University
Umultowska 87
61-614 Poznań
Poland