Vol. 9, No. 5, 2016

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A family of elliptic curves of rank $\geq 4$

Farzali Izadi and Kamran Nabardi

Vol. 9 (2016), No. 5, 733–736
Abstract

In this paper we consider a family of elliptic curves of the form y2 = x3 c2x + a2, where (a,b,c) is a primitive Pythagorean triple. First we show that the rank is positive. Then we construct a subfamily with rank 4.

Keywords
elliptic curves, rank, Pythagorean triple
Mathematical Subject Classification 2010
Primary: 11G05
Secondary: 14H52, 14G05
Milestones
Received: 7 May 2014
Revised: 30 September 2015
Accepted: 1 October 2015
Published: 25 August 2016

Communicated by Ken Ono
Authors
Farzali Izadi
Department of Mathematics
Urmia University
Urmia
Iran
Kamran Nabardi
Department of Mathematics
Azarbaijan Shahid Madani University
Tabriz
Iran