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Abstract
In this paper we consider a family of elliptic curves of the form
y 2
= x 3
− c 2 x
+ a 2 , 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