Elliptic curves and Pythagorean triples

Authors

  • Kamran Nabardi Azarbaijan Shahid Madani University
  • Farzali Izadi Azarbaijan Shahid Madani University
  • Foad Khoshnam Azarbaijan Shahid Madani University

Keywords:

Elliptic curve, Rank, Pythagorean triples

Abstract

The aim of this paper is to study the  family of elliptic curves
of the form  y^2=x(x-a^2)(x-b^2),   where (a,b,c) is a primitive  Pythagorean triple. First we show that the rank is  positive. Then we construct some subfamilies
 with rank>= 2 by  different methods.

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Published

2014-05-08

Issue

Vol. 7 No. 2: (April 2014)

Section

Number Theory

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How to Cite

Elliptic curves and Pythagorean triples. (2014). European Journal of Pure and Applied Mathematics, 7(2), 131-139. https://www.ejpam.com/index.php/ejpam/article/view/1857