Elliptic curves and Pythagorean triples

Kamran Nabardi, Farzali Izadi, Foad Khoshnam


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.


Elliptic curve, Rank, Pythagorean triples

Full Text: