Elliptic curves and Pythagorean triples (European Journal of Pure and Applied Mathematics, 2014)
The aim of this paper is to study the  family of elliptic curvesof 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.