Elliptic curves and Pythagorean triples
Keywords:
Elliptic curve, Rank, Pythagorean triplesAbstract
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.
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Published
2014-05-08
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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