On a Family Of Elliptic Curves With Positive Rank arising from Pythagorean Triples

Details On a Family Of Elliptic Curves With Positive Rank arising from Pythagorean Triples On a Family Of Elliptic Curves With Positive Rank arising from Pythagorean Triples

2010-12-28

arxiv.org/abs/1012.5837v4

Mathematics

Number Theory

Scientific paper

The aim of this paper is to introduce a new family of elliptic curves in the
form of $y^2=x(x-a^2)(x-b^2)$ that have positive ranks. We first generate a
list of pythagorean triples $(a,b,c)$ and then construct this family of
elliptic curves. It turn out that this new family have positive ranks and
search for the upper bound for their ranks.

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