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arXiv · 2005.10706

High rank elliptic curves induced by rational Diophantine triples

Andrej Dujella·Juan Carlos Peral
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Abstract

A rational Diophantine triple is a set of three nonzero rational a,b,c with the property that ab+1, ac+1, bc+1 are perfect squares. We say that the elliptic curve y^2 = (ax+1)(bx+1)(cx+1) is induced by the triple {a,b,c}. In this paper, we describe a new method for construction of elliptic curves over Q with reasonably high rank based on a parametrization of rational Diophantine triples. In particular, we construct an elliptic curve induced by a rational Diophantine triple with rank equal to 12, and an infinite family of such curves with rank >= 7, which are both the current records for that kind of curves.

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Andrej Dujella, Juan Carlos Peral. 2020-05-21. High rank elliptic curves induced by rational Diophantine triples. https://doi.org/10.3336/gm.55.2.05

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