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Diophantine triples and construction of high-rank elliptic curves

Andrej Dujella
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Abstract

Using the theory of Diophantine m-tuples, i.e. sets with the property that the product of its any two distinct elements increased by 1 is a perfect square, we construct an elliptic curve over Q(t) of rank at least 4 with three non-trivial torsion points. By specialization, we obtain an example of elliptic curve over Q with torsion group Z/2Z * Z/2Z whose rank is equal 7.

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Andrej Dujella. 1998-06-09. Diophantine triples and construction of high-rank elliptic curves. https://doi.org/10.1216/rmjm/1022008982

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