Diophantine triples and construction of high-rank elliptic curves
Number Theory
2021-08-30 v1
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.
Keywords
Cite
@article{arxiv.math/9806170,
title = {Diophantine triples and construction of high-rank elliptic curves},
author = {Andrej Dujella},
journal= {arXiv preprint arXiv:math/9806170},
year = {2021}
}