Diophantine triples and construction of high-rank elliptic curves

Details Diophantine triples and construction of high-rank elliptic curves Diophantine triples and construction of high-rank elliptic curves

1998-06-09

arxiv.org/abs/math/9806170v1

Rocky Mountain J. Math. 30 (2000), 157-164.

Mathematics

Number Theory

Scientific paper

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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