Publication: On elliptic curves induced by rational diophantine quadruples
Date
2022-01-01
Authors
Soydan, Gökhan
Authors
Dujella, Andrej
Journal Title
Journal ISSN
Volume Title
Publisher
Japan Acad
Abstract
In this paper, we consider elliptic curves induced by rational Diophantine quadruples, i.e. sets of four non-zero rationals such that the product of any two of them plus 1 is a perfect square. We show that for each of the groups Z/2Z x Z/kZ for k = 2, 4, 6, 8, there are infinitely many rational Diophantine quadruples with the property that the induced elliptic curve has this torsion group. We also construct curves with moderately large rank in each of these four cases.
Description
Keywords
Rank, Construction, Sextuples, Triples, Q(t), Diophantine quadruples, Elliptic curves, Torsion group, Rank, Science & technology, Physical sciences, Mathematics