<abstract xmlns="http://www.w3.org/1999/xhtml"><p>A <italic>D</italic>(4)-<italic>m</italic>-tuple is a set of <italic>m</italic> integers such that the product of any two of them increased by 4 is a perfect square. A problem of extendibility of <italic>D</italic>(4)-<italic>m</italic>-tuples is closely connected with the properties of elliptic curves associated with them. In this paper we prove that the torsion group of an elliptic curve associated with a <italic>D</italic>(4)-triple can be either ℤ/2ℤ × ℤ/2ℤ or ℤ/2ℤ × ℤ/6ℤ, except for the <italic>D</italic>(4)-triple {−1, 3, 4} when the torsion group is ℤ/2ℤ × ℤ/4ℤ.</p></abstract>

A D(4)-m-tuple is a set of m integers such that the product of any two of them increased by 4 is a perfect square. A problem of extendibility of D(4)-m-tuples is closely connected with the properties of elliptic curves associated with them. In this paper we prove that the torsion group of an elliptic curve associated with a D(4)-triple can be either ℤ/2ℤ × ℤ/2ℤ or ℤ/2ℤ × ℤ/6ℤ, except for the D(4)-triple {−1, 3, 4} when the torsion group is ℤ/2ℤ × ℤ/4ℤ.

On the torsion group of elliptic curves induced by <italic>D</italic>(4)-triples

Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia.

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On the torsion group of elliptic curves induced by (4)-triples

A D(4)-m-tuple is a set of m integers such that the product of any two of them increased by 4 is a perfect square. A problem of extendibility of D(4)-m-tuples...

On the torsion group of elliptic curves induced by D(4)-triples

Published Online: Oct 20, 2015

Page range: 79 - 90

Received: Apr 01, 2013

Accepted: Jun 01, 2013

DOI: https://doi.org/10.2478/auom-2014-0033

Keywords
(4)-triples, elliptic curves, torsion group

© 2014 Andrej Dujella et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On the torsion group of elliptic curves induced by D(4)-triples

Published Online: Oct 20, 2015

Page range: 79 - 90

Received: Apr 01, 2013

Accepted: Jun 01, 2013

DOI: https://doi.org/10.2478/auom-2014-0033

Keywords(4)-triples, elliptic curves, torsion group

© 2014 Andrej Dujella et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
(4)-triples, elliptic curves, torsion group