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2015 On the Mordell-Weil group of elliptic curves induced by families of Diophantine triples
Miljen Mikić
Rocky Mountain J. Math. 45(5): 1565-1589 (2015). DOI: 10.1216/RMJ-2015-45-5-1565

Abstract

The problem of the extendibility of Diophantine triples is closely connected with the Mordell-Weil group of the associated elliptic curve. In this paper, we examine Diophantine triples $\{k-1,k+1,c_l(k)\}$ and prove that the torsion group of the associated curves is $\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z}$ for $l=3,4$ and $l\equiv 1$ or $2 \pmod{4}$. Additionally, we prove that the rank is greater than or equal to 2 for all $l\ge2$. This represents an improvement of previous results by Dujella, Peth\H{o} and Najman, where cases $k=2$ and $l\le3$ were considered.

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Miljen Mikić. "On the Mordell-Weil group of elliptic curves induced by families of Diophantine triples." Rocky Mountain J. Math. 45 (5) 1565 - 1589, 2015. https://doi.org/10.1216/RMJ-2015-45-5-1565

Information

Published: 2015
First available in Project Euclid: 26 January 2016

zbMATH: 1333.11052
MathSciNet: MR3452229
Digital Object Identifier: 10.1216/RMJ-2015-45-5-1565

Subjects:
Primary: 11G05

Rights: Copyright © 2015 Rocky Mountain Mathematics Consortium

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Vol.45 • No. 5 • 2015
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