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January 2022 On elliptic curves induced by rational Diophantine quadruples
Andrej Dujella, Gökhan Soydan
Proc. Japan Acad. Ser. A Math. Sci. 98(1): 1-6 (January 2022). DOI: 10.3792/pjaa.98.001

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 $\mathbf{Z}/2\mathbf{Z} \times \mathbf{Z}/k\mathbf{Z}$ 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.

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Andrej Dujella. Gökhan Soydan. "On elliptic curves induced by rational Diophantine quadruples." Proc. Japan Acad. Ser. A Math. Sci. 98 (1) 1 - 6, January 2022. https://doi.org/10.3792/pjaa.98.001

Information

Published: January 2022
First available in Project Euclid: 4 March 2022

Digital Object Identifier: 10.3792/pjaa.98.001

Subjects:
Primary: 11G05

Keywords: Diophantine quadruples , Elliptic curves , ‎rank‎ , torsion group

Rights: Copyright © 2022 The Japan Academy

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Vol.98 • No. 1 • January 2022
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