Izadi, F.
, Khoshnam, F.
, Moody, D.
and Zargar, A.
(2014),
Elliptic Curves arising from Brahmagupta Quadrilaterals, Bulletin of the Australian Mathematical Society, [online], https://doi.org/10.1017/S0004972713001172, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=917344
(Accessed December 26, 2024)
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Elliptic Curves arising from Brahmagupta Quadrilaterals
Published
Author(s)
Farzali Izadi, Foad Khoshnam, , Arman Zargar
Abstract
A Brahmagupta quadrilateral is a cyclic quadrilateral whose sides, diagonals, and area are all integer values. In this article, we characterize the notions of Brahmagupta, introduced by K. R. S. Sastry, by means of elliptic curves. Motivated by these characterizations, we use Brahmagupta quadrilaterals to construct infinite families of elliptic curves with torsion group Z/2Z x Z/2Z having ranks (at least) 4, 5, and 6. Furthermore, by specializing we give examples from these families of specific curves with rank 9.Citation
Bulletin of the Australian Mathematical Society
Volume
90
Issue
1
Pub Type
Journals
Download Paper
Keywords
Brahmagupta quadrilateral, elliptic curve, Heron triangle, rank
Citation
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Created July 31, 2014, Updated October 12, 2021