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Elliptic Curves arising from Brahmagupta Quadrilaterals

Published

Author(s)

Farzali Izadi, Foad Khoshnam, Dustin Moody, 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

Keywords

Brahmagupta quadrilateral, elliptic curve, Heron triangle, rank
Created August 1, 2014, Updated November 10, 2018