Elliptic Curves arising from Brahmagupta Quadrilaterals

Published

August 1, 2014

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

Pub Type

Journals

Download Paper

https://doi.org/10.1017/S0004972713001172

Local Download

Keywords

Brahmagupta quadrilateral, elliptic curve, Heron triangle, rank

Citation

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 October 1, 2025)