Elliptic curves arising from Brahmagupta quadrilaterals

Authors

  • F. Izadi Department of Pure Mathematics Azarbaijan Shahid Madani University
  • F. Khoshnam Department of Pure Mathematics Azarbaijan Shahid Madani University
  • D. Moody National Institute of Standards and Technology (NIST)
  • A. S. Zargar Department of Pure Mathematics Azarbaijan Shahid Madani University

Keywords:

Brahmagupta quadrilateral, elliptic curves, Heron triangle, rank

Abstract

A Brahmagupta quadrilateral is a cyclic quadrilateral whose sides, diagonals and area are all integer values. In this article, we characterise the notions of Brahmagupta, introduced by K. R. S. Sastry [‘Brahmagupta quadrilaterals’, Forum Geom. 2 (2002), 167–173], by means of elliptic curves. Motivated by these characterisations, we use Brahmagupta quadrilaterals to construct infinite families of elliptic curves with torsion group \(Z/2Z×Z/2Z\) having ranks (at least) four, five and six. Furthermore, by specialising we give examples from these families of specific curves with rank nine. DOI: 10.1017/S0004972713001172

Author Biography

D. Moody, National Institute of Standards and Technology (NIST)

Mathematician Ph. D. in Mathematics

Published

2014-06-03

Issue

Vol. 90 No. 1 (2014)

Section

Articles
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