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Elliptic Curves arising from Brahmagupta Quadrilaterals



Farzali Izadi, Foad Khoshnam, Dustin Moody, Arman Zargar


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.
Bulletin of the Australian Mathematical Society


Brahmagupta quadrilateral, elliptic curve, Heron triangle, rank


Izadi, F. , Khoshnam, F. , Moody, D. and Zargar, A. (2014), Elliptic Curves arising from Brahmagupta Quadrilaterals, Bulletin of the Australian Mathematical Society, [online],, (Accessed April 23, 2024)
Created July 31, 2014, Updated October 12, 2021