Elliptic Curves Arising from Brahmagupta Quadrilaterals

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... See full 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.
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