ELLIPTIC CURVES ARISING FROM BRAHMAGUPTA QUADRILATERALS

DOI10.1017/S0004972713001172zbMath1315.14040arXiv1512.03913OpenAlexW1996412435MaRDI QIDQ5495458

Dustin Moody, Foad Khoshnam, Farzali Izadi, Arman Shamsi Zargar

Publication date: 4 August 2014

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.03913

zbMATH Keywords

elliptic curverankHeron triangleBrahmagupta quadrilateral

Mathematics Subject Classification ID

Elliptic curves (14H52)

Related Items (5)

Integral isosceles triangle-parallelogram and Heron triangle-rhombus pairs with a common area and common perimeter ⋮ Integral triangles and perpendicular quadrilateral pairs with a common area and a common perimeter ⋮ Families of elliptic curves of rank \(\geq 5\) over \(\mathbb Q(t)\) ⋮ Unnamed Item ⋮ Hyperbolic Congruent Numbers

Uses Software

• SageMath

Cites Work

• Paramesvara's rule for the circumradius of a cyclic quadrilateral
• An example of elliptic curve over \(\mathbb{Q}\) with rank \(\geq 20\)
• Irregular Diophantine \(m\)-tuples and elliptic curves of high rank
• On the rank of elliptic curves coming from rational Diophantine triples
• Heron quadrilaterals with sides in arithmetic or geometric progression
• Diophantine triples and construction of high-rank elliptic curves over \(\mathbb{Q}\) with three nontrivial 2-torsion points

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