Elliptic curves coming from Heron triangles

DOI10.1216/RMJ-2014-44-4-1145zbMath1305.14017OpenAlexW1973470723WikidataQ57595824 ScholiaQ57595824MaRDI QIDQ470395

Juan Carlos Peral, Andrej Dujella

Publication date: 12 November 2014

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmjm/1414760946

zbMATH Keywords

rank of elliptic curvesHeron triangles

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Elliptic curves (14H52)

Related Items (10)

Integral isosceles triangle-parallelogram and Heron triangle-rhombus pairs with a common area and common perimeter ⋮ A Heron triangle and a Diophantine equation ⋮ Spherical Heron triangles and elliptic curves ⋮ PERFECT TRIANGLES ON THE CURVE ⋮ On certain Diophantine equations of the form \(z^2=f(x)^2\pm g(y)^2\) ⋮ On rational triangles via algebraic curves ⋮ On Ceva points of (almost) equilateral triangles ⋮ Families of elliptic curves of rank \(\geq 5\) over \(\mathbb Q(t)\) ⋮ Heron triangles with two rational medians and Somos-5 sequences ⋮ Construction of an infinite family of elliptic curves of 2-Selmer rank 1 from Heron triangles

Uses Software

• PARI/GP
• mwrank
• ecdata

Cites Work

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• An elliptic \(K3\) surface associated to Heron triangles
• An example of elliptic curve over \(\mathbb{Q}\) with rank \(\geq 20\)
• Rational triangles with equal area
• Diophantine \(m\)-tuples and elliptic curves
• On the rank of elliptic curves coming from rational Diophantine triples
• Heron triangles via elliptic curves
• On Rational Triangles
• An Infinite Set of Heron Triangles with Two Rational Medians
• A remark on the injectivity of the specialization homomorphism
• High-rank elliptic curves with torsion induced by Diophantine triples
• Sums of two biquadrates and elliptic curves of rank $\geq 4$
• On Mordell-Weil groups of elliptic curves induced by Diophantine triples
• Diophantine triples and construction of high-rank elliptic curves over \(\mathbb{Q}\) with three nontrivial 2-torsion points

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