On the rank of elliptic curves coming from rational Diophantine triples

DOI10.1216/RMJ-2012-42-6-1759zbMath1293.11074OpenAlexW2027177425WikidataQ57595854 ScholiaQ57595854MaRDI QIDQ1945721

Julián Aguirre, Juan Carlos Peral, Andrej Dujella

Publication date: 9 April 2013

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

Full work available at URL: https://projecteuclid.org/euclid.rmjm/1361800604

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09) Elliptic curves over global fields (11G05) Computer solution of Diophantine equations (11Y50)

Related Items (10)

On the torsion group of elliptic curves induced by Diophantine triples over quadratic fields ⋮ High-rank elliptic curves with given torsion group and some applications ⋮ Elliptic curves coming from Heron triangles ⋮ Families of elliptic curves of rank \(\geq 5\) over \(\mathbb Q(t)\) ⋮ Diophantine quadruples with the properties \(D(n_1)\) and \(D(n_2)\) ⋮ Construction of high rank elliptic curves ⋮ Elliptic curves induced by Diophantine triples ⋮ High rank elliptic curves induced by rational Diophantine triples ⋮ ELLIPTIC CURVES ARISING FROM BRAHMAGUPTA QUADRILATERALS ⋮ On elliptic curves induced by rational Diophantine quadruples

Uses Software

• Mathematica
• PARI/GP
• ecdata

Cites Work

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• Diophantine triples and construction of high-rank elliptic curves over \(\mathbb{Q}\) with three nontrivial 2-torsion points

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