Elliptic Curves from Mordell to Diophantus and Back

DOI10.2307/3072428zbMath1083.11037OpenAlexW4245639648MaRDI QIDQ4417754

Bruce T. Myers, Ezra A. Brown

Publication date: 29 July 2003

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/3072428

zbMATH Keywords

elliptic curvesrankintegral pointsDiophantus

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Global ground fields in algebraic geometry (14G25)

Related Items (10)

On the family of elliptic curves \(y^2=x^3-m^2x+p^2\) ⋮ AT LEAST RANK 2 IN SEVERAL ELLIPTIC CURVES ⋮ Specializations of a generic rank-2 curve of Shioda ⋮ A note on lower bounds for ranks using Pell equations ⋮ Two infinite families of elliptic curves with rank greater than one ⋮ Unnamed Item ⋮ FAMILY OF ELLIPTIC CURVES <em>E^{</em>(<em>p</em>,<em>q</em>)}: <em>y</em>²=<em>x</em>²-<em>p</em>²<em>x</em>+<em>q</em>² ⋮ Finding numerical solutions of Diophantine equations using ant colony optimization ⋮ The Mordell-Weil bases for the elliptic curve $y^2=x^3-m^2x+m^2$ ⋮ On a family of elliptic curves of rank at least 2

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