Conics - a Poor Man's Elliptic Curves

Publication date: 18 November 2003

Abstract: The aim of this article is to show that the arithmetic of Pell conics admits a description which is completely analogous to that of elliptic curves: there is a theory of 2-descent with associated Selmer and Tate-Shafarevich groups, and there should be an analog of the conjecture of Birch and Swinnerton-Dyer.

Mathematics Subject Classification ID

Quadratic extensions (11R11) Elliptic curves over global fields (11G05)

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