Conics - a Poor Man's Elliptic Curves
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🧮 math.NT
math.HO
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conicscurvesellipticthereadmitsanaloganalogousarithmetic
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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.
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