Conics - a Poor Man's Elliptic Curves

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.

11 pages

References in corpus (3)

• Higher Descent on Pell Conics I. From Legendre to Selmer
• Higher Descent on Pell Conics III. The First 2-Descent
• Higher Descent on Pell Conics II. Two Centuries of Missed Opportunities

Cited by in corpus (1)

• Analogy between arithmetic of elliptic curves and conics