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 (7)

• Fast algorithms for ell-adic towers over finite fields
• On integral well-rounded lattices in the plane
• Arithmetic matrices for number fields I
• A binomial identity on the least prime factor of an integer
• Analogy between arithmetic of elliptic curves and conics
• Arithmetic complexity revisited
• An isomorphism between the narrow ideal class group of squared ideals of a quadratic number field and the kernel of a homomorphism between cohomology groups for Pell conics