Two and three descent for elliptic curves associated with perfect cuboids

Abstract

A rational perfect cuboid is a rectangular parallelepiped whose edges and face diagonals are given by rational numbers and whose space diagonal is equal to unity. Recently it was shown that the Diophantine equations describing such a cuboid lead to a couple of parametric families of elliptic curves. Two and three descent methods for calculating their ranks are discussed in the present paper. The elliptic curves in each parametric family are subdivided into two subsets admitting 2-descent and 3-descent methods respectively.

AmSTeX, 37 pages, amsppt style

References in corpus (2)

• Elementary 3-descent with a 3-isogeny
• A note on rational and elliptic curves associated with the cuboid factor equations

Cited by in corpus (5)

• Asymptotic estimates for roots of the cuboid characteristic equation in the linear region
• A strategy of numeric search for perfect cuboids in the case of the second cuboid conjecture
• Reverse asymptotic estimates for roots of the cuboid characteristic equation in the case of the second cuboid conjecture
• A note on invertible quadratic transformations of the real plane
• A fast modulo primes algorithm for searching perfect cuboids and its implementation