A note on rational and elliptic curves associated with the cuboid factor equations
arXiv:1209.5706
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. It is described by a system of four equations with respect to six variables. The cuboid factor equations were derived from these four equations by symmetrization procedure. They constitute a system of eight polynomial equations, which has been solved parametrically. In the present paper its parametric solution is expressed through intersections or rational and elliptic curves arranged into parametric families.
AmSTeX, 15 pages, amsppt style, 1 ancillary file. arXiv admin note: substantial text overlap with arXiv:1209.0723
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Cited by in corpus (7)
- Two and three descent for elliptic curves associated with perfect cuboids
- A strategy of numeric search for perfect cuboids in the case of the second cuboid conjecture
- Asymptotic estimates for roots of the cuboid characteristic equation in the linear region
- Reverse asymptotic estimates for roots of the cuboid characteristic equation in the case of the second cuboid conjecture
- Perfect Cuboid and Congruent Number Equation Solutions
- A note on invertible quadratic transformations of the real plane
- A fast modulo primes algorithm for searching perfect cuboids and its implementation