Biquadrates and Elliptic Curves
Number Theory
2012-03-13 v1
Abstract
The elliptic curve y^2= x^3-Nx where N=m^4+n^4 has rank at least 2 over Q(m,n). When N can be written in two different ways as sum of two fourth powers, then we prove that the rank is at least 4.
Keywords
Cite
@article{arxiv.1203.2576,
title = {Biquadrates and Elliptic Curves},
author = {Julián Aguirre and Juan Carlos Peral},
journal= {arXiv preprint arXiv:1203.2576},
year = {2012}
}
Comments
5 pages