English

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

R2 v1 2026-06-21T20:32:48.431Z