Biquadrates and Elliptic Curves

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.

arXiv comment5 pages

References in corpus (1)

• Sums of two biquadrates and elliptic curves of rank $\ge 4$

Cited by in corpus (1)

• Partitions with equal products and elliptic curves