Biquadrates and Elliptic Curves

2012/03/12 by Aguirre, Julián, Peral, Juan Carlos
#14H52 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1203.2576

Abstract

The elliptic curve y²= x³-Nx where N=m⁴+n⁴ 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.

Related

• Sums of two biquadrates and elliptic curves of rank ≥ 4
• Infinite family of elliptic curves of rank at least 4
• Two infinite families of elliptic curves with rank greater than one
• Elliptic Curves x³ + y³ = k of High Rank
• Rank of the family of elliptic curves y² = x³- 5px