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

Abstract

If an integer $n$ is written as a sum of two biquadrates in two different ways, then the elliptic curve $y^2=x^3-nx$ has rank $\ge 3$. If moreover $n$ is odd and the parity conjecture is true, then it has even rank $\ge 4$. Finally, some examples of ranks equal to 4, 5, 6, 7, 8 and 10, are also obtained.

arXiv comment11 pages, 2 tables

Cited by in corpus (2)

• Biquadrates and Elliptic Curves
• Partitions with equal products and elliptic curves