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

Autor:	Izadi, F. A., Khoshnam, F., Nabardi, K.
Rok vydání:	2012
Předmět:	Mathematics - Number Theory
Druh dokumentu:	Working Paper
Popis:	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 $\geq 3$. If moreover $n$ is odd and the parity conjecture is true, then it has even rank $\geq 4$. Finally, some examples of ranks equal to 4, 5, 6, 7, 8 and 10, are also obtained. Comment: 11 pages, 2 tables
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1202.5676 Zobrazit plný text záznamu View this record from Arxiv