On elliptic curves y2=x3−n2x with rank zero

✍ Scribed by Keqin Feng; Maosheng Xiong

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 329 KB
• Volume: 109
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1016/j.jnt.2003.12.015

✦ Synopsis

In this paper we determine all elliptic curves E n :

xÞ based on the 2-descent method. The values of n for such curves E n are described in terms of graph-theory language. It is well known that the rank of the group E n ðQÞ for such curves E n is zero, the order of its Tate-Shafarevich group is odd, and such integers n are non-congruent numbers.