Quadratic Twists of Elliptic Curves with Small Selmer Rank
Abstract
Given an elliptic curve E over the rational with no rational 2torsion points, we prove the existence of a quadratic twist of E for which the 2Selmer rank is less than or equal to 1. By the author's earlier result, we establish a lower bound on the number of D's for which the twists E(D) have 2Selmer rank <= 1. We include in the introduction our (brief) opinion about why it is supposed to be hard to push our technique to make the Selmer group trivial.
 Publication:

arXiv eprints
 Pub Date:
 September 2008
 arXiv:
 arXiv:0809.5019
 Bibcode:
 2008arXiv0809.5019C
 Keywords:

 Mathematics  Number Theory;
 11G05
 EPrint:
 cited the work of Mazur and Rubin [arxiv:0904.3709]