On the Selmer groups and MordellWeil groups of elliptic curves $ y^{2} = x (x \pm p) (x \pm q) $ over imaginary quadratic number fields of class number one
Abstract
Let $ p $ and $ q $ be odd prime numbers with $ q  p = 2, $ the $\varphi $Selmer groups, ShafarevichTate groups ($ \varphi  $ and $ 2$part) and their dual ones as well the MordellWeil groups of elliptic curves $ y^{2} = x (x \pm p) (x \pm q) $ over imaginary quadratic number fields of class number one are determined explicitly in many cases.
 Publication:

arXiv eprints
 Pub Date:
 July 2012
 arXiv:
 arXiv:1207.0287
 Bibcode:
 2012arXiv1207.0287L
 Keywords:

 Mathematics  Number Theory;
 14H52 (Primary) 11G05 (Secondary)
 EPrint:
 12