• Corpus ID: 119628029

On the Selmer groups and Mordell-Weil groups of elliptic curves $ y^{2} = x (x \pm p) (x \pm q) $ over imaginary quadratic number fields of class number one

@article{Li2012OnTS,
  title={On the Selmer groups and Mordell-Weil groups of elliptic curves \$ y^\{2\} = x (x \pm p) (x \pm q) \$ over imaginary quadratic number fields of class number one},
  author={Xiumei Li},
  journal={arXiv: Number Theory},
  year={2012}
}
  • Xiumei Li
  • Published 2 July 2012
  • Mathematics
  • arXiv: Number Theory
Let $ p $ and $ q $ be odd prime numbers with $ q - p = 2, $ the $\varphi -$Selmer groups, Shafarevich-Tate groups ($ \varphi - $ and $ 2-$part) and their dual ones as well the Mordell-Weil 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. 

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On the equation y 2 = x ( x − 2 m ) ( x + q − 2 m )