• 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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• Mathematics
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