On the Selmer groups and Mordell-Weil groups of elliptic curves y² = x (x ± p) (x ± q) over imaginary quadratic number fields of class number one

2012/07/02 by Li, Xiumei
#14H52 (Primary) 11G05 (Secondary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1207.0287

Abstract

Let p and q be odd prime numbers with q - p = 2, the φ-Selmer groups, Shafarevich-Tate groups ( φ- and 2-part) and their dual ones as well the Mordell-Weil groups of elliptic curves y² = x (x ± p) (x ± q) over imaginary quadratic number fields of class number one are determined explicitly in many cases.

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