A note on the Selmer group of the elliptic curve \(y^ 2=x^ 3+Dx\). (English) Zbl 1040.11042

Summary: We present an explicit formula for the Selmer rank of the elliptic curve \(y^2=x^3+Dx\). Using this formula, we give some results analogous to B. Iskra’s theorem [ibid. 72, 168–169 (1996; Zbl 0877.11014)].


11G05 Elliptic curves over global fields


Zbl 0877.11014
Full Text: DOI


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