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 Iskra's theorem.
Takeshi Goto. "A note on the Selmer group of the elliptic curve $y^2 = x^3 + Dx$." Proc. Japan Acad. Ser. A Math. Sci. 77 (7) 122 - 125, Sept. 2001. https://doi.org/10.3792/pjaa.77.122