Selmer groups of supersingular elliptic curves

The orders of growth of the Selmer groups of supersingular elliptic curves in cyclotomic 2-extensions are established. These orders have the form $2^n/3$ or $2^{n+1}/3$ which alternate depending on the parity of $n$ – the number of the level of the cyclotomic extension. This agrees with the hypothetical formulas indicated earlier by A. G. Nasybullin. Bibl. 3 titles.