Kummer map of an elliptic curve (source code)

= Kummer map of an elliptic curve
{wiki=Selmer_group#The_φ-Selmer_group}

The multiplication-by-$n$ sequence gives an injective connecting map
$$
E(K)/nE(K)\hookrightarrow H^1(K,E[n]).
$$
Local conditions restrict its image to the finite $n$-Selmer group.