Elliptic Curves over Q - Elliptic Curves: Number Theory and Cryptography - page 254

(c) Suppose we choose Q with nQ = P , and thus obtain a cocycle

δ P is a coboundary.
(d) Suppose that δ P ( σ ) is a coboundary. Show that there exists Q

δ P . Show that δ P −

∈

E ( Q ) such that nQ = P .

This shows that we have an injection E ( Q ) /nE ( Q ) → H 1 ( G, E [ n ]).
This is the map of Equation 8.18.