https://www.estudiosirlandeses.org/2018/03/irish-film-and-television-2017/

Arbitrarily large 2-torsion in Tate–Shafarevich groups of abelian varieties

“…A file which checks the above maps has been placed at [10]. We now describe the map which allows descent to be performed via this isogeny (sometimes referred to as the Cassels map for the descent).…”

“…Replacing y by y v/(v 2 − 1)/(x−v) g+1 and x by v/(x−v) takes this to (1) with each a i = α 2 i (a check of the above map has been included in the file at [10]), so these are birationally equivalent over C. We have already seen that (1), with each a i = α 2 i , is birationally equivalent to C 1 (as in ( 14) with k = 1), so C 1 must also have absolutely simple Jacobian.…”