Descent calculations for the elliptic curves of conductor 11

Let A be one of the three elliptic curves over Q with conductor 11. We show that A has Mordell-Weil rank zero over its field of 5-division points. In each case we also compute the 5-primary part of the Tate-Shafarevich group. Our calculations make use of the Galois equivariance of the Cassels-Tate pairing