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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.

Descent calculations for the elliptic curves of conductor 11   (31 pages)          

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This article has appeared in the Proceedings of the London Mathematical Society. The preprint cited as "Rational Points on X(11) over Q(mu₁₁) via Galois equivariance of the Cassels-Tate pairing" is available here.