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Descent Calculations for the Elliptic Curves of Conductor 11

Published online by Cambridge University Press:  09 June 2003

Tom Fisher
Tom Fisher
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB. E-mail: T.A.Fisher@dpmms.cam.ac.uk
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Abstract

Let $A$ be any one of the three elliptic curves over $\mathbb{Q}$ 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.

Keywords

elliptic curvesdescent calculationsCassels–Tate pairingnon-abelian Iwasawa theory11G0511Y4011R23
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 86 , Issue 3 , May 2003 , pp. 583 - 606
Copyright
2003 London Mathematical Society

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