Descent Calculations for the Elliptic Curves of Conductor 11 |
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| Authors: | Fisher Tom |
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| Institution: | Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences Wilberforce Road, Cambridge CB3 0WB. E-mail: T.A.Fisher{at}dpmms.cam.ac.uk |
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| Abstract: | Let A be any one of the three elliptic curves over Q with conductor11. We show that A has Mordell–Weil rank zero over itsfield of 5-division points. In each case we also compute the5-primary part of the Tate–Shafarevich group. Our calculationsmake use of the Galois equivariance of the Cassels–Tatepairing. 2000 Mathematics Subject Classification 11G05, 11Y40,11R23. |
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| Keywords: | elliptic curves descent calculations Cassels– Tate pairing non-abelian Iwasawa theory |
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