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Bulletin of the London Mathematical Society Advance Access originally published online on October 3, 2008
Bulletin of the London Mathematical Society 2008 40(6):1091-1093; doi:10.1112/blms/bdn093
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© 2008 London Mathematical Society

Rational points of order 7

Neil Dummigan

University of Sheffield
Department of Pure Mathematics
Hicks Building
Hounsfield Road
Sheffield, S3 7RH
United Kingdom

Received 14 November 2007. Revision received 29 May 2008.

For an elliptic curve over the rationals, optimal in its isogeny class, with a rational point of order 7 but LE(1) != 0, we prove that 7 divides the product of the Tamagawa factors with the order of the Shafarevich–Tate group. This is a small consequence of the Birch and Swinnerton-Dyer conjecture.

2000 Mathematics Subject Classification 11G05, 11G18, 11G40.


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