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arXiv:1006.1782 [math.NT]AbstractReferencesReviewsResources

A local-global principle for rational isogenies of prime degree

Andrew V. Sutherland

Published 2010-06-09, updated 2011-11-02Version 4

Let K be a number field. We consider a local-global principle for elliptic curves E/K that admit (or do not admit) a rational isogeny of prime degree n. For suitable K (including K=Q), we prove that this principle holds when n = 1 mod 4, and for n < 7, but find a counterexample when n = 7 for an elliptic curve with j-invariant 2268945/128. For K = Q we show that, up to isomorphism, this is the only counterexample.

Comments: 11 pages, minor edits, to appear in Journal de Th\'eorie des Nombres de Bordeaux
Journal: Journal de Th\'eorie des Nombres de Bordeaux 24 (2012), 475-485
Categories: math.NT
Subjects: 11G05
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