A local-global principle for rational isogenies of prime degree
Number Theory
2015-12-15 v4
Abstract
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.
Keywords
Cite
@article{arxiv.1006.1782,
title = {A local-global principle for rational isogenies of prime degree},
author = {Andrew V. Sutherland},
journal= {arXiv preprint arXiv:1006.1782},
year = {2015}
}
Comments
11 pages, minor edits, to appear in Journal de Th\'eorie des Nombres de Bordeaux