A local-global principle for rational isogenies of prime degree

Andrew V. Sutherland

Type: Article

Publication Date: 2012-01-01

Citations: 19

DOI: https://doi.org/10.5802/jtnb.807

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.

Locations

Journal de Théorie des Nombres de Bordeaux - View - PDF
arXiv (Cornell University) - View - PDF
French digital mathematics library (Numdam) - View - PDF
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