On the number of elliptic curves with prescribed isogeny or torsion group over number fields of prime degree

2011/09/28 by Filip Najman, Najman, Filip
Mathematics · Social Sciences · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Vietnamese History and Culture Studies #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.1109.6278

11 pages

openalex publication_date 2011/09/28 · arxiv created 2014/02/26 · arxiv updated 2014/02/27 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

Let p be a prime and K a number field of degree p. We count the number of elliptic curves, up to K-isomorphism, having a prescribed property, where this property is either that the curve contains a fixed torsion group as a subgroup, or that it has an isogeny of prescribed degree.

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