Criteria for p-ordinarity of families of elliptic curves over infinitely\n many number fields

2014/04/12 by Nuno Freitas, Freitas, Nuno, Panagiotis Tsaknias +1
Mathematics · Social Sciences · #11D41 #11G05 #Algebraic Geometry and Number Theory #FOS: Mathematics #Historical and Political Studies #Number Theory (math.NT) #Vietnamese History and Culture Studies

paper · pdf · doi:10.48550/arxiv.1404.3278

openalex publication_date 2014/04/12 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

Let K_i be a number field for all i \∈ \ℤ_{> 0} and let\n\E be a family of elliptic curves containing infinitely many members\ndefined over K_i for all i. Fix a rational prime p. We give sufficient\nconditions for the existence of an integer i₀ such that, for all i > i₀\nand all elliptic curve E \∈ \E having good reduction at all\n mathfrakp \| p in K_i, we have that E has good ordinary reduction at\nall primes mathfrakp \| p.\n

Related

• Computing all elliptic curves over an arbitrary number field with\n prescribed primes of bad reduction
• Critères d'irréductibilité pour les représentations des courbes elliptiques
• Elliptic curves of rank one over number fields
• Rank one elliptic curves and rank stability
• Elliptic curves with good reduction outside of the first six primes