2012/02/08 by Ágnes Dávid, David, Agnès
Mathematics · #11F80 #11G05 #11G15 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1202.1649
openalex publication_date 2012/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a fixed number field and an elliptic curve defined and semi-stable over this number field, we consider the set of prime numbers p such that the Galois representation attached to the p-torsion points of the elliptic curve is reducible. When the number field satisfies a certain necessary condition, we give an explicit bound, depending only on the number field and not on the semi-stable elliptic curve, for these primes. This generalizes previous results of Kraus.