Elliptic curves with complex multiplication and abelian division fields

2023/08/01 by Asimina S. Hamakiotes, Hamakiotes, Asimina S., Alvaro Lozano-Robledo +1 · 1 voice · 1 citation
Mathematics · #14H52 #14K22 #FOS: Mathematics #Number Theory (math.NT) #Primary: 11G05 #Secondary: 11G15 #math.NT

paper · pdf · doi:10.48550/arxiv.2308.00668

Abstract

Let K be an imaginary quadratic field, and let O_K,f be an order in K of conductor f≥ 1. Let E be an elliptic curve with CM by O_K,f, such that E is defined by a model over ℚ(j_K,f), where j_K,f=j(E). In this article, we classify the values of N≥ 2 and the elliptic curves E such that (i) the division field ℚ(j_K,f,E[N]) is an abelian extension of ℚ(j_K,f), and (ii) the N-division field coincides with the N-th cyclotomic extension of the base field.

Cited by

• Uniform bounds on the level of cyclotomic division fields of elliptic curves

Discussions

• New paper in the arXiv! Super excited to share this joint work with one of my current PhD students, Asimina Hamakiotes, who is in a sky-rocket trajectory. We extend some work of E. Gonzalez-Jimenez an [bsky, 3 points, 1 comments]

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