Class fields generated by coordinates of elliptic curves

2021/11/01 by Ho Yun Jung, Jung, Ho Yun, Ja Kyung Koo +3
Mathematics · #11F03 #11G15 #11R37 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Analytic and geometric function theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2111.01021

openalex publication_date 2021/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K be an imaginary quadratic field different from ℚ(√(-1)) and ℚ(√(-3)). For a nontrivial integral ideal \mathfrakm of K, let K_\mathfrakm be the ray class field modulo \mathfrakm. By using some inequalities on special values of modular functions, we show that a single x-coordinate of a certain elliptic curve generates K_\mathfrakm over K.

Related

• y-coordinates of elliptic curves
• Generation of class fields by using the Weber function
• Ray class fields generated by torsion points of certain elliptic curves
• On a problem of Hasse and Ramachandra
• On the modularity of elliptic curves over imaginary quadratic fields