Class fields generated by coordinates of elliptic curves

DOI10.1515/MATH-2022-0502zbMath1523.11064arXiv2111.01021MaRDI QIDQ6381889

Dong Hwa Shin, Ja Kyung Koo, Ho Yun Jung

Publication date: 1 November 2021

Abstract: Let $K$ be an imaginary quadratic field different from $mathbb{Q}(sqrt{-1})$ and $mathbb{Q}(sqrt{-3})$. For a nontrivial integral ideal $mathfrak{m}$ of $K$, let $K_mathfrak{m}$ be the ray class field modulo $mathfrak{m}$. By using some inequalities on special values of modular functions, we show that a single $x$-coordinate of a certain elliptic curve generates $K_mathfrak{m}$ over $K$.

Mathematics Subject Classification ID

Modular and automorphic functions (11F03) Complex multiplication and moduli of abelian varieties (11G15) Class field theory (11R37)

This page was built for publication: Class fields generated by coordinates of elliptic curves