Journal of the
Korean Mathematical Society JKMS

Let $K$ be an imaginary quadratic field with ring of integers $\mathcal{O}_K$. Let $E$ be an elliptic curve with complex multiplication by $\mathcal{O}_K$, and let $h_E$ be the Weber function on $E$. Let $N\in\{2,\,3,\,4,\,6\}$. We show that $h_E$ alone when evaluated at a certain $N$-torsion point on $E$ generates the ray class field of $K$ modulo $N\mathcal{O}_K$. This would be a partial answer to the question raised by Hasse and Ramachandra.

Keywords: class field theory, complex multiplication, Weber function

MSC numbers: Primary 11R37; Secondary 11G15, 11G16