Imaginary quadratic field
= Imaginary quadratic field
{title2=$K=\mathbb Q(\sqrt{-d}),\quad d>0$}
An imaginary quadratic field is a <quadratic number field> with no real embedding. Its two complex embeddings are interchanged by complex conjugation. The <endomorphism ring of an elliptic curve> in characteristic zero, when larger than the integers, is an order in such a field; this is <complex multiplication>.