  A simple algebraic global isometric embedding is presented for the
nonrotating BTZ black hole and its counterpart of Euclidean signature. The
image of the embedding, in Minkowski space of two extra dimensions, is the
interection of two quadric hypersurfaces. Furthermore an embedding into $AdS_4$
or $H_4$ is also obtained, showing that the spacetime is of embedding class one
with respect to maximally symmetric space of negative curvature. The rotating
solution of Euclidean signature is also shown to admit a quadratic algebraic
embedding, but seemingly requires more than two extra dimensions.
