  We derive and analyze an infinite-dimensional semidefinite program which
computes least distortion embeddings of flat tori $\mathbb{R}^n/L$, where $L$
is an $n$-dimensional lattice, into Hilbert spaces. This enables us to provide
a constant factor improvement over the previously best lower bound on the
minimal distortion of an embedding of an $n$-dimensional flat torus. As further
applications we prove that every $n$-dimensional flat torus has a finite
dimensional least distortion embedding, that the standard embedding of the
standard tours is optimal, and we determine least distortion embeddings of all
$2$-dimensional flat tori.
