  A loop whose inner mappings are automorphisms is an \emph{automorphic loop}
(or \emph{A-loop}). We characterize commutative (A-)loops with middle nucleus
of index 2 and solve the isomorphism problem. Using this characterization and
certain central extensions based on trilinear forms, we construct several
classes of commutative A-loops of order a power of 2. We initiate the
classification of commutative A-loops of small orders and also of order $p^3$,
where $p$ is a prime.
