  We apply Orlov's equivalence to derive formulas for the Betti numbers of
maximal Cohen-Macaulay modules over the cone an elliptic curve $(E,x)$ embedded
into $\mathbb{P}^{n-1}$, by the full linear system $|\mathcal{O}(nx)|$, for
$n>3$. The answers are given in terms of recursive sequences. These results are
applied to give a criterion of (Co-)Koszulity.
  In the last two sections of the paper we apply our methods to study the cases
$n=1,2$. Geometrically these cases correspond to the embedding of an elliptic
curve into a weighted projective space. The singularities of the corresponding
cones are called minimal elliptic. They were studied by K.Saito, where he
introduced the notation $\widetilde{E_8}$ for $n=1$, $\widetilde{E_7}$ for
$n=2$ and $\widetilde{E_6}$ for the cone over a smooth cubic, that is, for the
case $n=3$. For the singularities $\widetilde{E_7}$ and $\widetilde{E_8}$ we
obtain formulas for the Betti numbers and the numerical invariants of MCM
modules analogous to the case of a plane cubic.
