  We consider generalisations of the elliptic Calogero--Moser systems
associated to complex crystallographic groups in accordance to
\cite{EFMV11ecm}. In our previous work \cite{Argyres:2021iws}, we proposed
these systems as candidates for Seiberg--Witten integrable systems of certain
SCFTs. Here we examine that proposal for complex crystallographic groups of
rank one. Geometrically, this means considering elliptic curves $T^2$ with
$\Z_m$-symmetries, $m=2,3,4,6$, and Poisson deformations of the orbifolds
$(T^2\times\mathbb{C})/\Z_m$. The $m=2$ case was studied in
\cite{Argyres:2021iws}, while $m=3,4,6$ correspond to Seiberg--Witten
integrable systems for the rank 1 Minahan--Nemeshansky SCFTs of type
$E_{6,7,8}$. This allows us to describe the corresponding elliptic fibrations
and the Seiberg--Witten differential in a compact elegant form. This approach
also produces quantum spectral curves for these SCFTs, which are given by
Fuchsian ODEs with special properties.
