  We give explicitly in the closed formulae the genus zero primary potentials
of the three 6-dimensional FJRW theories of the simple-elliptic singularity
$\tilde E_7$ with the non-maximal symmetry groups. For each of these FJRW
theories we establish the CY/LG correspondence to the Gromov-Witten theory of
the orbifold $[\mathcal{E}/ (\mathbb{Z}/2\mathbb{Z})]$ --- the orbifold
quotient of the elliptic curve by the hyperelliptic involution. Namely, we give
explicitly the Givental's group elements, whose actions on the partition
function of the Gromov--Witten theory of $[\mathcal{E}/
(\mathbb{Z}/2\mathbb{Z})]$ give up to a linear change of the variables the
partition functions of the FJRW theories mentioned. We keep track of the linear
changes of the variables needed. We show that using only the axioms of
Fan--Jarvis--Ruan, the genus zero potential can only be reconstructed up to a
scaling.
