lattice polarization, namely elliptically fibered K3 surfaces with a type $II^*$ fiber and a type $III^*$ fiber with a global section, and they constructed the moduli of heterotic strings with unbroken $\mathfrak{e}_8\mathfrak{e}_7$ algebra as the heterotic duals of them on the 2-torus. The moduli space of the non-geometric heterotic strings with unbroken $\mathfrak{e}_8\mathfrak{e}_7$ algebra constructed in [@MM] is given by $$D_{2,3} / O^+(L^{2,3}).$$ Here $L^{2,3}$ denotes the orthogonal complement of $H\oplus E_8\oplus E_7$ inside the K3 lattice $\Lambda_{K3}$, and the non-geometric heterotic strings constructed in [@MM] possess $O^+(L^{2,3})$-symmetry. Here $O^+(L^{2,3})$[^3] mixes the complex structure moduli, the Kähler moduli and the moduli of Wilson line values. Therefore, the resulting heterotic strings do not have a geometric interpretation[^4]; for this reason, the resulting heterotic strings are called [*non-geometric*]{} heterotic strings. A single Wilson line expectation value is non-zero for the non-geometric heterotic strings with unbroken $\mathfrak{e}_8\mathfrak{e}_7$ gauge algebra as constructed in [@MM]. The mathematical results of Kumar [@Kumar] and Clingher and Doran [@ClingherDoran2011; @ClingherDoran2012], which gave the Weierstrass equations of elliptic K3 surfaces with a global section with $E_8 E_7$ singularity, the coefficients of which are expressed as Siegel modular forms of even weight, were used in their construction.

Clingher, Malmendier, and 