surfaces is known to be parametrized by three integers. The transcendental lattice $T(S)$ of a K3 surface $S$ is the orthogonal complement of the Néron–Severi lattice $NS(S)$ inside the K3 lattice $\Lambda_{K3}$, and the transcendental lattices $T(S)$ of attractive K3 surfaces are positive-definite, even 2 $\times$ 2 lattices. The complex structure of an attractive K3 surface is determined by the transcendental lattice [@PS-S; @SI]. The intersection form of the transcendental lattice of an attractive K3 surface can be transformed into the following form under the $GL_2(\Z)$ action: $$\label{general intersection form in 2.3}
\begin{pmatrix}
2a & b \\
b & 2c \\
\end{pmatrix}.$$ Here $a,b,c$ are integers, $a,b,c\in\Z$, and satisfy the relations: $$a \ge c \ge b  \ge 0.$$ Thus, the triplet of integers, $a,b,c$, parameterizes the complex structure moduli of the attractive K3 surfaces. We denote an attractive K3 surface, whose transcendental lattice has the intersection form (\[general intersection form in 2.3\]) as $S_{[2a \hspace{1mm} b \hspace{1mm} 2c]}$ in this note.

An elliptic attractive K3 surfaces with a section is said to be [*extremal*]{} when it has Mordell–Weil rank 0. This condition is equivalent to an elliptic K3 surface with a section having singularity rank 18. Thus, the non-Abelian gauge 