On maximizing curves of degree 7

In the present paper we investigate an intriguing question on the existence of maximizing curves of degree 7 with some prescribed \(\textrm{ADE}\) $\text{ADE}$ singularities. We give a result proving the non-existence of such maximizing septics and we give new examples of conic-line arrangements with some \(\textrm{ADE}\) $\text{ADE}$ singularities that are free but not maximizing.