We give a classification of all complex Delsarte surfaces with only isolated ADE singularities. This results in 83 types of surfaces. For each of these types, we give a closed formula for the Picard number depending only on the degree.
Bas HEIJNE. "Picard numbers of Delsarte surfaces." J. Math. Soc. Japan 68 (1) 101 - 118, January, 2016. https://doi.org/10.2969/jmsj/06810101