| Summary: | We consider a family of higher degree Enneper minimal surface <inline-formula> <math display="inline"> <semantics> <msub> <mi>E</mi> <mi>m</mi> </msub> </semantics> </math> </inline-formula> for positive integers <i>m</i> in the three-dimensional Euclidean space <inline-formula> <math display="inline"> <semantics> <msup> <mi mathvariant="double-struck">E</mi> <mn>3</mn> </msup> </semantics> </math> </inline-formula>. We compute algebraic equation, degree and integral free representation of Enneper minimal surface for <inline-formula> <math display="inline"> <semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> </mrow> </semantics> </math> </inline-formula>. Finally, we give some results and relations for the family <inline-formula> <math display="inline"> <semantics> <msub> <mi>E</mi> <mi>m</mi> </msub> </semantics> </math> </inline-formula>.
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