EQ[x_,y_]:=x^4-4x^3*y-4x^2y^2+x*y^3+y^4;
PT={x,y}/.FindInstance[EQ[x,y]==1,{x,y},Integers,10];
ContourPlot[EQ[x,y]==1,{x,-5,5},{y,-5,5},
ContourStyle->Dotted,ImageSize->500,
Epilog->{Table[Style[Text[CharacterRange["\[WhiteKing]",
"\[BlackPawn]"][[i]],PT[[i]]],Hue[i/10],Large],{i,10}]}]
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