Dumbbell Curve

Algebraic Equation: x6-a2x4+a4y2 = 0

Degree: 6

Singularities: [0:0:1], [0:1:0]

Multiplicity: 2, 4

Branching Number of each Singularity: 2, 2

Genus: 0

Parameterized Equation: x = (t2+1)2/(2t(t2-1)), y = -(t2+1)3/(2at(t2-1)2)

Delta Invariant: 10

Milnor Number: 3

Tjurina Number: 17





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