Lemniscate of Gerono/ Eight Curve

Algebraic Equation: x4-a2x2+a2y2 = 0

Degree: 4

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

Multiplicity: 2, 2

Branching Number of each Singularity: 2, 2

Genus: 0

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

Delta Invariant: 3

Milnor Number: 1

Tjurina Number: 4

Projective Plane: 1 node, 1 cusp





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