Butterfly Catastrophe Curve Algebraic Equation: 13824a5x2+4096a4y3-86400a3x2y-24576a2y4+144000ax2y2+84375x4+36864y5= 0 Degree: 5 Singularities: [0:0:1], [0:a2/3:1], [16ia2√(2a)/75√(15):4a2/15:1], [-16ia2√(2a)/75√(15):4a2/15:1], [16ia2√(a)/25√5:3a2/5:1], [-16ia2√(a)/25√5:3a2/5:1] Multiplicity: 2, 2, 2, 2, 2, 2 Branching Number of each Singularity: 1, 2, __, __, __, __ Genus: 0 Parameterized Equation: Delta Invariant: 6 Milnor Number: 2 Tjurina Number: 9 All Curves Curves by Degree Curves by Genus