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A Gallery of Cubic Plane Curves

The equation of each curve is a third-degree polynomial function of two variables, and can be written in the form   $a_1x^3+a_2x^2y+a_3xy^2+a_4y^3+a_5x^2+a_6xy+a_7y^2+a_8x+a_9y+a_{10}=0$.   One property common to each of these curves is that it will intersect any given line at most 3 times.

Each of the graphs on this page is a cubic plane curve, displayed in the window   $[-5,5]\times[-5,5]$.