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I wan to draw the ECC and the auxiliary line. I tried this: ECCPlot[a_, b_, c_, d_]:=ContourPlot[{y^2 == a x^3 + b x^2 + c x + d,y == x + 1, (x + 1)^2 == a x^3 + b x^2 + c x + d }, {x,-5,5}, {y, -5, 5}, Axes -> True,Frame -> False, Mesh -> {{0.}}]

and what I want is like this: enter image description here

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Add:

Epilog -> Line[{{-2, 4}, {3, 8}}]

or whatever you want the line to be.

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