Something like this?
Blue curve is the intersection of the two surfaces $ 0 = y^2 - x(x^2 + 1) $ and $ 0 = z^2 - y(y^2 + 1) $.
The 3D plots were generated with Mathematica output, as documented here.
Blue curve is the intersection of the two surfaces $ 0 = y^2 - x(x^2 + 1) $ and $ 0 = z^2 - y(y^2 + 1) $.