They're curves (one-dimensional), not surfaces. An example of an elliptic curve is y^2 = x^3 + 1. The polynomial P(x,y) = x^3 + 1 - y^2 has degree 3. A surface

They're curves (one-dimensional), not surfaces. An example of an elliptic curve is y^2 = x^3 + 1. The polynomial P(x,y) = x^3 + 1 - y^2 has degree 3. A surface is a 2 dimensional geometric shape.