Elliptic Curve -- from Wolfram MathWorld

Informally, an elliptic curve is a type of cubic curve whose solutions are confined to a region of space that is topologically equivalent to a torus. The Weierstrass elliptic function P(z;g_2,g_3) describes how to get from this torus to the algebraic form of an elliptic curve. Formally, an elliptic curve over a field K is a nonsingular cubic curve in two variables, f(X,Y)=0, with a K-rational point (which may be a point at infinity). The field K is usually taken to be the complex numbers C,...