The representation depends on the model of the elliptic curve, the point is associated with. Moreover it contains a boolean value which is true if and only if the point is the point at infinity, the zero of the corresponding group of points.
Any point holds also a reference to the elliptic curve it sits on.
Relevant addition routines are then optimized for working with such curves. In addition to functions for points defined over arbitrary fields the class offers special functions only for points defined over finite fields. However for efficiency reasons the following functions are also defined. If P is a point defined on a given curve, the following assignments exist which use the same curve. They should for this reason be used with care.