elliptic module provides elliptic curves.
A factory function to create an instance of ECoverQ or ECoverFp or ECoverF2. and their are subclass of ECGeneric, see also as use.
If characteristic is set, create elliptic curve over finite field(ECoverFp or ECoverF2). if set index>2, you should take elliptic curve over finite extended field(i.e. E/F_q, q=characteristic^index). Elliptic curve over finite extended field is under construction(not implemented).
Otherwise (if characteristic not given or 0), create elliptic curve over rational field(ECoverQ) .
How to asssign curves in Weierstrass list form given by the equation:
E: y^2 + a1 xy + a3 y = x^3 + a2 x^2 + a4 x + a6
>>> E=EC([a1,a2,a3,a4,a6],characteristic)
or for
E: y^2= x^3 + A x + B
>>> E=EC([A,B],characteristic)