engleski

A proof of the associativity of the group law on elliptic curves

We first review standars proofs of associativity of the group law on elliptic curves. After that we presnt a proof based on the following well-known facts: Let phi: C_1 --> C_2 be a rational map of nonsimgular curves. Then: (i) phi is a morphism. (ii) The morphism phi is surjective or constant. (iii) If psi: C_1 --> C_2 is a morphism such that psi <> phi then the set of all P in C_1 such that phi(P) = psi(P) is finite.

Elliptic curves

nije evidentirano