Generalization of Vélu's formulae for isogenies between elliptic curves.
Given an elliptic curve E and a finite subgroup G, Vélu's formulae concern to a separable isogeny IG: E → E' with kernel G. In particular, for a point P ∈ E these formulae express the first elementary symmetric polynomial on the abscissas of the points in the set P+G as the difference between the abscissa of IG(P) and the first elementary symmetric polynomial on the abscissas of the nontrivial points of the kernel G. On the other hand, they express Weierstrass...