What is "isogeny"

n. The condition of being isogenous

In mathematics, an isogeny is a morphism of algebraic groups that is surjective and has a finite kernel.

If the groups are abelian varieties, then any morphism f : A → B of the underlying algebraic varieties which is surjective with finite fibres is automatically an isogeny, provided that f(1) = 1. Such an isogeny f then provides a group homomorphism between the groups of k-valued points of A and B, for any field k over which f is defined.

The terms "isogeny" and "isogenous" come from the Greek word ισογενη-ς, meaning "equal in kind or nature".