Isogeny
![Isogenous elliptic curves to E can be obtained by quotienting E by finite subgroups, here subgroups of the 4-torsion subgroup.](/Images/godic/202501/21/Lattice_torsion_points.svg1926.png")
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(1A) = 1B. 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.