If is an elliptic curve over a field we let be the ring of all endomorphisms of that are defined over .
A complex lattice
is a subgroup abstractly
isomorphic to
such that
.
Using the Weirestrass -function associated to the lattice
, one proves that there is a group isomorphism
Now suppose is a CM elliptic curve, and let
be a lattice such that
.
Then