This is a typical example of an elliptic curve with complex multiplication.

The cost of the convolution can be associated to the number of complex multiplications involved in the operation.

It turns out that the number of complex multiplications of the overlap-add method are:

The case of elliptic curves with complex multiplication was proved by Shimura in 1964.

There is a Gross-Deligne conjecture in the theory of complex multiplication.

It is isogenous to a product of simple abelian varieties with complex multiplication.

Over the complex numbers, all elliptic curves with complex multiplication can be similarly constructed.

It is known that, in a general sense, the case of complex multiplication is the hardest to resolve for the Hodge conjecture.

When the elliptic curve has complex multiplication, this has been improved to by Laurent.

These classical results are the starting point for the theory of complex multiplication.