Endomorphism Rings of Elliptic Curves

[Eric Zhu]

Is there a way to get the endomorphism ring of an elliptic curve in Sage? 

[Nils Bruin]

On Tuesday, January 21, 2020 at 5:23:43 PM UTC-8, Eric Zhu wrote:

Is there a way to get the endomorphism ring of an elliptic curve in Sage? 

with

d=E.cm_discriminant() 

you know that End(E) is the cm order of discriminant d. If E does not have cm, then End(E)=Z

[John Cremona]

I suspect the question might have been referring to elliptic curves over finite fields. In the ordinary case you can ask for the Frobenius order and know that the endomorphism ring is between that and the maximal order of its field of fractions (an imaginary quadratic field) but as far as I know Sage jas no implementation of finding the exact endomorphism ring such as Kohel's algorithm.

[Eric Zhu]

In the ordinary case, is it possible to get the regular function corresponding to some endomorphism?