Finding an Elliptic curve from a Lattes map

[Nathabolin]

Problem Description

Sagemath has pre-existing functions to take any elliptic curve and produce its lattes map. We want to make a function which would invert this process.

Pull request for code can be found at Fixes #38330

Proposed Solution

Our solution is to construct a symbolic lattes map from a short form elliptic curve and a symbolic conjugating matrix.

We then conjugate the map with the matrix producing a general form a conjugated lattes map.

We then create an ideal from the set of equations generated by matching term by term the input map and symbolic map.

Finding the variety of that ideal gives back the entries of the matrix and desired coefficients for a short form elliptic curve.

Alternatives Considered

There is no other function that produces these results already extant in sagemath

Additional Information

No response

Is there an existing issue for this?

• I have searched the existing issues for a bug report that matches the one I want to file, without success.