This repository contains the code and data attached to On 12-congruences of elliptic curves by Sam Frengley, DOI 10.1142/S1793042124500301, arXiv:2208.05842. All of the code in this repository is written in Magma.

The directories are arranged as follows:

• In the directory verify we provide code which checks the claims made in the paper.

• The directory Z2_3_4 contains files related to 2, 3, and 4-congruences of elliptic curves. In particular, we record the polynomials in Theorem 3.3 and the symmetrical 2-parameter families in Remark 3.4.

• The directory Z12-r contains files related to 12-congruences. We record the equations for the surfaces Z(12, r), examples of rational points and curves of low genus on these surfaces, and the corresponding pairs of (12, r)-congruent elliptic curves.