The code and data attached to the paper N-congruences of elliptic curves arising from non-surjective mod N Galois representations by Sam Frengley, arXiv:2111.05813, DOI 10.1090/mcom/3770. All code is written in Magma.

We would like to acknowledge our use of code written by Jeremy Rouse, Andrew V. Sutherland, and David Zureick-Brown in the very useful repository ell-adic-galois-images which is associated to their paper l-adic images of Galois for elliptic curves over Q arXiv:2106.11141 (2021). In particular we make use of the functions in the file groups/gl2.m. For the convenience of the user, we have copied the relevant parts of their code into the directory RSZ21.

We have arranged the directories as follows:

• functions contains Magma code for (1) manipulating subgroups of GL_2(Z/NZ) for the purposes of our paper, (2) performing the Mordell-Weil sieve as described in Section 7.2 on double covers of elliptic curves over Q, and (3) doing 2-cover descent on a genus 2 curve admitting a Richelot isogeny as described in Section 8.

• models contains equations and j-maps for the modular curves computed in Sections 6 and 7, this includes canonical models for all the curves of genus <= 4 appearing in Section 7.1.

• RSZ21 contains the code of Rouse--Sutherland--Zureick-Brown which is relevant for us.

• verify contains Magma scripts to verify the claims we make in the paper which require checking.