mdmagma

Magma code for computing with modular curves by Maarten Derickx and Andrew V. Sutherland.

Requirements

This requires Andrew V. Sutherlands magma package. It is known to work with the version commit 6a5a68a8c5ba..., and should also work with later versions.

Research Papers

The code in this project has been used for the following research papers:

Gonality of the modular curve X₁(N)

Torsion subgroups of elliptic curves over quintic and sextic number fields

Version 2

A version 2 that is more consistent and organized is under development. V2 will use intrinsics, user defined types and have automated tests. This is currently done in the v2 subfolder.

Using V2

To use V2 run

cd v2
magma

And then from withing magma run

AttachSpec("mdmagma.spec");

Dependencies

mdmagma depends on https://github.com/AndrewVSutherland/Magma . Note that AttachSpec("mdmagma.spec"); also makes sure that all external dependencies are attached. If you want to attach the files from mdmagma without also attaching the dependencies then you need to attach mdmagma_internal.spec instead. This is usefull if you already have the dependencies of mdmagma attached by default or if you are using CHIMP. There is no guarantee that mdmagma will work with dependencies other than those listed by running:

git submodule

Testing

To run the tests for this repository execute. At the momemnt it is only possible to run the tests from the tests folder. Running them from any other folder will result in an error.

cd tests
magma v2/modular_curves/test_all.m

Copyright

copyright (C) 2025 Maarten Derickx, Andrew Sutherland
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program.  If not, see [http://www.gnu.org/licenses/].