Branching data for curves up to genus 48

This project arose from my work decomposing Jacobian varieties of curves since in that work I needed to know the generating vectors for a given group acting on a curve. Thomas Breuer had programs which computed this information, but he did not record it with data he generated from those programs. I have added functionality to his program to record these generating vectors, and run the programs in Magma and GAP up to genus 48. The data for these generating vectors is below.

The details of this project may be found in this writeup [pdf] and also posted on ArXiV.

I have no plans to publish this work, as it is just a modification of Breuer's original work. If you use the generating vector data, you can cite this page or the ArXiV page mentioned above. I would love to hear from you if you use it.

Finally, thank you to Thomas Breuer for giving me permission to repost this data.


Breuer's code, translated to Magma and modified to print generating vectors.
Last Modified: May 10, 2016

My code to read the data into Magma, or search the data for specific types of examples.
Last Modified: April 24, 2016

Groups and Signatures only

This file gives the list of groups and signatures for all genus from 2 to 48, except two curves of genus 46 of size 2160. It is simply a compliation of data Breuer created, updated for the larger current Magma or GAP databases.
Last Modified: December 23, 2015
groupsignaturedata (2.7 MB)

Magma: large groups

For genus g from 2 to 48, this gives the generating vectors for all groups of order greater than 4(g-1) (again except for the genus 46 examples of size 2160).
Last Modified: December 23, 2015
GenVectMagma-LargeGps (2.5 MB zipped)

WARNING: This data was computed using Magma V2.19-9. Changes in newer versions of Magma mean that in a couple of cases an error may be returned. I am working on a permanent fix, but in the short term, if you run into an error and are running a newer verion of Magma, email me and I can give you a workaround. Thanks to Michela Artebani and her student, Cristian Monsalve, at Universidad de Concepcion for pointing out the issue.

In genus 46 there is are two groups acting on curves of this genus but which are beyond the size of the SmallGroup database. Their information is recorded here.

Magma: complete data for genus 2 through 20

For genus g from 2 to 20, this gives the generating vectors for all groups.
Last Modified: May 16, 2016
GenVectMagmaToGenus20 (44.0 MB zipped)

WARNING: See the warning under the previous section.

GAP: full data to genus 40

This is the full data for GAP. Currently up to genus 40, except genus 33.
Last Modified: December 23, 2015
GenVectGAP (40.9 MB zipped)

Magma: other available versions

Full data for higher genus is available upon request.


Last Updated: May 31, 2016