Computing things for all degree d numberfields in the LMFDB

[Maarten Derickx]

Hi,

Is it possible to obtain defining equations for all degree d numberfields in the LMFDB, where d=2, 3, 4?

Motivation: For a project I am working on I want to compute certain things regarding isogenies over degree d number fields (using code that is almost finished implementing). The code is quite fast for degree 2, 3, still performs ok for degree 4 but gets quite slow for degrees > 4.  A back of the envelope estimation with how many number fields there are in the lmfdb (and checking runtimes for certain complicated large discriminant fields) shows that it should be reasonable to run this computation for all number fields of degree 2, 3 and maybe even degree 4 in the lmfdb. And it would be nice to have some numerics on the outcomes of these computations on an lmfdb scale dataset.

Thanks,
Maarten

[Andrew Sutherland]

Yes, but given the large number of them you will need to do this by accessing the database directly from Sage and writing the results to a file, which you can do using your account on legendre.  If you need to update your ssh key on legendre, email your public key to me, Edgar Costa, or David Roe.  If you need help figuring out how to use db_backend, feel free to come to LMFDB Fridays or post a question on the LMFDB Zulip (email me if you need access).

Drew