LMFDB-magma

A magma interface to the LMFDB.

Security warning

This code has not been designed with security in mind, and might lead to arbitrary code exectution on the machine it is used on if either one of the following two things is compromised:

1. The data in the database at devmirror.lmfdb.xyz .
2. Your connection to devmirror.lmfdb.xyz .

Note that lmfdb-lite/psycodict/psycopg2 doesn't require a fully verified ssl connection by default making a man in the middle attack feasible regarding point 2. On top of this lmfdb.xyz doesn't have a valid ssl certificate at the time of writing so it is not even possible to run lmfdb-lite with sslmode=verify-full.

It is therefore advised to only use lmfdb-magma on a (virtual) machine whose secturity you don't care to much about, like a temporary docker container.

Requirements

This requires python 3.10 or later and lmfdb-lite. lmfdb-lite is installed as follows:

pip3 install -U "lmfdb-lite[pgbinary] @ git+https://github.com/roed314/lmfdb-lite.git"

Installation

The recommended way of installation at the moment is git using the command:

git clone --recurse-submodules https://github.com/nt-lib/lmfdb-magma.git

Note that this will also download Andrew V. Sutherland's Magma for more congruence subgroup related functionality.

Example usage:

All functions in this package are prefixed with MD in order to avoid namespace collisions with other packages.

At the moment there is only a high level implementation for creating subgroups in GL_2(Zhat). This is done as below

> AttachSpec("lmfdb-magma/lmfdb.spec");
> G := MDGL2FromLMFDBLabel("11.12.1.a.1"); G;
MatrixGroup(2, IntegerRing(11)) of order 2^2 * 5^2 * 11
Generators:
    [5 2]
    [0 2]

    [6 3]
    [0 3]
> // We can also lookup the label given the group
> MDGL2LMFDBLabel(G);
11.12.1.a.1

Lookup by label

There is also lower level functionality to obtain any lmfdb object from any table listed on https://www.lmfdb.org/api/ using the label:

> AttachSpec("lmfdb-magma/lmfdb.spec");
> MDLMFDBLookup("gps_gl2zhat_fine", "11.12.1.a.1");
Associative Array with index universe String structure
> G := MDLMFDBLookup("gps_gl2zhat_fine", "11.12.1.a.1");
> G;
Associative Array with index universe String structure
> G["generators"];
[
    [ 5, 2, 0, 2 ],
    [ 6, 3, 0, 3 ]
]

Searching

There is also limited search functionality similar to that of https://github.com/roed314/psycodict/blob/ab514e1a87ec73a2f27f59ef6c3ec927954a6623/psycodict/searchtable.py#L712 . Currently only the query and the limit arguments are supported. The result is a list of associative arrays, where each associative array contains the information of one lmfdb entry.

The below shows there is only one modular curve containing -1 in the LMFDB whose CPlabel is 9A1.

> lmfdb_data := MDLMFDBSearch("gps_gl2zhat_fine",[*<"CPlabel","9A1">,<"contains_negative_one","true">*]);
> print #lmfdb_data;
1
> // manually turn the lmfdb result into a subgroup of GL2
> G := MDGL2FromAssoc(lmfdb_data[1]);
> print G;
MatrixGroup(2, IntegerRing(9)) of order 2^2 * 3^4
Generators:
    [2 1]
    [3 8]

    [5 7]
    [6 7]
> // the below shows which data is available for this modular curve
> print Keys(lmfdb_data[1]);
{ q_gonality, rank, coarse_class_num, num_known_degree1_noncusp_points, 
coarse_index, bad_primes, qbar_gonality, num_known_degree1_noncm_points, 
determinant_label, kummer_orbits, has_obstruction, level_is_squarefree, Glabel, 
CPlabel, RZBlabel, coarse_level, lattice_labels, pointless, psl2level, 
psl2index, traces, RSZBlabel, Slabel, trace_hash, q_gonality_bounds, power, 
models, genus, coarse_class, level, parents_conj, sl2level, index, nu2, 
rational_cusps, coarse_label, psl2label, nu3, squarefree, canonical_generators, 
fine_num, cusp_widths, coarse_num, conductor, reductions, scalar_label, parents,
label, sl2label, contains_negative_one, curve_label, lattice_x, newforms, 
cm_discriminants, cusp_orbits, generators, SZlabel, mults, name, factorization, 
obstructions, simple, all_degree1_points_known, cusps, num_known_degree1_points,
isogeny_orbits, canonical_conjugator, num_bad_primes, level_radical, 
genus_minus_rank, orbits, qbar_gonality_bounds, log_conductor, dims }
> // We look up the Q-gonality of this curve
> lmfdb_data[1]["q_gonality"];
2

Troubleshooting

An error as below means that lmfdb-lite is not installed in the python environment that is used.

> AttachSpec("lmfdb-magma/lmfdb.spec");
> MDGL2FromLabel("11.12.1.a.1");
Traceback (most recent call last):
  File "<string>", line 1, in <module>
  File "~/lmfdb-magma/py_src/lmfdb_magma/db.py", line 4, in lmfdb_lookup
    from lmf import db
ModuleNotFoundError: No module named 'lmf'

MDGL2FromLabel(
    label: 11.12.1.a.1
)
MDLMFDBLookup(
    table: gps_gl2zhat_fine,
    label: 11.12.1.a.1
)
MDLMFDBLookupStr(
    table: gps_gl2zhat_fine,
    label: 11.12.1.a.1
)
In file "~/lmfdb-magma/magma_src/d\
b.m", line 14, column 18:
>>     entry := Pipe(full_cmd, "");
                    ^
Runtime error in 'Pipe': Subprocess failed with exit status 1

The important line that indicates this is what is going wrong is the line

ModuleNotFoundError: No module named 'lmf'

To solve this make sure that lmfdb-lite is installed as mentioned above. If you are sure lmfdb-lite is installed then it is because lmfdb-magma is picking up the wrong python environment. You can configure which python installation to use as follows:

> python_path := "~/python_env/bin/python";
> MDSetPythonInterpreter(python_path);
> MDGL2FromLabel("11.12.1.a.1");                                               
MatrixGroup(2, IntegerRing(11)) of order 2^2 * 5^2 * 11
Generators:
    [5 2]
    [0 2]

    [6 3]
    [0 3]