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This is a very basic API for accessing the LMFDB Database.
It lists available databases and collections,
links to their respective descriptions,
and has very limited query capabilities.
Queries are url encoded
key=value
parameters, where the value has a prefix to specify the type.
Keys starting with "_
" are meta-parameters further refining query.
They can be combined by specifying several ones delimited by &
to further drill down to the desired objects.
The result formats are JSON, YAML or HTML (default).
Each list is limited by a maximum of 100 results and the next
entry contains the query to request more objects.
The overall limit is at about 10000 results and beyond that it is necessary to further refine the query to the results in question.
Please use this API responsibly!
Type-prefixes for query values
- s: string
- i: integer
- f: float
- ls: list of strings, delimiter is "," by default or the value of the query key
_delim
- li: list of integers
- lf: list of floats
- py: this evaluates the query literally following the Python syntax. This can be used to express a matrix as a nested list of lists.
- cs, ci, cf and cpy: queries, if the given string, integer, float or Python literal is contained in a list.
Meta-parameters
_format
is used to specify the encoding. Possible values are html (default), json and yaml.- To only retrieve a selected list of entries per document,
use
_fields=name1,name2
to reduce the amount of data sent back to only those fields namedname1
andname2
. - Sorting by fields is done via
_sort=name1,-name2
, where the prefix "-" indicates to sort in descending order. - Finally,
_delim
is used to specify the delimiter (default: ",
")
Examples
-
The query ?degree=i12&r2=i5&_format=json
searches for numberfields of degree 12 with the signature
[2, 5]
and gives the result in the JSON format. -
To search for integers or floats, prefix the value with "i" or "f".
For example elliptic curves with rank 2 and torsion 5:
?rank=i2&torsion=i5
. -
A string encoding a list of integers for the
ainvs
parameter of an elliptic curve is?ainvs=li0;1;1;-840;39800&_format=yaml&_delim=;
, the result formatted in YAML. -
To see those elliptic curves, where the field
torsion_structure
is the list [2,2], encoded as a list of integers: ?torsion_structure=li2;2&_delim=;.
Available Collections
-
artin
field_data (606677) · old2new_labels (1631776) · reps (798140) -
av
fq_endalg_data (2659523) · fq_endalg_factors (4084993) · fq_isog (2945722) -
belyi
galmap_portraits (915) · galmaps (1111) · galmaps_fixed (1111) · galmaps_prim (616) · passports (1007) · passports_fixed (1007) -
bmf
dims (400198) · forms (215630) -
char
dirichlet (562396733) · orbits (21045332) -
cluster
pictures (279) -
ec
classdata (2917287) · curvedata (3824372) · galrep (5482562) · iqf_labels (46358) · iwasawa (974104) · localdata (13178234) · mwbsd (3824372) · nfcurves (725223) · nfportraits (170119) · padic (6819842) · torsion_growth (16491706) -
fq
fields (35352) -
g2c
curves (66158) · endomorphisms (66158) · galrep (51890) · plots (66158) · ratpts (66158) · tamagawa (172938) -
gps
char (11067588) · char_test (0) · conj_classes (463372259) · crep (701) · families (8) · gl2zhat (3336) · gl2zhat_coarse (804450) · gl2zhat_fine (8166335) · gl2zhat_nonsurjdet (11182) · gmodules (73) · groups (544831) · groups_cc (39809857) · groups_cc_test (0) · groups_test (544831) · gsp4zhat (1662) · images (18062) · qchar (13418478) · qchar_test (0) · qrep (371) · small (92804) · smallhash (0) · special_names (3041) · st (10465) · st0 (25) · subgroups (86898892) · subgroups_test (0) · transitive (512614) -
halfmf
forms (3) -
hecke
algebras (1421) · ladic (3771) · orbits (454) -
hgcwa
complete (14) · passports (335012) · unique_groups (1299) -
hgm
euler_survey (97527) · families (61063) · monodromy (137565) · motives (285) -
hmf
fields (400) · forms (368356) · hecke (368356) -
inv
dbs (28) · fields_auto (951) · fields_human (951) · ops (2) · rollback (0) · tables (66) -
lat
lattices (39293) -
lf
fields (99426) -
lfunc
instances (24589089) · lfunctions (24201376) · rs_knowls (6) · search (24123388) -
maass
newforms (14995) · portraits (14995) · rigor (35416) · rigor_portraits (35416) -
mf
boxes (12) · gamma1 (1161064) · gamma1_portraits (27801) · hecke_cc (14417694) · hecke_charpolys (5472725) · hecke_lpolys (5472725) · hecke_nf (218909) · hecke_traces (184887242) · newform_portraits (281965) · newforms (1141508) · newspace_portraits (338553) · newspaces (2471024) · twists_cc (49165089) · twists_nf (1456304) -
modcurve
modelmaps (109042) · models (110173) · pictures (17618) · points (1848861) · teximages (5891) -
modlgal
reps (845) -
modlmf
forms (264) -
nf
fields (22175416) · fields_reflex (2865131) -
smf
dims (72) · ev (3094) · families (14) · fc (26212) · samples (129)