belyi_galmaps

see: https://beta.lmfdb.org/api/belyi_galmaps/ column name | type | description

id | bigint | (internal) label | text | '6T7-4.2_4.2_3.3-a', '6T14-4.1.1_4.1.1_3.3-a', '8T24-6.2_2.2.1.1.1.1_4.4-a', '9T16-6.3_4.4.1_2.2.2.1.1.TODO: resort the cycle type, e.g.: '6T7-4.2_3.3_4.2-a', '6T14-4.1.1_3.3_4.1.1-a', '8T24-6.2_2.2.1.1.1.1_4.4-a', '9T16-6.3_2.2.2.1.1.1_4.4.1-a' (Sam) deg | smallint | the degree of the belyi map group | text | e.g. '4T1' group_num | smallint | the 't' number in the 'dTt' notation geomtype | text | \in ['E', 'H', 'S'] ~ ['Euclidean', 'hyperbolic', 'spherical'] map | text | text of the map (deprecated) -> moved to models abc | smallint[] | e.g., [4, 4, 2] base_field | numeric[] | the (polredabs) coefficients of the field of definition base_field_label| text | the label of the field of definition TODO: fill this column moduli_field | numeric[] | the (polredabs) coefficients of the field of moduli moduli_field_label| text | the label of the field of moduli TODO: fill this column embeddings | jsonb | complex embeddings of the base_field TODO: sort triples | jsonb | generators as elements of the permutation group per embedding. triples_cyc | jsonb | generators in cyclic notation per embedding TODO: text -> integers, eg '(1, 4, 3, 6)(2, 5, 8, 7)' -> [[1,4,3,6], [2, 5, 8, 7]] g | smallint | genus curve | text | equation of the curve (deprecated) -> moved to models specializations | jsonb | a map t -> data about the specialization a_s | smallint | the smallest element of abc b_s | smallint | the second smallest element of abc c_s | smallint | the largest element of abc orbit_size | smallint | pass_size | smallint | aut_group | jsonb | containing the generators in one line notation e.g. [[7, 4, 5, 2, 3, 8, 1, 6], [8, 1, 2, 7, 4, 5, 6, 3]] TODO: move to the passport? plabel | text | passport label, e.g., '4T5-4_3.1_2.1.1' lambdas | jsonb | conjugacy type of each triple as a partition curve_label | text | the label of the curve on LMFDB friends | text[] | list of urls for other friends on LMFDB old_label | text | deprecated old_plabel | text | deprecated models | jsonb | a list of dictionaries with models TODO: new

belyi_passports

see: https://beta.lmfdb.org/api/belyi_passports/ column name | type | description

id | bigint | (internal) geomtype | text | \in ['E', 'H', 'S'] ~ ['Euclidean', 'hyperbolic', 'spherical'] abc | smallint[] | e.g., [4, 4, 2] a_s | smallint | the smallest element of abc b_s | smallint | the second smallest element of abc c_s | smallint | the largest element of abc group | text | the group in 'nTt' notation, e.g. '4T1' g | smallint | genus pass_size | smallint | maxdegbf | smallint | ? lambdas | jsonb | plabel | text | num_orbits | smallint | deg | smallint | the degree of the Belyi map old_plabel | text | deprecated