-
id: 1
{'_id': 0, 'data': {'type': "List(Dict{u'Size': Z, u'Representative': List(Z), u'Order': Z}) ", 'example': None, 'description': '(list of dicts): for each conjugacy class of the group: its Order (int), Representative (list of ints giving a permutation), and Size (int)'}, 'name': 'ConjClasses', 'table_id': 0}
-
id: 2
{'_id': 1, 'data': {'type': 'String ', 'example': None, 'description': "name for the Galois group, but we usually substitute a latex'ed name from the Galois group database, but this is a fallback"}, 'name': 'G-Name', 'table_id': 0}
-
id: 3
{'_id': 2, 'data': {'type': 'List(Z) ', 'example': None, 'description': 'coefficients for a defining polynomial over Qp used for explicitly writing roots. The first coefficient is the constant term'}, 'name': 'QpRts-minpoly', 'table_id': 0}
-
id: 4
{'_id': 3, 'data': {'type': 'Z ', 'example': None, 'description': 'index for ConjClasses to say where complex conjugation lies'}, 'name': 'ComplexConjugation', 'table_id': 0}
-
id: 5
{'_id': 4, 'data': {'type': "List(Dict({u'Classes': Z, u'Data': Z, u'Algorithm': String, u'CycleType': List(Z)})) ", 'example': None, 'description': None}, 'name': 'FrobResolvents', 'table_id': 0}
-
id: 6
{'_id': 5, 'data': {'type': 'Z ', 'example': None, 'description': 'p-adic roots are computed up to (p^prec)'}, 'name': 'QpRts-prec', 'table_id': 0}
-
id: 7
{'_id': 6, 'data': {'type': "List(Dict{u'GalConj': Z, u'Character': List(List(Z)), u'CharacterField': Z, u'Baselabel': String}) ", 'example': None, 'description': ' (list of pairs, [string, int]): the string is the baselabel of an entry from the Artin representation database, and the int is the GalOrbIndex for a particular character with that Baselabel'}, 'name': 'ArtinReps', 'table_id': 0}
-
id: 8
{'_id': 7, 'data': {'type': 'List(List(Z)) ', 'example': None, 'description': 'inner lists are permutations given as lists which generate the Galois group'}, 'name': 'G-Gens', 'table_id': 0}
-
id: 9
{'_id': 8, 'data': {'type': 'List(Z) ', 'example': None, 'description': 'coefficients of a polynomial defining this field, the comma-separated list of coefficients as a string. This is the main identifier for this field from the representations collection, and also matches entries in the number field database.'}, 'name': 'Polynomial', 'table_id': 0}
-
id: 10
{'_id': 9, 'data': {'type': 'List(List(Z)) ', 'example': None, 'description': 'each entry is a p-adic root, where entries in the list give the coefficients of powers of p in the p-adic approximation. They are themselves polynomials in a, where a is a root of the QpRts-minpoly'}, 'name': 'QpRts', 'table_id': 0}
-
id: 11
{'_id': 10, 'data': {'type': 'List(Z) ', 'example': None, 'description': 'if the i-th entry is j, then the Frobenius for the i-th prime lies in the j-th conjugacy class'}, 'name': 'Frobs', 'table_id': 0}
-
id: 12
{'_id': 11, 'data': {'type': 'Z ', 'example': None, 'description': 'the prime p used for computing the roots p-adicly'}, 'name': 'QpRts-p', 'table_id': 0}
-
id: 13
{'_id': 12, 'data': {'type': 'Z ', 'example': None, 'description': 'degree of the polynomial'}, 'name': 'TransitiveDegree', 'table_id': 0}
-
id: 14
{'_id': 13, 'data': {'type': 'Z ', 'example': None, 'description': 'order of the Galois group'}, 'name': 'Size', 'table_id': 0}
-
id: 15
{'_id': 14, 'data': {'type': 'String ', 'example': None, 'description': None}, 'name': 'Baselabel', 'table_id': 1}
-
id: 16
{'_id': 15, 'data': {'type': 'Z ', 'example': None, 'description': 'dimension'}, 'name': 'Dim', 'table_id': 1}
-
id: 17
{'_id': 16, 'data': {'type': 'Z ', 'example': None, 'description': 'conductor'}, 'name': 'Conductor', 'table_id': 1}
-
id: 18
{'_id': 17, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Galn', 'table_id': 1}
-
id: 19
{'_id': 18, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'Galt', 'table_id': 1}
-
id: 20
{'_id': 19, 'data': {'type': None, 'example': '`4t3 or 32`', 'description': 'Smallest permutation representation which has this representation as a factor. Permutation representations are ordered by degree, and then by T-number. If the degree is 32 or greater than 47, we just give the degree.'}, 'name': 'Container', 'table_id': 1}
-
id: 21
{'_id': 20, 'data': {'type': 'Z ', 'example': None, 'description': 'Frobenius-Schur indicator, 1 for orthogonal, -1 for symplectic, and 0 for other'}, 'name': 'Indicator', 'table_id': 1}
-
id: 22
{'_id': 21, 'data': {'type': 'List(Z) ', 'example': None, 'description': 'list of bad primes, i.e., primes dividing the conductor. Stored as strings since they may get too big'}, 'name': 'BadPrimes', 'table_id': 1}
-
id: 23
{'_id': 22, 'data': {'type': 'List(Z) ', 'example': None, 'description': 'primes dividing the polynomial discriminant for the defining field. These include the Bad Primes'}, 'name': 'HardPrimes', 'table_id': 1}
-
id: 24
{'_id': 23, 'data': {'type': "List(Dict{u'Character': List(List(Z)), u'GalOrbIndex': Z, u'HardFactors': List(Z), u'LocalFactors': List(List(List(Z))) u'Sign': Z} ", 'example': None, 'description': 'list of Galois conjugate character information.\n\nEach entry in the GaloisConjugates list is a dictionary with the following entries\n\n * *LocalFactors* (list of list of int-as-strings): local factors for the L-function \n\n * *Character* (list of list of ints): character for this representation. Each sublist are coefficients for the character value written on a power basis for Z[zeta_n]\n\n * *Sign* (int): sign of the functional equation when we know it is 1 or -1, otherwise we give 0.\n\n * *HardFactors* : local factors for bad primes\n\n * *GalOrbIndex*(ints): an index assigned to the given character'}, 'name': 'GaloisConjugates', 'table_id': 1}
-
id: 25
{'_id': 24, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'GalConjSigns', 'table_id': 1}
-
id: 26
{'_id': 25, 'data': {'type': 'Z ', 'example': None, 'description': 'the n for writing the character'}, 'name': 'CharacterField', 'table_id': 1}
-
id: 27
{'_id': 26, 'data': {'type': 'List(Z) ', 'example': None, 'description': 'list of Galois conjugate character information'}, 'name': 'NFGal', 'table_id': 1}
-
id: 28
{'_id': 27, 'data': {'type': 'Boolean ', 'example': None, 'description': "0 if we should show it when searching for Artin rep'ns, 1 if not. The representations are invariants of the Galois closure of the given field. More than one field can have the same Galois closure. We pick a best/minimal one and show that. We have data for others for linking to the number field database."}, 'name': 'Hide', 'table_id': 1}
-
id: 29
{'_id': 28, 'data': {'type': 'String', 'example': None, 'description': 'LMFDB Label. http://beta.lmfdb.org/Variety/Abelian/Fq/Labels[Labeling Scheme]'}, 'name': 'label', 'table_id': 2}
-
id: 30
{'_id': 29, 'data': {'type': 'Z', 'example': None, 'description': 'Genus. The degree of the Weil L-polynomial is 2g'}, 'name': 'g', 'table_id': 2}
-
id: 31
{'_id': 30, 'data': {'type': 'Z', 'example': None, 'description': 'Cardinality of Field. All of the roots of the Weil L-polynomial have absolute value $1/\\sqrt{q}$.'}, 'name': 'q', 'table_id': 2}
-
id: 32
{'_id': 31, 'data': {'type': 'List(Z)', 'example': None, 'description': None}, 'name': 'poly', 'table_id': 2}
-
id: 33
{'_id': 32, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'poly_str', 'table_id': 2}
-
id: 34
{'_id': 33, 'data': {'type': 'List(R)', 'example': None, 'description': None}, 'name': 'angles', 'table_id': 2}
-
id: 35
{'_id': 34, 'data': {'type': 'Z', 'example': None, 'description': None}, 'name': 'ang_rank', 'table_id': 2}
-
id: 36
{'_id': 35, 'data': {'type': 'N', 'example': None, 'description': 'The $p$-rank of the abelian variety. The rank of the $p$-torsion subgroup of the abelian variety. Equal to the number of occurences of the slope 0 in the Newton slopes.'}, 'name': 'p_rank', 'table_id': 2}
-
id: 37
{'_id': 36, 'data': {'type': 'List(Q)', 'example': None, 'description': None}, 'name': 'slps', 'table_id': 2}
-
id: 38
{'_id': 37, 'data': {'type': 'List(Z)', 'example': None, 'description': None}, 'name': 'A_cnts', 'table_id': 2}
-
id: 39
{'_id': 38, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'A_cnts_str', 'table_id': 2}
-
id: 40
{'_id': 39, 'data': {'type': 'List(Z)', 'example': None, 'description': None}, 'name': 'C_cnts', 'table_id': 2}
-
id: 41
{'_id': 40, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'C_cnts_str', 'table_id': 2}
-
id: 42
{'_id': 41, 'data': {'type': 'Z', 'example': None, 'description': None}, 'name': 'pt_cnt', 'table_id': 2}
-
id: 43
{'_id': 42, 'data': {'type': 'Z', 'example': None, 'description': None}, 'name': 'is_jac', 'table_id': 2}
-
id: 44
{'_id': 43, 'data': {'type': 'Z', 'example': None, 'description': None}, 'name': 'is_pp', 'table_id': 2}
-
id: 45
{'_id': 44, 'data': {'type': 'List(String*Z)', 'example': None, 'description': None}, 'name': 'decomp', 'table_id': 2}
-
id: 46
{'_id': 45, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'simple_factors', 'table_id': 2}
-
id: 47
{'_id': 46, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'simple_distinct', 'table_id': 2}
-
id: 48
{'_id': 47, 'data': {'type': 'Boolean', 'example': None, 'description': None}, 'name': 'is_simp', 'table_id': 2}
-
id: 49
{'_id': 48, 'data': {'type': 'List(Q)', 'example': None, 'description': None}, 'name': 'brauer_invs', 'table_id': 2}
-
id: 50
{'_id': 49, 'data': {'type': 'List(List(List(Q)))', 'example': None, 'description': 'The ideals corresponding to the Brauer invariants of the endomorphism algebra. The outer set of lists corresponds to the simple factors of the isogeny class (so in the example, this isogeny class is a product of two simple isogeny classes). For each simple factor, the list contains one list per prime above p in the number field defined by the Weil polynomial. This list describes the prime ideal above p by giving the second generator of the ideal (the first generator is p), as a list of the coefficients of the generator when written in terms of a specific basis for the number field. This basis contains the powers of a root of the P-polynomial (which is the Weil polynomial but reversed)'}, 'name': 'places', 'table_id': 2}
-
id: 51
{'_id': 50, 'data': {'type': 'List(String)', 'example': None, 'description': None}, 'name': 'prim_models', 'table_id': 2}
-
id: 52
{'_id': 51, 'data': {'type': 'Boolean', 'example': None, 'description': None}, 'name': 'is_prim', 'table_id': 2}
-
id: 53
{'_id': 52, 'data': {'type': 'String', 'example': None, 'description': None}, 'name': 'nf', 'table_id': 2}
-
id: 54
{'_id': 53, 'data': {'type': 'Z', 'example': None, 'description': 'The transitive label of the Galois group of the Weil polynomial. If the number field was not in the database when the isogeny class was added to the database, this string is empty. If the isogeny class is not simple, this is also an empty string.'}, 'name': 'galois_t', 'table_id': 2}
-
id: 55
{'_id': 54, 'data': {'type': 'Z', 'example': None, 'description': 'The degree label of the Galois group of the Weil polynomial. If the number field was not in the database when the isogeny class was added to the database, this string is empty. If the isogeny class is not simple, this is also an empty string.'}, 'name': 'galois_n', 'table_id': 2}
-
id: 56
{'_id': 55, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'dim1_factors', 'table_id': 2}
-
id: 57
{'_id': 56, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'dim2_factors', 'table_id': 2}
-
id: 58
{'_id': 57, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'dim3_factors', 'table_id': 2}
-
id: 59
{'_id': 58, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'dim4_factors', 'table_id': 2}
-
id: 60
{'_id': 59, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'dim5_factors', 'table_id': 2}
-
id: 61
{'_id': 60, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'dim1_distinct', 'table_id': 2}
-
id: 62
{'_id': 61, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'dim2_distinct', 'table_id': 2}
-
id: 63
{'_id': 62, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'dim3_distinct', 'table_id': 2}
-
id: 64
{'_id': 63, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'dim4_distinct', 'table_id': 2}
-
id: 65
{'_id': 64, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'dim5_distinct', 'table_id': 2}
-
id: 66
{'_id': 65, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'geomtype', 'table_id': 3}
-
id: 67
{'_id': 66, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'map', 'table_id': 3}
-
id: 68
{'_id': 67, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'abc', 'table_id': 3}
-
id: 69
{'_id': 68, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'base_field', 'table_id': 3}
-
id: 70
{'_id': 69, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'triples_cyc', 'table_id': 3}
-
id: 71
{'_id': 70, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'g', 'table_id': 3}
-
id: 72
{'_id': 71, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'curve', 'table_id': 3}
-
id: 73
{'_id': 72, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'orbit_size', 'table_id': 3}
-
id: 74
{'_id': 73, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'label', 'table_id': 3}
-
id: 75
{'_id': 74, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'a_s', 'table_id': 3}
-
id: 76
{'_id': 75, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'pass_size', 'table_id': 3}
-
id: 77
{'_id': 76, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'c_s', 'table_id': 3}
-
id: 78
{'_id': 77, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'aut_group', 'table_id': 3}
-
id: 79
{'_id': 78, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'deg', 'table_id': 3}
-
id: 80
{'_id': 79, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'group_num', 'table_id': 3}
-
id: 81
{'_id': 80, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'embeddings', 'table_id': 3}
-
id: 82
{'_id': 81, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'group', 'table_id': 3}
-
id: 83
{'_id': 82, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'triples', 'table_id': 3}
-
id: 84
{'_id': 83, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'b_s', 'table_id': 3}
-
id: 85
{'_id': 84, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'plabel', 'table_id': 3}
-
id: 86
{'_id': 85, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'lambdas', 'table_id': 3}
-
id: 87
{'_id': 86, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'geomtype', 'table_id': 4}
-
id: 88
{'_id': 87, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'pass_size', 'table_id': 4}
-
id: 89
{'_id': 88, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'abc', 'table_id': 4}
-
id: 90
{'_id': 89, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'group', 'table_id': 4}
-
id: 91
{'_id': 90, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'g', 'table_id': 4}
-
id: 92
{'_id': 91, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'maxdegbf', 'table_id': 4}
-
id: 93
{'_id': 92, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'lambdas', 'table_id': 4}
-
id: 94
{'_id': 93, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'plabel', 'table_id': 4}
-
id: 95
{'_id': 94, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'num_orbits', 'table_id': 4}
-
id: 96
{'_id': 95, 'data': {'type': None, 'example': None, 'description': None}, 'name': 'deg', 'table_id': 4}
-
id: 97
{'_id': 96, 'data': {'type': "FiniteMap(Z, Dict{u'cuspidal_dim': Z, u'new_dim': Z})", 'example': None, 'description': 'Dictionary keyed by weight with values dictionaries holding the cuspidal and new dimensions for the GL(2) level'}, 'name': 'gl2_dims', 'table_id': 5}
-
id: 98
{'_id': 97, 'data': {'type': "FiniteMap(Z, Dict{u'cuspidal_dim': Z, u'new_dim': Z})", 'example': None, 'description': 'Dictionary keyed by weight with values dictionaries holding the cuspidal and new dimensions for the SL(2) level'}, 'name': 'sl2_dims', 'table_id': 5}
-
id: 99
{'_id': 98, 'data': {'type': 'Z', 'example': None, 'description': 'absolute value of field discriminant'}, 'name': 'field_absdisc', 'table_id': 5}
-
id: 100
{'_id': 99, 'data': {'type': 'String', 'example': None, 'description': 'Full label of level (including base field)'}, 'name': 'label', 'table_id': 5}
