LMFDB - Abelian variety isogeny class data

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Column	Type
abvar_count	numeric
abvar_counts	numeric[]
abvar_counts_str	text
angle_corank	smallint
angle_rank	smallint
angles	double precision[]
center_dim	smallint
curve_count	integer
curve_counts	numeric[]
curve_counts_str	text
curves	text[]
dim1_distinct	smallint
dim1_factors	smallint
dim2_distinct	smallint
dim2_factors	smallint
dim3_distinct	smallint
dim3_factors	smallint
dim4_distinct	smallint
dim4_factors	smallint
dim5_distinct	smallint
dim5_factors	smallint
g	smallint
galois_groups	text[]
geom_dim1_distinct	smallint
geom_dim1_factors	smallint
geom_dim2_distinct	smallint
geom_dim2_factors	smallint
geom_dim3_distinct	smallint
geom_dim3_factors	smallint
geom_dim4_distinct	smallint
geom_dim4_factors	smallint
geom_dim5_distinct	smallint
geom_dim5_factors	smallint
geometric_center_dim	smallint
geometric_extension_degree	smallint
geometric_galois_groups	text[]
geometric_number_fields	text[]
geometric_splitting_field	text
geometric_splitting_polynomials	numeric[]
has_geom_ss_factor	boolean
has_jacobian	smallint
has_principal_polarization	smallint
hyp_count	integer
is_geometrically_simple	boolean
is_geometrically_squarefree	boolean
is_primitive	boolean
is_simple	boolean
is_squarefree	boolean
is_supersingular	boolean
jacobian_count	integer
label	text
max_divalg_dim	smallint
max_geom_divalg_dim	smallint
max_twist_degree	integer
newton_coelevation	smallint
newton_elevation	smallint
number_fields	text[]
p	smallint
p_rank	smallint
p_rank_deficit	smallint
pic_prime_gens	integer[]
poly	integer[]
poly_str	text
primitive_models	text[]
principal_polarization_count	integer
q	integer
real_poly	integer[]
simple_distinct	text[]
simple_factors	text[]
simple_multiplicities	smallint[]
size	integer
slopes	text[]
splitting_field	text
splitting_polynomials	numeric[]
twist_count	integer
twists	jsonb
zfv_index	numeric
zfv_index_factorization	numeric[]
zfv_is_bass	boolean
zfv_is_maximal	boolean
zfv_plus_index	numeric
zfv_plus_index_factorization	numeric[]
zfv_plus_norm	numeric

av_fq_isog • Show schema

{'abvar_count': 2, 'abvar_counts': [2, 220, 5018, 149600, 686422, 13799500, 237933026, 3753763200, 79235379158, 1121647869100], 'abvar_counts_str': '2 220 5018 149600 686422 13799500 237933026 3753763200 79235379158 1121647869100 ', 'angle_corank': 2, 'angle_rank': 2, 'angles': [0.0693533547549937, 0.25, 0.339907131294691, 0.770553776539698], 'center_dim': 8, 'curve_count': -1, 'curve_counts': [-1, 3, 11, 31, 19, 51, 111, 223, 587, 1043], 'curve_counts_str': '-1 3 11 31 19 51 111 223 587 1043 ', 'curves': [], 'dim1_distinct': 1, 'dim1_factors': 1, 'dim2_distinct': 0, 'dim2_factors': 0, 'dim3_distinct': 1, 'dim3_factors': 1, 'dim4_distinct': 0, 'dim4_factors': 0, 'dim5_distinct': 0, 'dim5_factors': 0, 'g': 4, 'galois_groups': ['2T1', '6T3'], 'geom_dim1_distinct': 1, 'geom_dim1_factors': 1, 'geom_dim2_distinct': 0, 'geom_dim2_factors': 0, 'geom_dim3_distinct': 1, 'geom_dim3_factors': 1, 'geom_dim4_distinct': 0, 'geom_dim4_factors': 0, 'geom_dim5_distinct': 0, 'geom_dim5_factors': 0, 'geometric_center_dim': 7, 'geometric_extension_degree': 4, 'geometric_galois_groups': ['1T1', '6T3'], 'geometric_number_fields': ['1.1.1.1', '6.0.2580992.1'], 'geometric_splitting_field': '6.0.2580992.1', 'geometric_splitting_polynomials': [[8, -8, 2, 0, 1, -2, 1]], 'has_geom_ss_factor': True, 'has_jacobian': -1, 'has_principal_polarization': 1, 'hyp_count': 0, 'is_geometrically_simple': False, 'is_geometrically_squarefree': True, 'is_primitive': True, 'is_simple': False, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 0, 'label': '4.2.ae_h_ag_e', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 4, 'max_twist_degree': 8, 'newton_coelevation': 4, 'newton_elevation': 2, 'number_fields': ['2.0.4.1', '6.0.2580992.1'], 'p': 2, 'p_rank': 2, 'p_rank_deficit': 2, 'pic_prime_gens': [], 'poly': [1, -4, 7, -6, 4, -12, 28, -32, 16], 'poly_str': '1 -4 7 -6 4 -12 28 -32 16 ', 'primitive_models': [], 'principal_polarization_count': 0, 'q': 2, 'real_poly': [1, -4, -1, 18, -16], 'simple_distinct': ['1.2.ac', '3.2.ac_b_a'], 'simple_factors': ['1.2.acA', '3.2.ac_b_aA'], 'simple_multiplicities': [1, 1], 'size': 3, 'slopes': ['0A', '0B', '1/2A', '1/2B', '1/2C', '1/2D', '1A', '1B'], 'splitting_field': '12.0.426337261060096.1', 'splitting_polynomials': [[64, 0, 0, -32, -12, 8, 8, 4, -3, -4, 0, 0, 1]], 'twist_count': 6, 'twists': [['4.2.a_ab_ac_e', '4.4.ac_j_au_bo', 2], ['4.2.a_ab_c_e', '4.4.ac_j_au_bo', 2], ['4.2.e_h_g_e', '4.4.ac_j_au_bo', 2], ['4.2.a_ab_ac_e', '4.16.o_dd_lc_bme', 4], ['4.2.ac_d_ae_e', '4.256.abi_sn_aomq_mfjc', 8], ['4.2.c_d_e_e', '4.256.abi_sn_aomq_mfjc', 8]], 'zfv_index': 4, 'zfv_index_factorization': [[2, 2]], 'zfv_is_bass': True, 'zfv_is_maximal': False, 'zfv_plus_index': 1, 'zfv_plus_index_factorization': [], 'zfv_plus_norm': 32}

Column	Type
base_label	text
extension_degree	smallint
extension_label	text
multiplicity	smallint

av_fq_endalg_factors • Show schema

id: 2577885
{'base_label': '4.2.ae_h_ag_e', 'extension_degree': 1, 'extension_label': '1.2.ac', 'multiplicity': 1}
id: 2577886
{'base_label': '4.2.ae_h_ag_e', 'extension_degree': 1, 'extension_label': '3.2.ac_b_a', 'multiplicity': 1}
id: 2577887
{'base_label': '4.2.ae_h_ag_e', 'extension_degree': 2, 'extension_label': '1.4.a', 'multiplicity': 1}
id: 2577888
{'base_label': '4.2.ae_h_ag_e', 'extension_degree': 2, 'extension_label': '3.4.ac_f_am', 'multiplicity': 1}
id: 2577889
{'base_label': '4.2.ae_h_ag_e', 'extension_degree': 4, 'extension_label': '1.16.i', 'multiplicity': 1}
id: 2577890
{'base_label': '4.2.ae_h_ag_e', 'extension_degree': 4, 'extension_label': '3.16.g_r_ce', 'multiplicity': 1}

Column	Type
brauer_invariants	text[]
center	text
center_dim	smallint
divalg_dim	smallint
extension_label	text
galois_group	text
places	text[]

av_fq_endalg_data • Show schema

{'brauer_invariants': ['0'], 'center': '2.0.4.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.2.ac', 'galois_group': '2T1', 'places': [['1', '1']]}

Column	Type
brauer_invariants	text[]
center	text
center_dim	smallint
divalg_dim	smallint
extension_label	text
galois_group	text
places	text[]

av_fq_endalg_data • Show schema

{'brauer_invariants': ['0', '0', '0'], 'center': '6.0.2580992.1', 'center_dim': 6, 'divalg_dim': 1, 'extension_label': '3.2.ac_b_a', 'galois_group': '6T3', 'places': [['1', '1', '0', '0', '0', '0'], ['0', '1/2', '1', '1/4', '3/2', '1/4'], ['1', '1/2', '0', '1/4', '1/2', '5/4']]}

Column	Type
brauer_invariants	text[]
center	text
center_dim	smallint
divalg_dim	smallint
extension_label	text
galois_group	text
places	text[]

av_fq_endalg_data • Show schema

{'brauer_invariants': ['0'], 'center': '2.0.4.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.4.a', 'galois_group': '2T1', 'places': [['1', '1']]}

Column	Type
brauer_invariants	text[]
center	text
center_dim	smallint
divalg_dim	smallint
extension_label	text
galois_group	text
places	text[]

av_fq_endalg_data • Show schema

{'brauer_invariants': ['0', '0', '0'], 'center': '6.0.2580992.1', 'center_dim': 6, 'divalg_dim': 1, 'extension_label': '3.4.ac_f_am', 'galois_group': '6T3', 'places': [['1', '1', '0', '0', '0', '0'], ['0', '1/2', '1', '1/4', '3/2', '1/4'], ['1', '1/2', '0', '1/4', '1/2', '5/4']]}

Column	Type
brauer_invariants	text[]
center	text
center_dim	smallint
divalg_dim	smallint
extension_label	text
galois_group	text
places	text[]

av_fq_endalg_data • Show schema

{'brauer_invariants': ['1/2'], 'center': '1.1.1.1', 'center_dim': 1, 'divalg_dim': 4, 'extension_label': '1.16.i', 'galois_group': '1T1', 'places': [['0']]}

Column	Type
brauer_invariants	text[]
center	text
center_dim	smallint
divalg_dim	smallint
extension_label	text
galois_group	text
places	text[]

av_fq_endalg_data • Show schema

{'brauer_invariants': ['0', '0', '0'], 'center': '6.0.2580992.1', 'center_dim': 6, 'divalg_dim': 1, 'extension_label': '3.16.g_r_ce', 'galois_group': '6T3', 'places': [['1', '1', '0', '0', '0', '0'], ['0', '1/2', '1', '1/4', '3/2', '1/4'], ['1', '1/2', '0', '1/4', '1/2', '5/4']]}

Overview	Random
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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.