LMFDB - Abelian variety isogeny class data

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Column	Type
abvar_count	numeric
abvar_counts	numeric[]
abvar_counts_str	text
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
jacobian_count	integer
label	text
max_divalg_dim	smallint
max_geom_divalg_dim	smallint
max_twist_degree	integer
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': 480, 'abvar_counts': [480, 614400, 337540320, 267386880000, 205873812434400, 149908514931302400, 109249924156545473760, 79739985108381204480000, 58144318987151370415534560, 42389769541564608377871360000], 'abvar_counts_str': '480 614400 337540320 267386880000 205873812434400 149908514931302400 109249924156545473760 79739985108381204480000 58144318987151370415534560 42389769541564608377871360000 ', 'angle_rank': 1, 'angles': [0.0, 0.0, 0.5, 0.608173447969393], 'center_dim': 5, 'curve_count': 6, 'curve_counts': [6, 96, 630, 6204, 59046, 530784, 4775574, 43032444, 387384390, 3486670176], 'curve_counts_str': '6 96 630 6204 59046 530784 4775574 43032444 387384390 3486670176 ', 'curves': [], 'dim1_distinct': 3, 'dim1_factors': 3, 'dim2_distinct': 0, 'dim2_factors': 0, 'dim3_distinct': 0, 'dim3_factors': 0, 'dim4_distinct': 0, 'dim4_factors': 0, 'dim5_distinct': 0, 'dim5_factors': 0, 'g': 3, 'galois_groups': ['1T1', '2T1', '2T1'], 'geom_dim1_distinct': 2, 'geom_dim1_factors': 3, 'geom_dim2_distinct': 0, 'geom_dim2_factors': 0, 'geom_dim3_distinct': 0, 'geom_dim3_factors': 0, 'geom_dim4_distinct': 0, 'geom_dim4_factors': 0, 'geom_dim5_distinct': 0, 'geom_dim5_factors': 0, 'geometric_center_dim': 3, 'geometric_extension_degree': 4, 'geometric_galois_groups': ['1T1', '2T1'], 'geometric_number_fields': ['1.1.1.1', '2.0.8.1'], 'geometric_splitting_field': '2.0.8.1', 'geometric_splitting_polynomials': [[2, 0, 1]], 'has_geom_ss_factor': True, 'has_jacobian': 0, 'has_principal_polarization': 1, 'hyp_count': 0, 'is_geometrically_simple': False, 'is_geometrically_squarefree': False, 'is_primitive': True, 'is_simple': False, 'is_squarefree': True, 'label': '3.9.ae_p_acu', 'max_divalg_dim': 4, 'max_geom_divalg_dim': 4, 'max_twist_degree': 20, 'number_fields': ['1.1.1.1', '2.0.4.1', '2.0.8.1'], 'p': 3, 'p_rank': 1, 'p_rank_deficit': 2, 'poly': [1, -4, 15, -72, 135, -324, 729], 'poly_str': '1 -4 15 -72 135 -324 729 ', 'primitive_models': [], 'q': 9, 'real_poly': [1, -4, -12], 'simple_distinct': ['1.9.ag', '1.9.a', '1.9.c'], 'simple_factors': ['1.9.agA', '1.9.aA', '1.9.cA'], 'simple_multiplicities': [1, 1, 1], 'slopes': ['0A', '1/2A', '1/2B', '1/2C', '1/2D', '1A'], 'splitting_field': '4.0.256.1', 'splitting_polynomials': [[1, 0, 0, 0, 1]], 'twist_count': 38, 'twists': [['3.9.ai_bn_afo', '3.81.o_add_adjg', 2], ['3.9.e_p_cu', '3.81.o_add_adjg', 2], ['3.9.i_bn_fo', '3.81.o_add_adjg', 2], ['3.9.f_bh_dm', '3.729.adw_gxr_aihrs', 3], ['3.9.ao_dj_amm', '3.6561.anu_dggd_amgbey', 4], ['3.9.ak_bn_aee', '3.6561.anu_dggd_amgbey', 4], ['3.9.ac_aj_bk', '3.6561.anu_dggd_amgbey', 4], ['3.9.ac_bb_abk', '3.6561.anu_dggd_amgbey', 4], ['3.9.c_aj_abk', '3.6561.anu_dggd_amgbey', 4], ['3.9.c_bb_bk', '3.6561.anu_dggd_amgbey', 4], ['3.9.k_bn_ee', '3.6561.anu_dggd_amgbey', 4], ['3.9.o_dj_mm', '3.6561.anu_dggd_amgbey', 4], ['3.9.af_bh_adm', '3.531441.azi_abegeb_cgwlokq', 6], ['3.9.ab_v_as', '3.531441.azi_abegeb_cgwlokq', 6], ['3.9.b_v_s', '3.531441.azi_abegeb_cgwlokq', 6], ['3.9.ac_j_a', '3.43046721.avde_abbvbun_dzmnryexw', 8], ['3.9.c_j_a', '3.43046721.avde_abbvbun_dzmnryexw', 8], ['3.9.al_cl_aja', '3.282429536481.adhcuo_dbldgqezv_abkijiojlpmdeq', 12], ['3.9.ai_bw_agg', '3.282429536481.adhcuo_dbldgqezv_abkijiojlpmdeq', 12], ['3.9.ah_bb_adm', '3.282429536481.adhcuo_dbldgqezv_abkijiojlpmdeq', 12], ['3.9.af_p_acc', '3.282429536481.adhcuo_dbldgqezv_abkijiojlpmdeq', 12], ['3.9.ae_y_acc', '3.282429536481.adhcuo_dbldgqezv_abkijiojlpmdeq', 12], ['3.9.ac_a_s', '3.282429536481.adhcuo_dbldgqezv_abkijiojlpmdeq', 12], ['3.9.ac_s_as', '3.282429536481.adhcuo_dbldgqezv_abkijiojlpmdeq', 12], ['3.9.ab_d_acc', '3.282429536481.adhcuo_dbldgqezv_abkijiojlpmdeq', 12], ['3.9.b_d_cc', '3.282429536481.adhcuo_dbldgqezv_abkijiojlpmdeq', 12], ['3.9.c_a_as', '3.282429536481.adhcuo_dbldgqezv_abkijiojlpmdeq', 12], ['3.9.c_s_s', '3.282429536481.adhcuo_dbldgqezv_abkijiojlpmdeq', 12], ['3.9.e_y_cc', '3.282429536481.adhcuo_dbldgqezv_abkijiojlpmdeq', 12], ['3.9.f_p_cc', '3.282429536481.adhcuo_dbldgqezv_abkijiojlpmdeq', 12], ['3.9.h_bb_dm', '3.282429536481.adhcuo_dbldgqezv_abkijiojlpmdeq', 12], ['3.9.i_bw_gg', '3.282429536481.adhcuo_dbldgqezv_abkijiojlpmdeq', 12], ['3.9.l_cl_ja', '3.282429536481.adhcuo_dbldgqezv_abkijiojlpmdeq', 12], ['3.9.af_y_acu', '3.12157665459056928801.acmvcgore_cqlnulsnmfeujln_abngnvhjlyzqjctcwmatdoe', 20], ['3.9.ab_m_abk', '3.12157665459056928801.acmvcgore_cqlnulsnmfeujln_abngnvhjlyzqjctcwmatdoe', 20], ['3.9.b_m_bk', '3.12157665459056928801.acmvcgore_cqlnulsnmfeujln_abngnvhjlyzqjctcwmatdoe', 20], ['3.9.f_y_cu', '3.12157665459056928801.acmvcgore_cqlnulsnmfeujln_abngnvhjlyzqjctcwmatdoe', 20]]}

Column	Type
base_label	text
extension_degree	smallint
extension_label	text
multiplicity	smallint

av_fq_endalg_factors • Show schema

id: 1418021
{'base_label': '3.9.ae_p_acu', 'extension_degree': 1, 'extension_label': '1.9.ag', 'multiplicity': 1}
id: 1418022
{'base_label': '3.9.ae_p_acu', 'extension_degree': 1, 'extension_label': '1.9.a', 'multiplicity': 1}
id: 1418023
{'base_label': '3.9.ae_p_acu', 'extension_degree': 1, 'extension_label': '1.9.c', 'multiplicity': 1}
id: 1418024
{'base_label': '3.9.ae_p_acu', 'extension_degree': 2, 'extension_label': '1.81.as', 'multiplicity': 1}
id: 1418025
{'base_label': '3.9.ae_p_acu', 'extension_degree': 2, 'extension_label': '1.81.o', 'multiplicity': 1}
id: 1418026
{'base_label': '3.9.ae_p_acu', 'extension_degree': 2, 'extension_label': '1.81.s', 'multiplicity': 1}
id: 1418027
{'base_label': '3.9.ae_p_acu', 'extension_degree': 4, 'extension_label': '1.6561.agg', 'multiplicity': 2}
id: 1418028
{'base_label': '3.9.ae_p_acu', 'extension_degree': 4, 'extension_label': '1.6561.abi', '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': ['1/2'], 'center': '1.1.1.1', 'center_dim': 1, 'divalg_dim': 4, 'extension_label': '1.9.ag', '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'], 'center': '2.0.4.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.9.a', 'galois_group': '2T1', 'places': [['0', '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'], 'center': '2.0.8.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.9.c', 'galois_group': '2T1', 'places': [['2', '1'], ['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': ['1/2'], 'center': '1.1.1.1', 'center_dim': 1, 'divalg_dim': 4, 'extension_label': '1.81.as', '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'], 'center': '2.0.8.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.81.o', 'galois_group': '2T1', 'places': [['1', '1'], ['2', '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': ['1/2'], 'center': '1.1.1.1', 'center_dim': 1, 'divalg_dim': 4, 'extension_label': '1.81.s', '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': ['1/2'], 'center': '1.1.1.1', 'center_dim': 1, 'divalg_dim': 4, 'extension_label': '1.6561.agg', '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'], 'center': '2.0.8.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.6561.abi', 'galois_group': '2T1', 'places': [['2', '1'], ['1', '1']]}

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

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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.