LMFDB - Abelian variety isogeny class data

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Column	Type
abvar_count	numeric
abvar_counts	numeric[]
abvar_counts_str	text
all_polarized_product	boolean
all_unpolarized_product	boolean
angle_corank	smallint
angle_rank	smallint
angles	double precision[]
center_dim	smallint
cohen_macaulay_max	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
endomorphism_ring_count	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[]
group_structure_count	smallint
has_geom_ss_factor	boolean
has_jacobian	smallint
has_principal_polarization	smallint
hyp_count	integer
is_cyclic	boolean
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
noncyclic_primes	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[]
singular_primes	text[]
size	integer
slopes	text[]
splitting_field	text
splitting_polynomials	numeric[]
twist_count	integer
twists	jsonb
weak_equivalence_count	smallint
zfv_index	numeric
zfv_index_factorization	numeric[]
zfv_is_bass	boolean
zfv_is_maximal	boolean
zfv_pic_size	integer
zfv_plus_index	numeric
zfv_plus_index_factorization	numeric[]
zfv_plus_norm	numeric
zfv_singular_count	smallint
zfv_singular_primes	text[]

av_fq_isog • Show schema

{'abvar_count': 70, 'abvar_counts': [70, 26460, 4873120, 817084800, 137610200350, 23276009352960, 3936680039061070, 665433838241625600, 112458489573068467360, 19005135175967126514300], 'abvar_counts_str': '70 26460 4873120 817084800 137610200350 23276009352960 3936680039061070 665433838241625600 112458489573068467360 19005135175967126514300 ', 'angle_corank': 0, 'angle_rank': 2, 'angles': [0.0772104791556333, 0.312832958189001], 'center_dim': 4, 'cohen_macaulay_max': 2, 'curve_count': 3, 'curve_counts': [3, 157, 2220, 28609, 370623, 4822234, 62737419, 815751841, 10604790060, 137859735157], 'curve_counts_str': '3 157 2220 28609 370623 4822234 62737419 815751841 10604790060 137859735157 ', 'curves': ['y^2=5*x^6+2*x^5+3*x^4+11*x^3+5*x^2+3*x+5'], 'dim1_distinct': 2, 'dim1_factors': 2, 'dim2_distinct': 0, 'dim2_factors': 0, 'dim3_distinct': 0, 'dim3_factors': 0, 'dim4_distinct': 0, 'dim4_factors': 0, 'dim5_distinct': 0, 'dim5_factors': 0, 'endomorphism_ring_count': 4, 'g': 2, 'galois_groups': ['2T1', '2T1'], 'geom_dim1_distinct': 2, 'geom_dim1_factors': 2, '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': 4, 'geometric_extension_degree': 1, 'geometric_galois_groups': ['2T1', '2T1'], 'geometric_number_fields': ['2.0.3.1', '2.0.4.1'], 'geometric_splitting_field': '4.0.144.1', 'geometric_splitting_polynomials': [[1, 0, -1, 0, 1]], 'group_structure_count': 1, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 1, 'is_cyclic': True, 'is_geometrically_simple': False, 'is_geometrically_squarefree': True, 'is_primitive': True, 'is_simple': False, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 1, 'label': '2.13.al_cc', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 12, 'newton_coelevation': 2, 'newton_elevation': 0, 'noncyclic_primes': [], 'number_fields': ['2.0.3.1', '2.0.4.1'], 'p': 13, 'p_rank': 2, 'p_rank_deficit': 0, 'poly': [1, -11, 54, -143, 169], 'poly_str': '1 -11 54 -143 169 ', 'primitive_models': [], 'q': 13, 'real_poly': [1, -11, 28], 'simple_distinct': ['1.13.ah', '1.13.ae'], 'simple_factors': ['1.13.ahA', '1.13.aeA'], 'simple_multiplicities': [1, 1], 'singular_primes': ['3,-8*F+4'], 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '4.0.144.1', 'splitting_polynomials': [[1, 0, -1, 0, 1]], 'twist_count': 24, 'twists': [['2.13.ad_ac', '2.169.an_ee', 2], ['2.13.d_ac', '2.169.an_ee', 2], ['2.13.l_cc', '2.169.an_ee', 2], ['2.13.ac_s', '2.2197.w_adas', 3], ['2.13.b_g', '2.2197.w_adas', 3], ['2.13.an_cq', '2.28561.bv_rgq', 4], ['2.13.ab_aq', '2.28561.bv_rgq', 4], ['2.13.b_aq', '2.28561.bv_rgq', 4], ['2.13.n_cq', '2.28561.bv_rgq', 4], ['2.13.aj_bu', '2.4826809.agua_zqkzm', 6], ['2.13.ag_bi', '2.4826809.agua_zqkzm', 6], ['2.13.ab_g', '2.4826809.agua_zqkzm', 6], ['2.13.c_s', '2.4826809.agua_zqkzm', 6], ['2.13.g_bi', '2.4826809.agua_zqkzm', 6], ['2.13.j_bu', '2.4826809.agua_zqkzm', 6], ['2.13.al_ce', '2.23298085122481.fllyy_adjxboqopfm', 12], ['2.13.ai_bm', '2.23298085122481.fllyy_adjxboqopfm', 12], ['2.13.ae_o', '2.23298085122481.fllyy_adjxboqopfm', 12], ['2.13.ab_ae', '2.23298085122481.fllyy_adjxboqopfm', 12], ['2.13.b_ae', '2.23298085122481.fllyy_adjxboqopfm', 12], ['2.13.e_o', '2.23298085122481.fllyy_adjxboqopfm', 12], ['2.13.i_bm', '2.23298085122481.fllyy_adjxboqopfm', 12], ['2.13.l_ce', '2.23298085122481.fllyy_adjxboqopfm', 12]], 'weak_equivalence_count': 5, 'zfv_index': 27, 'zfv_index_factorization': [[3, 3]], 'zfv_is_bass': False, 'zfv_is_maximal': False, 'zfv_plus_index': 1, 'zfv_plus_index_factorization': [], 'zfv_plus_norm': 108, 'zfv_singular_count': 2, 'zfv_singular_primes': ['3,-8*F+4']}

Column	Type
base_label	text
extension_degree	smallint
extension_label	text
multiplicity	smallint

av_fq_endalg_factors • Show schema

id: 9690
{'base_label': '2.13.al_cc', 'extension_degree': 1, 'extension_label': '1.13.ah', 'multiplicity': 1}
id: 9691
{'base_label': '2.13.al_cc', 'extension_degree': 1, 'extension_label': '1.13.ae', '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', '0'], 'center': '2.0.3.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.13.ah', 'galois_group': '2T1', 'places': [['9', '1'], ['3', '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'], 'center': '2.0.4.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.13.ae', 'galois_group': '2T1', 'places': [['8', '1'], ['5', '1']]}

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 $\F_{q}$
Belyi maps

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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.