Abelian variety isogeny class data - 2.71.ai_ga

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• av_fq_isog •

  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[]

  
  {'abvar_count': 4622, 'abvar_counts': [4622, 26687428, 128648419838, 645478039315088, 3254983880510851582, 16409702977549637915908, 82721300323801672099039118, 416997640619863582857034698752, 2102084994967328231483572726585838, 10596610565099049155855806807427714308], 'abvar_counts_str': '4622 26687428 128648419838 645478039315088 3254983880510851582 16409702977549637915908 82721300323801672099039118 416997640619863582857034698752 2102084994967328231483572726585838 10596610565099049155855806807427714308 ', 'all_polarized_product': False, 'all_unpolarized_product': False, 'angle_corank': 0, 'angle_rank': 2, 'angles': [0.395888795597621, 0.450965400242206], 'center_dim': 4, 'cohen_macaulay_max': 1, 'curve_count': 64, 'curve_counts': [64, 5290, 359440, 25400838, 1804085424, 128100441898, 9095130012928, 645753558351294, 45848500213257088, 3255243547540902090], 'curve_counts_str': '64 5290 359440 25400838 1804085424 128100441898 9095130012928 645753558351294 45848500213257088 3255243547540902090 ', 'curves': ['y^2=44*x^6+26*x^5+69*x^4+70*x^3+16*x^2+50*x+46', 'y^2=30*x^6+53*x^5+54*x^4+46*x^3+13*x^2+52*x+53', 'y^2=68*x^6+67*x^5+50*x^4+54*x^3+4*x^2+30*x+43', 'y^2=44*x^6+28*x^5+21*x^4+46*x^3+58*x^2+16*x+40', 'y^2=53*x^6+63*x^5+8*x^4+21*x^3+30*x^2+41*x', 'y^2=15*x^6+47*x^5+3*x^4+66*x^3+29*x^2+46*x+64', 'y^2=47*x^6+4*x^5+52*x^4+11*x^3+43*x^2+28*x+2', 'y^2=46*x^6+48*x^5+2*x^4+50*x^3+47*x^2+42*x+24', 'y^2=66*x^6+63*x^5+6*x^4+50*x^3+61*x^2+13*x+15', 'y^2=63*x^6+69*x^5+27*x^4+56*x^3+55*x^2+41*x+42', 'y^2=57*x^6+27*x^5+51*x^4+27*x^3+54*x^2+10*x+10', 'y^2=18*x^6+67*x^4+5*x^3+38*x^2+57*x+58', 'y^2=10*x^6+26*x^5+16*x^4+49*x^3+48*x^2+9*x+58', 'y^2=67*x^6+42*x^5+26*x^4+30*x^3+44*x^2+27*x+4', 'y^2=46*x^6+52*x^4+64*x^3+30*x^2+20*x+17', 'y^2=38*x^6+28*x^5+16*x^4+52*x^3+28*x^2+57*x+20', 'y^2=64*x^6+22*x^5+15*x^4+21*x^3+12*x^2+42*x+45', 'y^2=31*x^6+63*x^5+35*x^4+27*x^3+12*x^2+53*x+50', 'y^2=30*x^6+37*x^5+3*x^4+63*x^3+67*x^2+12*x+63', 'y^2=7*x^6+50*x^5+58*x^4+53*x^3+67*x^2+6*x+46', 'y^2=58*x^6+13*x^5+45*x^4+11*x^3+63*x^2+18*x+11', 'y^2=42*x^6+41*x^5+17*x^4+46*x^3+29*x^2+19*x+62', 'y^2=37*x^6+53*x^5+46*x^4+51*x^3+69*x^2+25*x+47', 'y^2=48*x^6+46*x^5+58*x^4+21*x^3+55*x^2+28*x+28', 'y^2=63*x^6+40*x^5+40*x^4+7*x^3+29*x^2+59*x+4', 'y^2=44*x^6+20*x^5+55*x^4+15*x^3+41*x^2+4*x+69', 'y^2=54*x^6+4*x^5+47*x^4+27*x^3+35*x^2+57*x+5', 'y^2=52*x^6+30*x^5+42*x^4+15*x^3+26*x^2+38*x+18', 'y^2=28*x^6+61*x^5+57*x^4+15*x^3+46*x^2+31*x+38', 'y^2=20*x^6+51*x^5+18*x^4+4*x^3+13*x^2+65*x+8', 'y^2=42*x^6+5*x^5+69*x^4+29*x^3+59*x^2+39*x+6', 'y^2=63*x^6+28*x^5+19*x^4+44*x^3+22*x^2+63*x+59', 'y^2=58*x^6+62*x^5+15*x^4+51*x^3+6*x^2+61*x+21', 'y^2=x^6+52*x^5+39*x^4+30*x^3+9*x^2+47*x+34'], 'dim1_distinct': 0, 'dim1_factors': 0, 'dim2_distinct': 1, 'dim2_factors': 1, 'dim3_distinct': 0, 'dim3_factors': 0, 'dim4_distinct': 0, 'dim4_factors': 0, 'dim5_distinct': 0, 'dim5_factors': 0, 'endomorphism_ring_count': 1, 'g': 2, 'galois_groups': ['4T3'], 'geom_dim1_distinct': 0, 'geom_dim1_factors': 0, 'geom_dim2_distinct': 1, 'geom_dim2_factors': 1, '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': ['4T3'], 'geometric_number_fields': ['4.0.4520192.2'], 'geometric_splitting_field': '4.0.4520192.2', 'geometric_splitting_polynomials': [[4481, -8, 132, 0, 1]], 'group_structure_count': 1, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 34, 'is_cyclic': True, 'is_geometrically_simple': True, 'is_geometrically_squarefree': True, 'is_primitive': True, 'is_simple': True, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 34, 'label': '2.71.ai_ga', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 2, 'newton_coelevation': 2, 'newton_elevation': 0, 'noncyclic_primes': [], 'number_fields': ['4.0.4520192.2'], 'p': 71, 'p_rank': 2, 'p_rank_deficit': 0, 'pic_prime_gens': [[1, 2, 1, 2], [1, 7, 1, 34]], 'poly': [1, -8, 156, -568, 5041], 'poly_str': '1 -8 156 -568 5041 ', 'primitive_models': [], 'principal_polarization_count': 34, 'q': 71, 'real_poly': [1, -8, 14], 'simple_distinct': ['2.71.ai_ga'], 'simple_factors': ['2.71.ai_gaA'], 'simple_multiplicities': [1], 'singular_primes': [], 'size': 34, 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '4.0.4520192.2', 'splitting_polynomials': [[4481, -8, 132, 0, 1]], 'twist_count': 2, 'twists': [['2.71.i_ga', '2.5041.jo_blmg', 2]], 'weak_equivalence_count': 1, 'zfv_index': 1, 'zfv_index_factorization': [], 'zfv_is_bass': True, 'zfv_is_maximal': True, 'zfv_pic_size': 34, 'zfv_plus_index': 1, 'zfv_plus_index_factorization': [], 'zfv_plus_norm': 70628, 'zfv_singular_count': 0, 'zfv_singular_primes': []}
• av_fq_endalg_factors •

  Column	Type
  base_label	text
  extension_degree	smallint
  extension_label	text
  multiplicity	smallint

  
  {'base_label': '2.71.ai_ga', 'extension_degree': 1, 'extension_label': '2.71.ai_ga', 'multiplicity': 1}
• av_fq_endalg_data •

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

  
  {'brauer_invariants': ['0', '0', '0', '0'], 'center': '4.0.4520192.2', 'center_dim': 4, 'divalg_dim': 1, 'extension_label': '2.71.ai_ga', 'galois_group': '4T3', 'places': [['57', '1', '0', '0'], ['10', '1', '0', '0'], ['1144/71', '130/71', '67/71', '2/71'], ['2777/71', '130/71', '67/71', '2/71']]}