Abelian variety isogeny class data - 3.2.ac_b_a

Formats: - HTML - YAML - JSON - 2025-10-16T12:53:52.615009

• 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_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[]
  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': 2, 'abvar_counts': [2, 44, 386, 5984, 16742, 212300, 2105602, 16683392, 164730518, 1094290604], 'abvar_counts_str': '2 44 386 5984 16742 212300 2105602 16683392 164730518 1094290604 ', 'angle_corank': 1, 'angle_rank': 2, 'angles': [0.0693533547549937, 0.339907131294691, 0.770553776539698], 'center_dim': 6, 'cohen_macaulay_max': 1, 'curve_count': 1, 'curve_counts': [1, 3, 7, 23, 11, 51, 127, 255, 619, 1043], 'curve_counts_str': '1 3 7 23 11 51 127 255 619 1043 ', 'curves': ['x^4+x^3*z+x*y^3+x*z^3+y^4=0'], 'dim1_distinct': 0, 'dim1_factors': 0, 'dim2_distinct': 0, 'dim2_factors': 0, 'dim3_distinct': 1, 'dim3_factors': 1, 'dim4_distinct': 0, 'dim4_factors': 0, 'dim5_distinct': 0, 'dim5_factors': 0, 'endomorphism_ring_count': 1, 'g': 3, 'galois_groups': ['6T3'], 'geom_dim1_distinct': 0, 'geom_dim1_factors': 0, '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': 6, 'geometric_extension_degree': 1, 'geometric_galois_groups': ['6T3'], 'geometric_number_fields': ['6.0.2580992.1'], 'geometric_splitting_field': '6.0.2580992.1', 'geometric_splitting_polynomials': [[8, -8, 2, 0, 1, -2, 1]], 'group_structure_count': 1, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 0, 'is_geometrically_simple': True, 'is_geometrically_squarefree': True, 'is_primitive': True, 'is_simple': True, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 1, 'label': '3.2.ac_b_a', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 2, 'newton_coelevation': 3, 'newton_elevation': 1, 'number_fields': ['6.0.2580992.1'], 'p': 2, 'p_rank': 2, 'p_rank_deficit': 1, 'poly': [1, -2, 1, 0, 2, -8, 8], 'poly_str': '1 -2 1 0 2 -8 8 ', 'primitive_models': [], 'q': 2, 'real_poly': [1, -2, -5, 8], 'simple_distinct': ['3.2.ac_b_a'], 'simple_factors': ['3.2.ac_b_aA'], 'simple_multiplicities': [1], 'singular_primes': [], 'slopes': ['0A', '0B', '1/2A', '1/2B', '1A', '1B'], 'splitting_field': '6.0.2580992.1', 'splitting_polynomials': [[8, -8, 2, 0, 1, -2, 1]], 'twist_count': 2, 'twists': [['3.2.c_b_a', '3.4.ac_f_am', 2]], 'weak_equivalence_count': 1, 'zfv_index': 1, 'zfv_index_factorization': [], 'zfv_is_bass': True, 'zfv_is_maximal': True, 'zfv_plus_index': 1, 'zfv_plus_index_factorization': [], 'zfv_plus_norm': 8, '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': '3.2.ac_b_a', 'extension_degree': 1, 'extension_label': '3.2.ac_b_a', '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'], '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']]}