Abelian variety isogeny class data - 2.81.abe_op

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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_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': 4481, 'abvar_counts': [4481, 42125881, 282333399104, 1853095978864809, 12157570794021386801, 79766164027081734071296, 523347315301061296337714801, 3433683598435900758172770717129, 22528399462262267650518070295833664, 147808829433613660216210758339712522201], 'abvar_counts_str': '4481 42125881 282333399104 1853095978864809 12157570794021386801 79766164027081734071296 523347315301061296337714801 3433683598435900758172770717129 22528399462262267650518070295833664 147808829433613660216210758339712522201 ', 'angle_corank': 0, 'angle_rank': 2, 'angles': [0.0439844089044582, 0.263626170191107], 'center_dim': 4, 'cohen_macaulay_max': 1, 'curve_count': 52, 'curve_counts': [52, 6420, 531262, 43048484, 3486757252, 282428548446, 22876778566372, 1853020069124804, 150094634746167262, 12157665460641750900], 'curve_counts_str': '52 6420 531262 43048484 3486757252 282428548446 22876778566372 1853020069124804 150094634746167262 12157665460641750900 ', 'curves': ['y^2=a^2*x^6+(a^3+a^2+2*a+1)*x^5+(a^3+a)*x^4+2*a^2*x^3+(2*a^2+2*a+2)*x^2+(a^3+a^2+a+2)*x+a^3+a+1', 'y^2=(a^3+a^2+2*a+1)*x^6+(a+1)*x^5+(a^2+2*a+1)*x^4+2*a^2*x^3+(2*a^3+a^2+2*a)*x^2+(a^3+2*a^2+a+1)*x+2*a^3+a^2+2', 'y^2=(2*a^3+a+1)*x^6+(2*a^3+2*a^2+1)*x^5+(2*a^3+2*a+2)*x^4+(a^2+2)*x^3+(2*a^3+1)*x^2+(a^3+2*a^2+a)*x+2*a^3+2*a^2+a+2', 'y^2=(2*a^2+1)*x^6+a^3*x^5+(a^3+a^2+a)*x^4+(a^3+a^2)*x^3+(2*a^3+2*a^2+2*a+1)*x^2+(2*a^3+2*a+1)*x+2*a^3+a^2+a+1', 'y^2=a^3*x^6+(a^3+1)*x^5+(2*a^3+2)*x^4+(2*a^3+2*a)*x^3+(2*a^3+2*a+1)*x^2+(a^3+2*a^2)*x+2*a^3', 'y^2=(a^3+2*a+2)*x^6+(2*a^3+2*a+1)*x^5+(2*a^3+2*a^2+2*a)*x^4+(2*a^3+a^2+2*a)*x^3+(2*a^3+a^2+2*a+1)*x^2+(2*a^2+2*a)*x+a^3+2*a^2+2', 'y^2=(2*a^3+2*a^2+2*a+1)*x^6+(2*a^2+1)*x^5+2*a^3*x^4+(2*a^3+1)*x^3+(a^3+a^2+1)*x^2+(2*a^3+2*a^2+2)*x+a^3+a^2+2*a', 'y^2=(2*a^2+1)*x^6+(a^3+a^2+2)*x^5+(a^3+a^2)*x^4+(2*a^3+a^2)*x^3+(a^3+1)*x^2+(a^3+a^2+2*a)*x+2*a^3+a', 'y^2=(2*a^3+a^2+1)*x^6+(a^3+a^2+1)*x^5+(2*a^3+2*a^2)*x^4+(a^3+a^2+a)*x^3+(a^3+a^2+2*a+2)*x^2+2*x+a^2', 'y^2=(a^3+2*a^2+2*a)*x^6+(a^3+a^2+2*a)*x^5+(a^3+a+1)*x^4+(a^3+2*a^2+2)*x^3+(2*a^3+2*a^2+a+2)*x^2+(a^3+a^2+a)*x+a^3+2*a^2+a+2', 'y^2=(2*a^2+2*a)*x^6+(2*a^2+a+2)*x^5+(a^2+1)*x^4+(2*a^3+a)*x^3+(a^3+a^2+2*a+1)*x^2+(a^3+2*a^2+1)*x+2*a^3+2*a', 'y^2=(a^3+a+2)*x^6+(a^3+a+1)*x^5+(a^3+a^2+2*a+1)*x^4+(2*a^3+a^2+2*a)*x^2+(2*a^3+a^2+2*a)*x+a^3+1'], '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': 2, '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': ['4.0.69184.1'], 'geometric_splitting_field': '4.0.69184.1', 'geometric_splitting_polynomials': [[79, -14, 17, -2, 1]], 'group_structure_count': 1, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 12, 'is_geometrically_simple': True, 'is_geometrically_squarefree': True, 'is_primitive': True, 'is_simple': True, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 12, 'label': '2.81.abe_op', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 2, 'newton_coelevation': 2, 'newton_elevation': 0, 'number_fields': ['4.0.69184.1'], 'p': 3, 'p_rank': 2, 'p_rank_deficit': 0, 'poly': [1, -30, 379, -2430, 6561], 'poly_str': '1 -30 379 -2430 6561 ', 'primitive_models': [], 'q': 81, 'real_poly': [1, -30, 217], 'simple_distinct': ['2.81.abe_op'], 'simple_factors': ['2.81.abe_opA'], 'simple_multiplicities': [1], 'singular_primes': ['2,5*F+V-27'], 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '4.0.69184.1', 'splitting_polynomials': [[79, -14, 17, -2, 1]], 'twist_count': 2, 'twists': [['2.81.be_op', '2.6561.afm_qfr', 2]], 'weak_equivalence_count': 2, 'zfv_index': 4, 'zfv_index_factorization': [[2, 2]], 'zfv_is_bass': True, 'zfv_is_maximal': False, 'zfv_plus_index': 2, 'zfv_plus_index_factorization': [[2, 1]], 'zfv_plus_norm': 1081, 'zfv_singular_count': 2, 'zfv_singular_primes': ['2,5*F+V-27']}
• av_fq_endalg_factors •

  Column	Type
  base_label	text
  extension_degree	smallint
  extension_label	text
  multiplicity	smallint

  
  {'base_label': '2.81.abe_op', 'extension_degree': 1, 'extension_label': '2.81.abe_op', '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'], 'center': '4.0.69184.1', 'center_dim': 4, 'divalg_dim': 1, 'extension_label': '2.81.abe_op', 'galois_group': '4T3', 'places': [['2/9', '16/9', '26/9', '1/9'], ['2', '1', '0', '0']]}