Abelian variety isogeny class data - 2.31.a_abi

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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': 928, 'abvar_counts': [928, 861184, 887562400, 854308306944, 819628273402528, 787767013893760000, 756943935176969972128, 727425271523747393961984, 699053619999091149343069600, 671790506560809188110316790784], 'abvar_counts_str': '928 861184 887562400 854308306944 819628273402528 787767013893760000 756943935176969972128 727425271523747393961984 699053619999091149343069600 671790506560809188110316790784 ', 'angle_corank': 1, 'angle_rank': 1, 'angles': [0.15762102420564, 0.84237897579436], 'center_dim': 4, 'cohen_macaulay_max': 3, 'curve_count': 32, 'curve_counts': [32, 894, 29792, 925054, 28629152, 887621118, 27512614112, 852893558014, 26439622160672, 819628259824254], 'curve_counts_str': '32 894 29792 925054 28629152 887621118 27512614112 852893558014 26439622160672 819628259824254 ', 'curves': ['y^2=23*x^6+28*x^5+30*x^4+26*x^3+28*x^2+4*x+1', 'y^2=12*x^6+4*x^5+17*x^4+7*x^3+5*x^2+10*x+7', 'y^2=26*x^6+25*x^5+18*x^4+7*x^3+10*x^2+18*x+12', 'y^2=21*x^6+25*x^5+23*x^4+9*x^3+26*x^2+17*x+3', 'y^2=25*x^6+10*x^5+5*x^4+2*x^3+10*x^2+11*x+1', 'y^2=13*x^6+27*x^4+15*x^3+x^2+27*x+1', 'y^2=8*x^6+19*x^4+14*x^3+3*x^2+19*x+3', 'y^2=7*x^6+17*x^5+9*x^4+16*x^3+28*x^2+11*x+24', 'y^2=23*x^6+22*x^5+8*x^4+27*x^3+20*x^2+10', 'y^2=24*x^6+27*x^5+30*x^4+x^3+x^2+6*x', 'y^2=14*x^6+16*x^5+10*x^4+24*x^3+29*x^2+18*x+17', 'y^2=23*x^6+6*x^5+18*x^4+12*x^3+12*x^2+4*x+7', 'y^2=18*x^6+23*x^5+15*x^4+28*x^2+22*x+13', 'y^2=3*x^6+27*x^5+28*x^4+26*x^3+17*x+1', 'y^2=9*x^6+19*x^5+22*x^4+16*x^3+20*x+3', 'y^2=x^6+22*x^5+x^4+27*x^3+6*x^2+5*x+6', 'y^2=30*x^6+10*x^5+5*x^4+26*x^3+15*x^2+10*x+19', 'y^2=28*x^6+30*x^5+15*x^4+16*x^3+14*x^2+30*x+26', 'y^2=7*x^6+8*x^5+4*x^4+20*x^3+23*x^2+16*x+15', 'y^2=30*x^6+11*x^5+18*x^4+8*x^3+2*x^2+19*x', 'y^2=5*x^6+20*x^5+24*x^4+30*x^3+24*x^2+29*x+6', 'y^2=15*x^6+29*x^5+10*x^4+28*x^3+10*x^2+25*x+18', 'y^2=17*x^5+29*x^4+17*x^3+7*x^2+26*x+15', 'y^2=22*x^6+26*x^5+16*x^3+12*x+20', 'y^2=22*x^6+29*x^5+23*x^4+6*x^3+27*x^2+2*x+27', 'y^2=14*x^6+16*x^5+3*x^4+7*x^3+5*x^2+10*x+12', 'y^2=11*x^6+20*x^5+x^4+8*x^3+16*x^2+10*x+12', 'y^2=21*x^6+9*x^5+23*x^4+29*x^3+28*x^2+25*x+18', 'y^2=19*x^6+22*x^5+21*x^4+20*x^3+25*x^2+26*x+8', 'y^2=7*x^6+29*x^5+x^4+10*x^3+8*x^2+18*x+13', 'y^2=30*x^6+7*x^5+14*x^4+27*x^3+26*x^2+15*x+17', 'y^2=25*x^5+3*x^4+27*x^3+9*x^2+8*x', 'y^2=29*x^6+30*x^5+21*x^4+22*x^2+29*x+2', 'y^2=25*x^6+28*x^5+x^4+4*x^2+25*x+6'], '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': 14, 'g': 2, 'galois_groups': ['4T2'], 'geom_dim1_distinct': 1, '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': 2, 'geometric_extension_degree': 2, 'geometric_galois_groups': ['2T1'], 'geometric_number_fields': ['2.0.168.1'], 'geometric_splitting_field': '2.0.168.1', 'geometric_splitting_polynomials': [[42, 0, 1]], 'group_structure_count': 6, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 34, 'is_cyclic': False, 'is_geometrically_simple': False, 'is_geometrically_squarefree': False, 'is_primitive': True, 'is_simple': True, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 34, 'label': '2.31.a_abi', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 4, 'newton_coelevation': 2, 'newton_elevation': 0, 'noncyclic_primes': [2], 'number_fields': ['4.0.28224.4'], 'p': 31, 'p_rank': 2, 'p_rank_deficit': 0, 'poly': [1, 0, -34, 0, 961], 'poly_str': '1 0 -34 0 961 ', 'primitive_models': [], 'q': 31, 'real_poly': [1, 0, -96], 'simple_distinct': ['2.31.a_abi'], 'simple_factors': ['2.31.a_abiA'], 'simple_multiplicities': [1], 'singular_primes': ['2,8*F-7*V-5'], 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '4.0.28224.4', 'splitting_polynomials': [[58, 8, -7, -2, 1]], 'twist_count': 2, 'twists': [['2.31.a_bi', '2.923521.cgy_fimhq', 4]], 'weak_equivalence_count': 23, 'zfv_index': 64, 'zfv_index_factorization': [[2, 6]], 'zfv_is_bass': False, 'zfv_is_maximal': False, 'zfv_plus_index': 4, 'zfv_plus_index_factorization': [[2, 2]], 'zfv_plus_norm': 784, 'zfv_singular_count': 2, 'zfv_singular_primes': ['2,8*F-7*V-5']}
• av_fq_endalg_factors •

  Column	Type
  base_label	text
  extension_degree	smallint
  extension_label	text
  multiplicity	smallint

  
  
  • id: 20638
    {'base_label': '2.31.a_abi', 'extension_degree': 1, 'extension_label': '2.31.a_abi', 'multiplicity': 1}
  • id: 20639
    {'base_label': '2.31.a_abi', 'extension_degree': 2, 'extension_label': '1.961.abi', 'multiplicity': 2}
• 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': '4.0.28224.4', 'center_dim': 4, 'divalg_dim': 1, 'extension_label': '2.31.a_abi', 'galois_group': '4T2', 'places': [['464/31', '1', '6/31', '957/31'], ['15', '1', '0', '0']]}
• 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': '2.0.168.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.961.abi', 'galois_group': '2T1', 'places': [['19', '1'], ['12', '1']]}