Abelian variety isogeny class data - 2.31.ac_ah

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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': 891, 'abvar_counts': [891, 907929, 880518276, 855778466169, 819782834354451, 787694127395907600, 756958483408532023971, 727421961136051782387369, 699053566642978831689307716, 671790516757352110096301772009], 'abvar_counts_str': '891 907929 880518276 855778466169 819782834354451 787694127395907600 756958483408532023971 727421961136051782387369 699053566642978831689307716 671790516757352110096301772009 ', 'all_polarized_product': False, 'all_unpolarized_product': False, 'angle_corank': 0, 'angle_rank': 2, 'angles': [0.181881757293455, 0.730096920819084], 'center_dim': 4, 'cohen_macaulay_max': 1, 'curve_count': 30, 'curve_counts': [30, 944, 29556, 926644, 28634550, 887538998, 27513142890, 852889676644, 26439620142636, 819628272264704], 'curve_counts_str': '30 944 29556 926644 28634550 887538998 27513142890 852889676644 26439620142636 819628272264704 ', 'curves': ['y^2=12*x^6+2*x^4+6*x^3+29*x^2+12*x+27', 'y^2=12*x^6+7*x^5+22*x^4+7*x^3+13*x^2+5*x+25', 'y^2=10*x^6+5*x^5+29*x^4+10*x^3+27*x^2+27*x+5', 'y^2=26*x^6+13*x^5+10*x^4+5*x^3+30*x^2+5*x+16', 'y^2=9*x^6+11*x^5+5*x^4+9*x^3+13*x^2+8*x+9', 'y^2=24*x^6+16*x^5+2*x^4+22*x^3+17*x^2+9*x+9', 'y^2=23*x^6+18*x^5+16*x^4+27*x^3+20*x^2+28*x+18', 'y^2=28*x^6+12*x^5+29*x^4+14*x^3+2*x^2+6*x+9', 'y^2=28*x^6+30*x^5+x^4+6*x^3+14*x^2+13', 'y^2=22*x^6+14*x^5+x^4+3*x^3+24*x^2+23*x+7', 'y^2=17*x^6+24*x^5+27*x^4+7*x^3+17*x^2+29', 'y^2=11*x^6+16*x^5+4*x^4+11*x^3+22*x^2+30*x+14', 'y^2=25*x^6+4*x^5+27*x^4+21*x^3+8*x^2+25*x+2', 'y^2=13*x^6+26*x^5+22*x^4+11*x^3+5*x^2+3*x+18', 'y^2=23*x^6+24*x^5+x^4+19*x^3+28*x^2+19*x+11', 'y^2=17*x^6+23*x^5+22*x^4+16*x^3+17*x^2+19*x+6', 'y^2=25*x^6+29*x^5+7*x^3+11*x^2+7*x+28', 'y^2=11*x^6+3*x^5+19*x^4+2*x^3+4*x^2+25*x+8', 'y^2=13*x^6+25*x^5+3*x^4+8*x^3+13*x+27', 'y^2=26*x^6+18*x^5+4*x^4+4*x^3+9*x^2+23*x+20', 'y^2=25*x^6+14*x^5+16*x^4+16*x^3+21*x^2+x+18', 'y^2=29*x^6+14*x^5+20*x^4+19*x^3+11*x^2+27*x+24', 'y^2=13*x^6+2*x^5+16*x^4+16*x^3+16*x^2+2', 'y^2=30*x^6+25*x^5+x^4+5*x^3+13*x^2+20*x+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': ['4.0.22030400.3'], 'geometric_splitting_field': '4.0.22030400.3', 'geometric_splitting_polynomials': [[961, -62, -7, -2, 1]], 'group_structure_count': 2, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 24, 'is_geometrically_simple': True, 'is_geometrically_squarefree': True, 'is_primitive': True, 'is_simple': True, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 24, 'label': '2.31.ac_ah', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 2, 'newton_coelevation': 2, 'newton_elevation': 0, 'number_fields': ['4.0.22030400.3'], 'p': 31, 'p_rank': 2, 'p_rank_deficit': 0, 'pic_prime_gens': [[1, 2, 1, 2], [1, 11, 1, 4], [1, 23, 1, 4], [1, 31, 1, 8]], 'poly': [1, -2, -7, -62, 961], 'poly_str': '1 -2 -7 -62 961 ', 'primitive_models': [], 'principal_polarization_count': 24, 'q': 31, 'real_poly': [1, -2, -69], 'simple_distinct': ['2.31.ac_ah'], 'simple_factors': ['2.31.ac_ahA'], 'simple_multiplicities': [1], 'singular_primes': ['3,4*F-10*V+18'], 'size': 48, 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '4.0.22030400.3', 'splitting_polynomials': [[961, -62, -7, -2, 1]], 'twist_count': 2, 'twists': [['2.31.c_ah', '2.961.as_coh', 2]], 'weak_equivalence_count': 2, 'zfv_index': 3, 'zfv_index_factorization': [[3, 1]], 'zfv_is_bass': True, 'zfv_is_maximal': False, 'zfv_pic_size': 32, 'zfv_plus_index': 1, 'zfv_plus_index_factorization': [], 'zfv_plus_norm': 2529, 'zfv_singular_count': 2, 'zfv_singular_primes': ['3,4*F-10*V+18']}
• av_fq_endalg_factors •

  Column	Type
  base_label	text
  extension_degree	smallint
  extension_label	text
  multiplicity	smallint

  
  {'base_label': '2.31.ac_ah', 'extension_degree': 1, 'extension_label': '2.31.ac_ah', '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': '4.0.22030400.3', 'center_dim': 4, 'divalg_dim': 1, 'extension_label': '2.31.ac_ah', 'galois_group': '4T3', 'places': [['14', '1', '0', '0'], ['15', '1', '0', '0'], ['16', '7/31', '2/31', '960/31'], ['17', '7/31', '2/31', '960/31']]}