Abelian variety isogeny class data - 2.31.af_cg

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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': 860, 'abvar_counts': [860, 1014800, 895882640, 852143796800, 819588963586500, 787659228711276800, 756934725593164732340, 727422373618116167532800, 699054035897583652206828560, 671790595609587333970514250000], 'abvar_counts_str': '860 1014800 895882640 852143796800 819588963586500 787659228711276800 756934725593164732340 727422373618116167532800 699054035897583652206828560 671790595609587333970514250000 ', 'all_polarized_product': False, 'all_unpolarized_product': False, 'angle_corank': 0, 'angle_rank': 2, 'angles': [0.328899069140533, 0.520067493920394], 'center_dim': 4, 'cohen_macaulay_max': 1, 'curve_count': 27, 'curve_counts': [27, 1053, 30072, 922713, 28627777, 887499678, 27512279367, 852890160273, 26439637890792, 819628368469573], 'curve_counts_str': '27 1053 30072 922713 28627777 887499678 27512279367 852890160273 26439637890792 819628368469573 ', 'curves': ['y^2=6*x^5+17*x^4+22*x^3+9*x^2+26*x+27', 'y^2=7*x^6+3*x^5+19*x^4+25*x^3+21*x^2+2*x+26', 'y^2=4*x^6+5*x^5+23*x^4+2*x^3+x^2+7*x+4', 'y^2=13*x^6+17*x^5+29*x^4+20*x^3+8*x^2+25*x+25', 'y^2=16*x^6+12*x^5+23*x^4+18*x^3+16*x^2+18*x+3', 'y^2=21*x^6+29*x^5+17*x^4+6*x^3+27*x^2+3', 'y^2=14*x^6+18*x^5+13*x^4+30*x^3+19*x^2+22*x+19', 'y^2=10*x^6+21*x^5+16*x^4+24*x^3+5*x^2+18*x+9', 'y^2=3*x^5+18*x^4+19*x^3+3*x^2+16*x+7', 'y^2=7*x^6+7*x^5+6*x^4+7*x^3+26*x^2+16*x+20', 'y^2=22*x^6+16*x^5+4*x^4+x^3+23*x^2+5*x', 'y^2=6*x^6+29*x^5+26*x^4+2*x^3+21*x^2+22*x+29', 'y^2=29*x^6+26*x^5+18*x^4+3*x^3+8*x^2+6*x+15', 'y^2=20*x^6+17*x^5+3*x^4+19*x^3+23*x^2+24*x+4', 'y^2=14*x^6+28*x^5+12*x^4+23*x^3+14*x^2+19', 'y^2=6*x^6+9*x^5+17*x^4+14*x^3+13*x^2+11*x+17', 'y^2=3*x^6+7*x^5+20*x^4+11*x^3+26*x^2+23*x+19', 'y^2=10*x^6+9*x^5+14*x^4+26*x^3+19*x^2+22*x+27', 'y^2=30*x^6+9*x^5+23*x^4+12*x^3+14*x^2+24*x+4', 'y^2=5*x^6+29*x^5+8*x^4+11*x^3+11*x^2+19*x', 'y^2=10*x^6+29*x^5+15*x^4+5*x^3+24*x^2+13*x+11', 'y^2=12*x^6+12*x^5+11*x^4+18*x^3+12*x^2+30*x+6', 'y^2=29*x^6+11*x^5+19*x^3+8*x^2+6*x+17', 'y^2=10*x^6+10*x^5+26*x^4+24*x^3+26*x^2+29*x+23', 'y^2=15*x^6+28*x^5+5*x^4+10*x^3+27*x^2+7*x', 'y^2=11*x^6+10*x^5+x^4+26*x^3+17*x^2+11*x+14', 'y^2=19*x^6+10*x^5+13*x^4+22*x^3+14*x^2+22*x+29', 'y^2=15*x^6+12*x^5+11*x^4+2*x^3+16*x^2+15*x', 'y^2=30*x^6+14*x^5+10*x^4+19*x^3+19*x^2+20*x+5', 'y^2=24*x^6+20*x^5+2*x^4+18*x^3+14*x^2+6', 'y^2=17*x^6+20*x^5+3*x^4+8*x^3+24*x^2+22*x+15', 'y^2=30*x^6+17*x^5+20*x^4+22*x^3+7*x^2+3*x+29'], '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': ['4.0.4748825.1'], 'geometric_splitting_field': '4.0.4748825.1', 'geometric_splitting_polynomials': [[860, -50, 49, -1, 1]], 'group_structure_count': 2, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 32, 'is_cyclic': False, 'is_geometrically_simple': True, 'is_geometrically_squarefree': True, 'is_primitive': True, 'is_simple': True, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 32, 'label': '2.31.af_cg', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 2, 'newton_coelevation': 2, 'newton_elevation': 0, 'noncyclic_primes': [2], 'number_fields': ['4.0.4748825.1'], 'p': 31, 'p_rank': 2, 'p_rank_deficit': 0, 'pic_prime_gens': [[1, 5, 1, 2], [1, 5, 2, 2], [1, 23, 1, 4], [1, 31, 1, 12]], 'poly': [1, -5, 58, -155, 961], 'poly_str': '1 -5 58 -155 961 ', 'primitive_models': [], 'principal_polarization_count': 32, 'q': 31, 'real_poly': [1, -5, -4], 'simple_distinct': ['2.31.af_cg'], 'simple_factors': ['2.31.af_cgA'], 'simple_multiplicities': [1], 'singular_primes': ['2,-2*F^2-V+3'], 'size': 32, 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '4.0.4748825.1', 'splitting_polynomials': [[860, -50, 49, -1, 1]], 'twist_count': 2, 'twists': [['2.31.f_cg', '2.961.dn_fns', 2]], 'weak_equivalence_count': 2, 'zfv_index': 2, 'zfv_index_factorization': [[2, 1]], 'zfv_is_bass': True, 'zfv_is_maximal': False, 'zfv_pic_size': 24, 'zfv_plus_index': 1, 'zfv_plus_index_factorization': [], 'zfv_plus_norm': 11300, 'zfv_singular_count': 2, 'zfv_singular_primes': ['2,-2*F^2-V+3']}
• av_fq_endalg_factors •

  Column	Type
  base_label	text
  extension_degree	smallint
  extension_label	text
  multiplicity	smallint

  
  {'base_label': '2.31.af_cg', 'extension_degree': 1, 'extension_label': '2.31.af_cg', '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': '4.0.4748825.1', 'center_dim': 4, 'divalg_dim': 1, 'extension_label': '2.31.af_cg', 'galois_group': '4T3', 'places': [['7', '1', '0', '0'], ['21', '1', '0', '0'], ['581/31', '950/31', '29/31', '1/31'], ['147/31', '950/31', '29/31', '1/31']]}