Abelian variety isogeny class data - 2.47.ae_do

Formats: - HTML - YAML - JSON - 2025-11-08T17:45:29.934843

• 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': 2110, 'abvar_counts': [2110, 5262340, 10828809070, 23784619085200, 52593342959913550, 116192781534729001540, 256667353390805227562590, 566977352253787938787430400, 1252453025147983835966931830110, 2766668710998265579843426774101700], 'abvar_counts_str': '2110 5262340 10828809070 23784619085200 52593342959913550 116192781534729001540 256667353390805227562590 566977352253787938787430400 1252453025147983835966931830110 2766668710998265579843426774101700 ', 'all_polarized_product': False, 'all_unpolarized_product': False, 'angle_corank': 0, 'angle_rank': 2, 'angles': [0.394799799914954, 0.510436834756344], 'center_dim': 4, 'cohen_macaulay_max': 1, 'curve_count': 44, 'curve_counts': [44, 2378, 104300, 4874214, 229319764, 10779335786, 506623845268, 23811285811966, 1119130481431340, 52599132217501418], 'curve_counts_str': '44 2378 104300 4874214 229319764 10779335786 506623845268 23811285811966 1119130481431340 52599132217501418 ', 'curves': ['y^2=39*x^6+5*x^5+39*x^4+41*x^3+4*x^2+15*x+5', 'y^2=12*x^6+13*x^5+22*x^4+2*x^3+22*x^2+11*x+21', 'y^2=25*x^6+44*x^5+9*x^4+22*x^3+29*x^2+8*x+16', 'y^2=7*x^6+20*x^5+43*x^4+12*x^3+6*x^2+18*x+13', 'y^2=38*x^6+30*x^5+6*x^4+32*x^3+9*x^2+31*x+32', 'y^2=2*x^6+29*x^5+45*x^4+10*x^3+35*x^2+x+21', 'y^2=19*x^6+22*x^5+18*x^4+26*x^3+2*x^2+27*x+42', 'y^2=33*x^6+35*x^5+42*x^4+44*x^3+14*x^2+19*x+26', 'y^2=34*x^6+5*x^5+4*x^4+11*x^3+24*x^2+14*x+19', 'y^2=11*x^6+17*x^5+43*x^4+34*x^3+42*x^2+44*x+5', 'y^2=8*x^6+27*x^5+19*x^4+42*x^3+3*x^2+13*x+16', 'y^2=19*x^6+27*x^5+23*x^4+46*x^3+21*x^2+26*x+41', 'y^2=22*x^6+6*x^5+29*x^4+14*x^3+21*x^2+25*x+11', 'y^2=11*x^6+42*x^5+23*x^3+43*x^2+31*x+28', 'y^2=14*x^6+16*x^5+17*x^4+44*x^3+27*x^2+32*x+14', 'y^2=30*x^6+10*x^5+30*x^4+6*x^3+37*x^2+44*x+10', 'y^2=29*x^6+42*x^5+32*x^4+39*x^3+32*x^2+8*x+39', 'y^2=5*x^6+45*x^5+43*x^4+26*x^3+15*x^2+16*x+11', 'y^2=31*x^6+6*x^5+31*x^4+25*x^3+41*x^2+22*x+45', 'y^2=31*x^6+40*x^5+40*x^4+35*x^3+26*x^2+39*x+15', 'y^2=39*x^6+23*x^5+24*x^4+36*x^3+16*x^2+21*x+45', 'y^2=10*x^6+x^5+42*x^4+30*x^3+12*x^2+31*x+22', 'y^2=19*x^6+11*x^5+43*x^4+39*x^3+34*x^2+24*x+34', 'y^2=22*x^6+45*x^5+25*x^4+3*x^3+5*x^2+18*x+36', 'y^2=42*x^6+44*x^5+29*x^4+4*x^3+38*x^2+33*x+34', 'y^2=46*x^6+11*x^5+18*x^4+35*x^3+33*x^2+31*x+16', 'y^2=43*x^6+30*x^5+20*x^4+33*x^3+5*x^2+25*x+31', 'y^2=24*x^6+23*x^5+40*x^4+37*x^3+35*x^2+7*x+33', 'y^2=23*x^6+17*x^5+8*x^4+9*x^3+27*x^2+30*x+20', 'y^2=28*x^6+37*x^5+38*x^4+28*x^3+7*x^2+13*x+45', 'y^2=2*x^6+35*x^5+10*x^4+6*x^3+x^2+9*x+5', 'y^2=10*x^6+7*x^5+24*x^4+4*x^3+41*x^2+24*x+38', 'y^2=44*x^6+18*x^5+26*x^4+4*x^3+17*x^2+12*x+28', 'y^2=4*x^6+15*x^5+40*x^4+35*x^2+21*x+30', 'y^2=30*x^6+37*x^5+27*x^4+36*x^3+37*x^2+28*x+39', 'y^2=9*x^6+18*x^5+18*x^4+12*x^3+17*x^2+35*x+16', 'y^2=40*x^6+29*x^5+13*x^4+32*x^3+5*x^2+6*x+25', 'y^2=6*x^6+31*x^5+4*x^4+18*x^3+12*x^2+41*x+13', 'y^2=20*x^6+5*x^5+40*x^4+17*x^3+15*x^2+30*x+16', 'y^2=39*x^6+5*x^5+37*x^4+39*x^3+17*x^2+33*x+38', 'y^2=24*x^6+6*x^5+35*x^4+x^3+18*x^2+22*x+23', 'y^2=42*x^6+38*x^5+40*x^4+38*x^3+28*x^2+30*x+16', 'y^2=17*x^6+32*x^5+7*x^4+2*x^3+6*x^2+39*x+25', 'y^2=21*x^6+37*x^5+46*x^4+30*x^3+30*x^2+8*x+39'], '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': 1, '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': ['4.0.18194688.1'], 'geometric_splitting_field': '4.0.18194688.1', 'geometric_splitting_polynomials': [[2110, -12, 86, 0, 1]], 'group_structure_count': 1, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 44, 'is_geometrically_simple': True, 'is_geometrically_squarefree': True, 'is_primitive': True, 'is_simple': True, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 44, 'label': '2.47.ae_do', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 2, 'newton_coelevation': 2, 'newton_elevation': 0, 'number_fields': ['4.0.18194688.1'], 'p': 47, 'p_rank': 2, 'p_rank_deficit': 0, 'pic_prime_gens': [[1, 2, 1, 2], [1, 5, 1, 22]], 'poly': [1, -4, 92, -188, 2209], 'poly_str': '1 -4 92 -188 2209 ', 'primitive_models': [], 'principal_polarization_count': 44, 'q': 47, 'real_poly': [1, -4, -2], 'simple_distinct': ['2.47.ae_do'], 'simple_factors': ['2.47.ae_doA'], 'simple_multiplicities': [1], 'singular_primes': [], 'size': 44, 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '4.0.18194688.1', 'splitting_polynomials': [[2110, -12, 86, 0, 1]], 'twist_count': 2, 'twists': [['2.47.e_do', '2.2209.gm_qvq', 2]], 'weak_equivalence_count': 1, 'zfv_index': 1, 'zfv_index_factorization': [], 'zfv_is_bass': True, 'zfv_is_maximal': True, 'zfv_pic_size': 44, 'zfv_plus_index': 1, 'zfv_plus_index_factorization': [], 'zfv_plus_norm': 31588, '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': '2.47.ae_do', 'extension_degree': 1, 'extension_label': '2.47.ae_do', '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': '4.0.18194688.1', 'center_dim': 4, 'divalg_dim': 1, 'extension_label': '2.47.ae_do', 'galois_group': '4T3', 'places': [['36', '1', '0', '0'], ['9', '1', '0', '0'], ['371/47', '40/47', '46/47', '1/47'], ['1640/47', '40/47', '46/47', '1/47']]}