Abelian variety isogeny class data - 2.71.as_hq

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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': 3944, 'abvar_counts': [3944, 25777984, 128468405000, 645788405377024, 3255251309812013384, 16409779335747246280000, 82721295303527512664145704, 416997633916426058657746550784, 2102084990672563050059115348905000, 10596610556848281725035997634310897984], 'abvar_counts_str': '3944 25777984 128468405000 645788405377024 3255251309812013384 16409779335747246280000 82721295303527512664145704 416997633916426058657746550784 2102084990672563050059115348905000 10596610556848281725035997634310897984 ', 'angle_corank': 0, 'angle_rank': 2, 'angles': [0.187913521440082, 0.423719104037511], 'center_dim': 4, 'cohen_macaulay_max': 2, 'curve_count': 54, 'curve_counts': [54, 5114, 358938, 25413054, 1804233654, 128101037978, 9095129460954, 645753547970494, 45848500119584118, 3255243545006293754], 'curve_counts_str': '54 5114 358938 25413054 1804233654 128101037978 9095129460954 645753547970494 45848500119584118 3255243545006293754 ', 'curves': ['y^2=56*x^6+63*x^5+21*x^4+38*x^3+2*x^2+32*x+62', 'y^2=49*x^6+39*x^5+57*x^4+35*x^3+4*x^2+51*x+9', 'y^2=63*x^6+40*x^5+30*x^4+40*x^3+2*x^2+10*x+3', 'y^2=58*x^6+20*x^5+11*x^4+23*x^3+9*x^2+68*x+22', 'y^2=69*x^6+66*x^5+33*x^4+67*x^3+61*x^2+3*x+38', 'y^2=58*x^6+59*x^5+14*x^4+13*x^3+59*x^2+52*x+19', 'y^2=55*x^6+19*x^5+69*x^4+51*x^3+31*x^2+20*x+40', 'y^2=70*x^6+60*x^5+7*x^4+31*x^3+52*x^2+3*x+26', 'y^2=9*x^6+6*x^5+47*x^4+27*x^3+5*x^2+12*x+21', 'y^2=12*x^6+5*x^5+49*x^4+33*x^3+5*x^2+30*x+66', 'y^2=38*x^6+53*x^5+32*x^4+66*x^3+48*x^2+30*x+28', 'y^2=56*x^6+21*x^5+51*x^3+54*x^2+15*x+7', 'y^2=47*x^6+39*x^5+5*x^4+47*x^3+48*x^2+13*x+51', 'y^2=28*x^6+29*x^5+13*x^4+53*x^3+13*x^2+54*x+51', 'y^2=22*x^6+40*x^5+23*x^4+46*x^3+47*x^2+3*x', 'y^2=13*x^6+50*x^5+12*x^4+47*x^3+46*x^2+23*x+13', 'y^2=67*x^6+27*x^5+18*x^4+12*x^3+50*x^2+16*x+65', 'y^2=63*x^6+13*x^5+39*x^4+56*x^3+24*x^2+11*x+59', 'y^2=57*x^6+62*x^5+59*x^4+56*x^3+56*x^2+28', 'y^2=3*x^6+64*x^5+6*x^4+41*x^3+13*x^2+9*x+36', 'y^2=36*x^6+10*x^5+57*x^4+22*x^3+19*x^2+65*x+53', 'y^2=18*x^6+62*x^5+16*x^4+27*x^3+3*x^2+65*x+33', 'y^2=21*x^6+63*x^5+45*x^4+36*x^3+42*x^2+4*x+7', 'y^2=27*x^6+65*x^5+x^4+39*x^3+54*x^2+56*x+42', 'y^2=66*x^6+52*x^5+32*x^4+65*x^3+7*x^2+69*x+52', 'y^2=68*x^6+15*x^5+43*x^4+31*x^3+52*x^2+22*x+26', 'y^2=68*x^6+38*x^5+5*x^4+8*x^3+36*x^2+16*x+35', 'y^2=21*x^6+4*x^5+41*x^4+14*x^3+67*x^2+24*x+61', 'y^2=64*x^6+17*x^5+9*x^4+33*x^3+18*x^2+27*x+37', 'y^2=18*x^6+58*x^5+54*x^4+54*x^3+21*x^2+26*x+69', 'y^2=7*x^6+22*x^5+41*x^4+68*x^3+12*x^2+11*x+31', 'y^2=38*x^6+8*x^5+40*x^4+15*x^3+60*x^2+7*x+66', 'y^2=13*x^6+52*x^5+59*x^4+17*x^3+33*x^2+7*x+26', 'y^2=40*x^6+32*x^5+29*x^4+12*x^3+35*x^2+4*x+19', 'y^2=23*x^6+23*x^5+35*x^4+33*x^3+62*x^2+64*x+51', 'y^2=25*x^6+63*x^5+40*x^4+31*x^3+54*x^2+53*x+62', 'y^2=58*x^6+49*x^5+68*x^4+26*x^3+68*x^2+49*x+58', 'y^2=69*x^6+44*x^5+50*x^4+7*x^3+64*x^2+44*x+47', 'y^2=41*x^6+30*x^5+2*x^4+46*x^3+2*x^2+30*x+41', 'y^2=8*x^6+22*x^5+17*x^4+28*x^3+39*x^2+61*x+25', 'y^2=65*x^6+13*x^5+14*x^4+64*x^3+57*x^2+32*x+70', 'y^2=8*x^6+53*x^5+26*x^4+51*x^3+58*x^2+27*x+42', 'y^2=51*x^6+56*x^5+50*x^4+6*x^3+50*x^2+38*x+11', 'y^2=11*x^6+69*x^5+53*x^4+51*x^3+38*x^2+25*x+38', 'y^2=47*x^6+18*x^5+53*x^4+56*x^3+26*x^2+47*x+33', 'y^2=60*x^6+39*x^5+37*x^4+58*x^3+49*x^2+62*x+47', 'y^2=11*x^6+25*x^5+32*x^4+45*x^3+52*x^2+7*x+67', 'y^2=11*x^6+14*x^5+35*x^4+9*x^3+17*x^2+70*x+19', 'y^2=44*x^6+59*x^5+36*x^4+7*x^3+36*x^2+59*x+44', 'y^2=2*x^6+25*x^5+46*x^4+20*x^3+33*x^2+56*x+38', 'y^2=24*x^6+55*x^5+4*x^4+33*x^3+4*x^2+55*x+24', 'y^2=14*x^6+10*x^5+6*x^4+63*x^3+58*x^2+18*x+47', 'y^2=28*x^5+57*x^4+4*x^3+17*x+66', 'y^2=66*x^6+4*x^5+13*x^4+15*x^3+37*x^2+68*x+62', 'y^2=44*x^6+28*x^5+42*x^4+56*x^3+21*x^2+58*x+66', 'y^2=19*x^6+56*x^5+65*x^4+61*x^3+59*x^2+70*x+33', 'y^2=16*x^6+44*x^5+53*x^4+50*x^3+43*x^2+6*x+54', 'y^2=67*x^6+45*x^5+7*x^4+47*x^3+34*x^2+43*x+61', 'y^2=20*x^6+70*x^5+62*x^4+47*x^3+56*x^2+6*x+15', 'y^2=25*x^6+24*x^5+51*x^4+32*x^3+55*x^2+55*x+15', 'y^2=59*x^6+16*x^5+14*x^4+21*x^3+68*x^2+42*x+4', 'y^2=11*x^6+63*x^5+39*x^4+3*x^3+17*x^2+38*x+37', 'y^2=25*x^6+7*x^5+38*x^4+31*x^3+57*x^2+55*x+55', 'y^2=11*x^6+62*x^5+14*x^4+64*x^3+31*x^2+38*x+60', 'y^2=28*x^6+44*x^5+66*x^4+65*x^3+33*x^2+40*x+47', 'y^2=7*x^6+40*x^5+60*x^4+37*x^3+18*x^2+8*x+68', 'y^2=66*x^6+63*x^5+34*x^4+14*x^3+50*x^2+23*x+63', 'y^2=67*x^6+50*x^5+20*x^4+61*x^3+56*x^2+70*x+32', 'y^2=20*x^6+65*x^5+x^4+14*x^3+32*x^2+33*x+30', 'y^2=63*x^6+22*x^5+39*x^4+6*x^3+39*x^2+22*x+63', 'y^2=64*x^6+48*x^5+66*x^4+45*x^3+6*x^2+39*x+14', 'y^2=28*x^6+68*x^5+32*x^4+11*x^3+32*x^2+68*x+28'], 'dim1_distinct': 2, 'dim1_factors': 2, 'dim2_distinct': 0, 'dim2_factors': 0, 'dim3_distinct': 0, 'dim3_factors': 0, 'dim4_distinct': 0, 'dim4_factors': 0, 'dim5_distinct': 0, 'dim5_factors': 0, 'endomorphism_ring_count': 8, 'g': 2, 'galois_groups': ['2T1', '2T1'], 'geom_dim1_distinct': 2, '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': 4, 'geometric_extension_degree': 1, 'geometric_galois_groups': ['2T1', '2T1'], 'geometric_number_fields': ['2.0.88.1', '2.0.67.1'], 'geometric_splitting_field': '4.0.34762816.1', 'geometric_splitting_polynomials': [[47, -78, 79, -2, 1]], 'group_structure_count': 3, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 72, 'is_cyclic': False, 'is_geometrically_simple': False, 'is_geometrically_squarefree': True, 'is_primitive': True, 'is_simple': False, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 72, 'label': '2.71.as_hq', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 2, 'newton_coelevation': 2, 'newton_elevation': 0, 'noncyclic_primes': [2], 'number_fields': ['2.0.88.1', '2.0.67.1'], 'p': 71, 'p_rank': 2, 'p_rank_deficit': 0, 'poly': [1, -18, 198, -1278, 5041], 'poly_str': '1 -18 198 -1278 5041 ', 'primitive_models': [], 'q': 71, 'real_poly': [1, -18, 56], 'simple_distinct': ['1.71.ao', '1.71.ae'], 'simple_factors': ['1.71.aoA', '1.71.aeA'], 'simple_multiplicities': [1, 1], 'singular_primes': ['2,-5*F+1', '5,F^2+9*F+3*V+34'], 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '4.0.34762816.1', 'splitting_polynomials': [[47, -78, 79, -2, 1]], 'twist_count': 4, 'twists': [['2.71.ak_di', '2.5041.cu_ewc', 2], ['2.71.k_di', '2.5041.cu_ewc', 2], ['2.71.s_hq', '2.5041.cu_ewc', 2]], 'weak_equivalence_count': 10, 'zfv_index': 200, 'zfv_index_factorization': [[2, 3], [5, 2]], 'zfv_is_bass': False, 'zfv_is_maximal': False, 'zfv_plus_index': 1, 'zfv_plus_index_factorization': [], 'zfv_plus_norm': 23584, 'zfv_singular_count': 4, 'zfv_singular_primes': ['2,-5*F+1', '5,F^2+9*F+3*V+34']}
• av_fq_endalg_factors •

  Column	Type
  base_label	text
  extension_degree	smallint
  extension_label	text
  multiplicity	smallint

  
  
  • id: 76613
    {'base_label': '2.71.as_hq', 'extension_degree': 1, 'extension_label': '1.71.ao', 'multiplicity': 1}
  • id: 76614
    {'base_label': '2.71.as_hq', 'extension_degree': 1, 'extension_label': '1.71.ae', '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': '2.0.88.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.71.ao', 'galois_group': '2T1', 'places': [['64', '1'], ['7', '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': '2.0.67.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.71.ae', 'galois_group': '2T1', 'places': [['34', '1'], ['36', '1']]}