Abelian variety isogeny class data - 2.71.ae_fq

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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': 4900, 'abvar_counts': [4900, 26832400, 128400388900, 645298183398400, 3255071787033062500, 16409821370804658000400, 82721291859332926649308900, 416997585024556984828382822400, 2102084983671193986608116607092900, 10596610585131803999459186359710250000], 'abvar_counts_str': '4900 26832400 128400388900 645298183398400 3255071787033062500 16409821370804658000400 82721291859332926649308900 416997585024556984828382822400 2102084983671193986608116607092900 10596610585131803999459186359710250000 ', 'angle_corank': 1, 'angle_rank': 1, 'angles': [0.462134322676343, 0.462134322676343], 'center_dim': 2, 'curve_count': 68, 'curve_counts': [68, 5318, 358748, 25393758, 1804134148, 128101366118, 9095129082268, 645753472257598, 45848499966877508, 3255243553694897798], 'curve_counts_str': '68 5318 358748 25393758 1804134148 128101366118 9095129082268 645753472257598 45848499966877508 3255243553694897798 ', 'curves': ['y^2=52*x^6+50*x^5+48*x^4+29*x^3+57*x^2+40*x+21', 'y^2=9*x^6+15*x^5+33*x^4+20*x^3+50*x^2+28*x+44', 'y^2=11*x^6+32*x^5+11*x^4+39*x^3+57*x^2+52*x+36', 'y^2=22*x^6+51*x^5+70*x^4+40*x^3+15*x^2+65*x+62', 'y^2=53*x^6+31*x^5+9*x^4+56*x^3+64*x^2+39*x+63', 'y^2=25*x^6+45*x^5+9*x^4+44*x^3+29*x^2+57*x+10', 'y^2=20*x^6+4*x^5+36*x^4+63*x^3+69*x^2+6*x+70', 'y^2=14*x^6+38*x^5+23*x^4+60*x^3+4*x^2+13*x+35', 'y^2=54*x^6+43*x^5+37*x^4+40*x^3+56*x^2+42*x+9', 'y^2=64*x^6+13*x^5+41*x^4+13*x^3+10*x^2+14*x+64', 'y^2=52*x^6+40*x^5+55*x^4+40*x^3+55*x^2+40*x+52', 'y^2=21*x^6+43*x^5+33*x^4+70*x^3+37*x^2+9', 'y^2=64*x^6+64*x^5+66*x^4+62*x^3+66*x^2+64*x+64', 'y^2=57*x^6+9*x^5+63*x^4+65*x^3+49*x^2+41*x+50', 'y^2=48*x^6+31*x^5+64*x^4+9*x^3+53*x^2+35*x+36', 'y^2=31*x^6+59*x^5+68*x^4+17*x^3+14*x^2+16*x+24', 'y^2=69*x^6+14*x^5+31*x^4+37*x^3+67*x^2+47*x+47', 'y^2=26*x^6+20*x^5+5*x^4+12*x^3+21*x^2+58*x+32', 'y^2=24*x^6+18*x^5+50*x^4+34*x^3+57*x^2+29*x+62', 'y^2=6*x^6+60*x^5+39*x^4+36*x^3+39*x^2+60*x+6', 'y^2=15*x^6+5*x^5+5*x^4+55*x^3+8*x^2+27*x+16', 'y^2=57*x^6+57*x^5+22*x^4+43*x^3+8*x^2+11*x+70', 'y^2=9*x^5+70*x^4+25*x^3+44*x^2+68*x+4', 'y^2=69*x^6+27*x^5+43*x^4+68*x^3+39*x^2+14*x+22', 'y^2=65*x^6+23*x^5+31*x^4+51*x^3+31*x^2+52*x+29', 'y^2=52*x^6+40*x^5+51*x^4+65*x^3+51*x^2+32*x+53', 'y^2=13*x^6+5*x^5+66*x^4+5*x^3+31*x^2+9*x+28', 'y^2=70*x^6+18*x^5+47*x^4+x^3+47*x^2+18*x+70', 'y^2=36*x^6+47*x^5+51*x^4+6*x^3+61*x+26', 'y^2=35*x^6+50*x^5+7*x^4+54*x^3+27*x^2+56*x+64', 'y^2=27*x^6+23*x^5+63*x^4+42*x^3+47*x^2+65*x+19', 'y^2=50*x^6+68*x^5+44*x^4+62*x^3+58*x^2+46*x+51', 'y^2=4*x^6+12*x^5+19*x^4+59*x^3+13*x^2+35*x+55', 'y^2=30*x^6+48*x^4+48*x^2+30', 'y^2=12*x^6+67*x^5+55*x^4+70*x^3+64*x^2+4*x+66', 'y^2=45*x^6+38*x^5+70*x^4+62*x^3+35*x^2+2*x+54', 'y^2=48*x^6+35*x^5+17*x^4+66*x^3+47*x^2+47*x+5', 'y^2=24*x^6+7*x^4+7*x^2+24', 'y^2=46*x^6+51*x^5+35*x^4+39*x^3+33*x^2+37*x+59', 'y^2=3*x^6+60*x^5+29*x^4+53*x^3+29*x^2+60*x+3', 'y^2=69*x^6+47*x^5+5*x^4+59*x^3+5*x^2+64*x+46', 'y^2=62*x^6+7*x^5+44*x^4+42*x^2+23*x+48', 'y^2=58*x^6+28*x^5+x^4+6*x^3+45*x^2+42*x+10', 'y^2=21*x^6+66*x^5+12*x^4+56*x^3+10*x^2+45*x+30', 'y^2=38*x^6+41*x^5+26*x^4+10*x^3+9*x^2+42*x+65', 'y^2=34*x^6+18*x^5+62*x^3+40*x^2+53*x+68', 'y^2=52*x^6+32*x^5+52*x^4+27*x^3+52*x^2+32*x+52', 'y^2=55*x^6+60*x^5+37*x^4+41*x^3+39*x^2+50*x+52', 'y^2=46*x^6+23*x^5+57*x^4+43*x^3+50*x^2+51*x+56', 'y^2=9*x^6+70*x^5+46*x^4+10*x^3+54*x^2+63*x+37'], 'dim1_distinct': 1, '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, 'g': 2, 'galois_groups': ['2T1'], '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': 1, 'geometric_galois_groups': ['2T1'], 'geometric_number_fields': ['2.0.280.1'], 'geometric_splitting_field': '2.0.280.1', 'geometric_splitting_polynomials': [[70, 0, 1]], 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 50, 'is_cyclic': False, 'is_geometrically_simple': False, 'is_geometrically_squarefree': False, 'is_primitive': True, 'is_simple': False, 'is_squarefree': False, 'is_supersingular': False, 'jacobian_count': 50, 'label': '2.71.ae_fq', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 6, 'newton_coelevation': 2, 'newton_elevation': 0, 'noncyclic_primes': [2, 5, 7], 'number_fields': ['2.0.280.1'], 'p': 71, 'p_rank': 2, 'p_rank_deficit': 0, 'poly': [1, -4, 146, -284, 5041], 'poly_str': '1 -4 146 -284 5041 ', 'primitive_models': [], 'q': 71, 'real_poly': [1, -4, 4], 'simple_distinct': ['1.71.ac'], 'simple_factors': ['1.71.acA', '1.71.acB'], 'simple_multiplicities': [2], 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '2.0.280.1', 'splitting_polynomials': [[70, 0, 1]], 'twist_count': 6, 'twists': [['2.71.a_fi', '2.5041.kq_brcg', 2], ['2.71.e_fq', '2.5041.kq_brcg', 2], ['2.71.c_acp', '2.357911.bge_byrju', 3], ['2.71.a_afi', '2.25411681.abank_lazjhe', 4], ['2.71.ac_acp', '2.128100283921.cjowy_cqjdsxifm', 6]]}
• av_fq_endalg_factors •

  Column	Type
  base_label	text
  extension_degree	smallint
  extension_label	text
  multiplicity	smallint

  
  {'base_label': '2.71.ae_fq', 'extension_degree': 1, 'extension_label': '1.71.ac', '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': '2.0.280.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.71.ac', 'galois_group': '2T1', 'places': [['70', '1'], ['1', '1']]}