Abelian variety isogeny class data - 2.67.au_ic

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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': 3340, 'abvar_counts': [3340, 20240400, 90633147820, 406038616320000, 1822791765092034700, 8182746825599686755600, 36732278470644346911921580, 164890987945168949218283520000, 740195518134665362540168603982860, 3322737658877873187586348094290410000], 'abvar_counts_str': '3340 20240400 90633147820 406038616320000 1822791765092034700 8182746825599686755600 36732278470644346911921580 164890987945168949218283520000 740195518134665362540168603982860 3322737658877873187586348094290410000 ', 'angle_corank': 0, 'angle_rank': 2, 'angles': [0.136004569043406, 0.399136977790122], 'center_dim': 4, 'cohen_macaulay_max': 1, 'curve_count': 48, 'curve_counts': [48, 4510, 301344, 20149678, 1350091008, 90458690830, 6060720400944, 406067749438558, 27206534553532368, 1822837803001863550], 'curve_counts_str': '48 4510 301344 20149678 1350091008 90458690830 6060720400944 406067749438558 27206534553532368 1822837803001863550 ', 'curves': ['y^2=28*x^6+16*x^5+48*x^4+39*x^3+15*x^2+47*x+51', 'y^2=30*x^6+40*x^5+49*x^4+x^3+38*x^2+39*x+6', 'y^2=5*x^6+19*x^5+55*x^4+60*x^3+24*x^2+11*x+33', 'y^2=38*x^6+43*x^5+9*x^4+61*x^3+11*x^2+64*x+19', 'y^2=56*x^6+30*x^5+65*x^4+39*x^3+31*x^2+39*x+28', 'y^2=51*x^6+50*x^5+30*x^4+32*x^3+49*x^2+33*x+17', 'y^2=5*x^6+37*x^5+56*x^4+12*x^3+12*x^2+54*x+40', 'y^2=60*x^6+25*x^5+65*x^4+53*x^3+39*x^2+16*x+5', 'y^2=51*x^6+51*x^5+23*x^4+41*x^3+66*x^2+33*x+31', 'y^2=57*x^6+21*x^5+3*x^3+19*x^2+37*x+31', 'y^2=57*x^6+14*x^5+28*x^4+64*x^3+30*x^2+3*x+33', 'y^2=49*x^6+28*x^5+46*x^4+22*x^3+62*x^2+47*x+60', 'y^2=26*x^6+45*x^5+39*x^4+5*x^3+31*x^2+18*x+45', 'y^2=34*x^6+9*x^5+7*x^4+21*x^3+15*x^2+60*x+3', 'y^2=9*x^6+8*x^5+62*x^4+13*x^3+36*x^2+36*x+30', 'y^2=30*x^6+x^5+36*x^4+7*x^3+28*x^2+8*x+19', 'y^2=11*x^6+28*x^5+14*x^4+18*x^3+32*x^2+28*x+48', 'y^2=28*x^6+10*x^5+7*x^4+66*x^3+31*x^2+36*x+41', 'y^2=9*x^6+65*x^5+8*x^4+40*x^3+49*x^2+32*x+42', 'y^2=37*x^6+21*x^5+5*x^4+46*x^3+29*x^2+29*x+50', 'y^2=42*x^6+6*x^5+7*x^4+13*x^3+25*x^2+31*x+53', 'y^2=45*x^6+22*x^5+7*x^4+36*x^3+65*x^2+42*x+58', 'y^2=42*x^6+17*x^5+5*x^4+16*x^3+51*x^2+64*x+52', 'y^2=38*x^6+2*x^5+26*x^4+47*x^3+13*x^2+55*x+25', 'y^2=14*x^6+64*x^5+20*x^4+44*x^3+31*x^2+63*x+62', 'y^2=46*x^6+55*x^5+23*x^4+35*x^3+46*x^2+44*x+27', 'y^2=45*x^6+45*x^5+62*x^4+40*x^3+x^2+36*x+24', 'y^2=2*x^6+3*x^5+20*x^4+26*x^3+52*x^2+42*x+38', 'y^2=11*x^6+58*x^5+24*x^4+38*x^3+28*x^2+50*x+66', 'y^2=27*x^6+31*x^5+49*x^4+9*x^3+45*x^2+44*x+9', 'y^2=10*x^6+66*x^5+26*x^4+62*x^3+43*x^2+47*x+34', 'y^2=19*x^6+27*x^5+57*x^4+64*x^3+6*x^2+10*x+31', 'y^2=20*x^6+60*x^5+4*x^4+50*x^3+23*x^2+27*x+52', 'y^2=42*x^6+17*x^5+x^4+64*x^3+35*x^2+21*x+15', 'y^2=4*x^6+64*x^5+4*x^4+25*x^3+16*x^2+27*x+28', 'y^2=55*x^6+43*x^5+40*x^4+25*x^3+22*x^2+52*x+54', 'y^2=40*x^6+33*x^5+36*x^4+12*x^3+2*x^2+22*x+61', 'y^2=28*x^6+21*x^5+58*x^4+66*x^3+59*x^2+2*x+30', 'y^2=66*x^6+36*x^5+5*x^4+59*x^3+55*x^2+66', 'y^2=45*x^6+41*x^5+56*x^4+31*x^3+49*x^2+20*x+41', 'y^2=34*x^6+48*x^5+50*x^4+4*x^3+34*x^2+42*x+21', 'y^2=7*x^6+60*x^5+47*x^4+21*x^3+20*x^2+57*x+31', 'y^2=23*x^6+33*x^5+26*x^4+31*x^3+48*x^2+11*x+15', 'y^2=19*x^6+41*x^5+25*x^4+34*x^3+42*x^2+53*x+18', 'y^2=34*x^6+x^5+17*x^4+48*x^3+32*x^2+59*x', 'y^2=53*x^6+11*x^5+22*x^4+62*x^3+11*x^2+15*x+63', 'y^2=19*x^6+26*x^5+60*x^4+9*x^3+29*x^2+61*x+45', 'y^2=35*x^6+41*x^5+29*x^4+64*x^3+16*x^2+55*x+44', 'y^2=63*x^6+3*x^5+53*x^4+6*x^3+3*x^2+24*x+51', 'y^2=61*x^6+17*x^5+x^4+63*x^3+41*x^2+18*x+5', 'y^2=12*x^6+48*x^5+4*x^4+20*x^3+52*x^2+39*x+29', 'y^2=3*x^6+2*x^5+24*x^4+41*x^3+41*x^2+14*x+10', 'y^2=41*x^6+43*x^5+34*x^4+51*x^3+56*x^2+52*x+15', 'y^2=3*x^6+18*x^5+29*x^4+51*x^3+4*x^2+35*x+24', 'y^2=20*x^6+59*x^5+16*x^4+45*x^3+47*x^2+39*x+25', 'y^2=58*x^6+58*x^5+30*x^4+58*x^3+3*x^2+61*x+39', 'y^2=31*x^6+31*x^5+22*x^4+33*x^3+40*x^2+53*x+37', 'y^2=16*x^6+5*x^5+32*x^4+4*x^3+30*x^2+7*x+35', 'y^2=53*x^6+9*x^5+30*x^4+59*x^3+31*x^2+55*x+37', 'y^2=32*x^6+5*x^5+61*x^4+25*x^2+5*x+46', 'y^2=26*x^6+61*x^5+7*x^4+44*x^3+31*x^2+51*x+57', 'y^2=61*x^6+25*x^5+60*x^4+36*x^3+57*x^2+17*x+57', 'y^2=5*x^6+2*x^5+61*x^4+6*x^3+7*x^2+58*x+64', 'y^2=45*x^6+5*x^5+49*x^4+30*x^3+66*x^2+51*x+43', 'y^2=30*x^6+15*x^5+17*x^4+47*x^3+64*x^2+48*x+7', 'y^2=8*x^6+12*x^5+15*x^4+48*x^3+44*x^2+62*x+61', 'y^2=57*x^6+27*x^5+13*x^4+44*x^3+14*x^2+52*x+39', 'y^2=50*x^6+40*x^5+22*x^4+7*x^3+12*x^2+13*x+31', 'y^2=47*x^6+2*x^5+51*x^4+36*x^3+40*x^2+13*x+54', 'y^2=16*x^6+18*x^5+50*x^4+60*x^3+44*x^2+13*x+27', 'y^2=66*x^6+33*x^5+54*x^4+34*x^3+56*x^2+6*x+10', 'y^2=31*x^6+29*x^5+22*x^4+18*x^3+60*x^2+51*x+46', 'y^2=23*x^6+56*x^5+62*x^4+45*x^3+52*x^2+32*x+41', 'y^2=12*x^6+5*x^5+22*x^4+8*x^3+40*x^2+65*x+1', 'y^2=20*x^6+24*x^5+49*x^4+38*x^3+51*x^2+10*x+37', 'y^2=66*x^6+40*x^5+38*x^4+28*x^3+x^2+40*x+44', 'y^2=46*x^5+49*x^4+15*x^3+25*x^2+19*x+11', 'y^2=56*x^6+56*x^5+42*x^4+57*x^3+23*x^2+6*x+18', 'y^2=57*x^6+17*x^4+52*x^3+52*x^2+40*x+1', 'y^2=28*x^6+20*x^5+24*x^4+2*x^3+47*x^2+33*x+37', 'y^2=13*x^6+22*x^5+40*x^4+61*x^3+29*x^2+x+50', 'y^2=48*x^6+11*x^5+14*x^4+59*x^3+10*x^2+19*x+63', 'y^2=63*x^6+21*x^5+34*x^4+27*x^3+30*x^2+2*x+42', 'y^2=52*x^6+30*x^5+35*x^4+26*x^3+51*x^2+35*x+44', 'y^2=62*x^6+10*x^5+63*x^4+2*x^3+6*x^2+8*x+28', 'y^2=x^6+11*x^5+13*x^4+21*x^3+20*x^2+34*x+59', 'y^2=56*x^6+12*x^5+36*x^4+14*x^3+52*x^2+31*x+3', 'y^2=43*x^6+31*x^5+37*x^4+19*x^3+62*x^2+12*x+18', 'y^2=11*x^6+23*x^5+49*x^4+57*x^3+64*x^2+4*x', 'y^2=51*x^6+45*x^5+26*x^4+28*x^3+22*x^2+33*x+53', 'y^2=x^6+32*x^5+5*x^4+38*x^3+46*x^2+52*x+58', 'y^2=47*x^6+53*x^5+61*x^4+11*x^3+51*x^2+5*x+52', 'y^2=61*x^6+63*x^5+57*x^4+41*x^3+54*x^2+10*x+61', 'y^2=44*x^6+60*x^5+12*x^4+58*x^3+19*x^2+55*x+58', 'y^2=5*x^6+28*x^5+20*x^4+34*x^3+25*x^2+38*x+16', 'y^2=47*x^6+17*x^5+46*x^4+42*x^3+31*x^2+29*x+31', 'y^2=63*x^6+13*x^5+17*x^4+19*x^2+55*x+14', 'y^2=50*x^6+11*x^5+27*x^4+49*x^3+12*x^2+45*x+32', 'y^2=26*x^6+x^5+51*x^4+11*x^3+25*x^2+11*x+66', 'y^2=60*x^6+37*x^5+46*x^4+21*x^3+32*x^2+40*x+18', 'y^2=34*x^6+37*x^5+18*x^4+44*x^3+46*x^2+54*x+27', 'y^2=59*x^6+13*x^5+62*x^4+47*x^3+5*x^2+7*x+46', 'y^2=46*x^6+59*x^5+54*x^4+8*x^3+4*x^2+47*x+37', 'y^2=13*x^6+61*x^5+2*x^4+27*x^3+2*x^2+15*x+62', 'y^2=63*x^6+32*x^5+6*x^4+62*x^3+25*x^2+61*x+65', 'y^2=66*x^6+43*x^5+19*x^4+53*x^3+36*x+50', 'y^2=55*x^6+63*x^5+64*x^4+11*x^3+8*x^2+57*x+51', 'y^2=51*x^6+26*x^5+51*x^4+49*x^3+19*x^2+3*x+32', 'y^2=22*x^6+55*x^5+17*x^4+12*x^3+53*x^2+9*x+53', 'y^2=41*x^6+57*x^5+61*x^4+36*x^3+66*x^2+43*x+16', 'y^2=12*x^6+18*x^5+58*x^4+37*x^3+10*x^2+43*x+8', 'y^2=36*x^6+8*x^5+8*x^4+26*x^3+5*x^2+17*x+46', 'y^2=27*x^6+21*x^5+52*x^4+x^3+42*x^2+52*x+4', 'y^2=53*x^6+43*x^5+5*x^4+17*x^3+60*x^2+49*x+45', 'y^2=48*x^5+21*x^4+60*x^3+9*x^2+57*x+57', 'y^2=5*x^6+66*x^5+29*x^4+41*x^3+46*x^2+40*x+3', 'y^2=45*x^6+8*x^5+50*x^4+28*x^3+7*x^2+32*x+19', 'y^2=66*x^6+41*x^5+46*x^4+43*x^3+43*x^2+55*x+2', 'y^2=58*x^6+39*x^5+58*x^4+13*x^3+6*x^2+66*x+66', 'y^2=44*x^6+37*x^5+25*x^4+9*x^3+16*x^2+14*x', 'y^2=46*x^6+44*x^5+62*x^4+61*x^3+7*x^2+8*x+45', 'y^2=50*x^6+62*x^5+31*x^4+26*x^3+50*x^2+36*x+25', 'y^2=32*x^6+31*x^5+7*x^4+16*x^3+32*x^2+34*x+56', 'y^2=52*x^6+18*x^5+66*x^4+52*x^3+54*x^2+50*x+45', 'y^2=43*x^6+24*x^5+48*x^4+24*x^3+51*x^2+59*x+35', 'y^2=63*x^6+41*x^5+42*x^4+35*x^3+64*x^2+9*x+37', 'y^2=55*x^6+17*x^5+43*x^4+12*x^3+32*x^2+32*x+32', 'y^2=38*x^6+34*x^5+6*x^4+27*x^3+66*x^2+48*x', 'y^2=53*x^6+57*x^5+57*x^4+23*x^3+3*x^2+37*x+32', 'y^2=61*x^6+32*x^5+29*x^4+32*x^3+57*x^2+24*x+14', 'y^2=62*x^6+19*x^5+57*x^4+42*x^3+6*x^2+43', 'y^2=31*x^6+39*x^5+18*x^4+4*x^3+43*x^2+59*x+9', 'y^2=51*x^6+3*x^5+42*x^4+28*x^3+27*x^2+2*x+24', 'y^2=27*x^6+7*x^5+21*x^4+57*x^3+33*x^2+35*x+18', 'y^2=63*x^6+16*x^5+63*x^4+40*x^3+31*x^2+33*x+54', 'y^2=36*x^6+42*x^4+50*x^3+59*x^2+49*x+35', 'y^2=40*x^6+58*x^5+21*x^4+57*x^3+42*x^2+3*x+4', 'y^2=32*x^6+66*x^5+40*x^4+19*x^3+56*x^2+31*x+18', 'y^2=52*x^6+45*x^5+35*x^4+31*x^3+43*x^2+49*x+48', 'y^2=60*x^6+44*x^5+60*x^4+3*x^2+14*x+58'], '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': 4, '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': ['4.0.1603584.2'], 'geometric_splitting_field': '4.0.1603584.2', 'geometric_splitting_polynomials': [[174, 0, 60, 0, 1]], 'group_structure_count': 2, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 140, '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': 140, 'label': '2.67.au_ic', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 2, 'newton_coelevation': 2, 'newton_elevation': 0, 'noncyclic_primes': [2], 'number_fields': ['4.0.1603584.2'], 'p': 67, 'p_rank': 2, 'p_rank_deficit': 0, 'poly': [1, -20, 210, -1340, 4489], 'poly_str': '1 -20 210 -1340 4489 ', 'primitive_models': [], 'q': 67, 'real_poly': [1, -20, 76], 'simple_distinct': ['2.67.au_ic'], 'simple_factors': ['2.67.au_icA'], 'simple_multiplicities': [1], 'singular_primes': ['2,F^2+F-2'], 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '4.0.1603584.2', 'splitting_polynomials': [[174, 0, 60, 0, 1]], 'twist_count': 2, 'twists': [['2.67.u_ic', '2.4489.u_auc', 2]], 'weak_equivalence_count': 4, 'zfv_index': 8, 'zfv_index_factorization': [[2, 3]], 'zfv_is_bass': True, 'zfv_is_maximal': False, 'zfv_plus_index': 2, 'zfv_plus_index_factorization': [[2, 1]], 'zfv_plus_norm': 11136, 'zfv_singular_count': 2, 'zfv_singular_primes': ['2,F^2+F-2']}
• av_fq_endalg_factors •

  Column	Type
  base_label	text
  extension_degree	smallint
  extension_label	text
  multiplicity	smallint

  
  {'base_label': '2.67.au_ic', 'extension_degree': 1, 'extension_label': '2.67.au_ic', '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': '4.0.1603584.2', 'center_dim': 4, 'divalg_dim': 1, 'extension_label': '2.67.au_ic', 'galois_group': '4T3', 'places': [['32', '1', '0', '0'], ['51', '1', '0', '0'], ['35', '1', '0', '0'], ['16', '1', '0', '0']]}