Abelian variety isogeny class data - 2.61.au_io

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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_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': 2704, 'abvar_counts': [2704, 14017536, 51898307344, 191900067840000, 713374923911023504, 2654324766268399051776, 9876810500678400133198864, 36751685911488957592535040000, 136753052995011561291989736156304, 508858111517299825401742886889071616], 'abvar_counts_str': '2704 14017536 51898307344 191900067840000 713374923911023504 2654324766268399051776 9876810500678400133198864 36751685911488957592535040000 136753052995011561291989736156304 508858111517299825401742886889071616 ', 'angle_corank': 1, 'angle_rank': 1, 'angles': [0.278857938376305, 0.278857938376305], 'center_dim': 2, 'curve_count': 42, 'curve_counts': [42, 3766, 228642, 13859758, 844634202, 51519904486, 3142735825362, 191707271553118, 11694146106042762, 713342914323062806], 'curve_counts_str': '42 3766 228642 13859758 844634202 51519904486 3142735825362 191707271553118 11694146106042762 713342914323062806 ', 'curves': ['y^2=6*x^6+58*x^5+35*x^3+58*x^2+7*x+21', 'y^2=32*x^6+23*x^5+46*x^4+39*x^3+13*x^2+33*x+35', 'y^2=16*x^6+20*x^5+45*x^4+24*x^3+39*x^2+34*x+13', 'y^2=28*x^6+41*x^5+18*x^4+28*x^3+18*x^2+41*x+28', 'y^2=47*x^6+25*x^4+25*x^2+47', 'y^2=52*x^6+53*x^4+53*x^2+52', 'y^2=24*x^6+10*x^4+10*x^2+24', 'y^2=59*x^6+18*x^4+18*x^2+59', 'y^2=51*x^6+24*x^5+3*x^4+49*x^3+15*x^2+51*x+31', 'y^2=17*x^6+45*x^4+45*x^2+17', 'y^2=43*x^6+22*x^5+5*x^4+18*x^3+31*x^2+18*x+18', 'y^2=7*x^6+29*x^5+5*x^4+8*x^3+x^2+28*x+43', 'y^2=14*x^6+33*x^5+42*x^4+3*x^3+51*x^2+34*x+16', 'y^2=2*x^6+38*x^3+54', 'y^2=40*x^6+24*x^5+27*x^4+11*x^3+25*x^2+2*x+43', 'y^2=27*x^6+39*x^5+19*x^4+32*x^3+19*x^2+39*x+27', 'y^2=32*x^6+32*x^5+55*x^4+8*x^3+50*x^2+28*x+18', 'y^2=39*x^6+32*x^5+9*x^4+12*x^3+60*x^2+26*x+13', 'y^2=17*x^6+53*x^5+36*x^4+38*x^3+36*x^2+53*x+17', 'y^2=2*x^6+2*x^3+43', 'y^2=48*x^6+41*x^5+49*x^4+2*x^3+25*x^2+3*x+15', 'y^2=43*x^6+2*x^5+4*x^4+x^3+57*x^2+51*x+21', 'y^2=23*x^6+15*x^4+15*x^2+23', 'y^2=46*x^6+33*x^5+58*x^4+17*x^3+25*x^2+10*x+55', 'y^2=41*x^6+27*x^5+21*x^4+12*x^3+12*x^2+14*x+46', 'y^2=6*x^6+56*x^5+47*x^4+54*x^3+34*x^2+34*x+59', 'y^2=2*x^6+2*x^3+6', 'y^2=38*x^6+38*x^5+42*x^4+11*x^3+42*x^2+38*x+38', 'y^2=23*x^6+28*x^5+11*x^4+10*x^3+11*x^2+28*x+23', 'y^2=21*x^6+5*x^5+55*x^4+26*x^3+32*x^2+27*x+54', 'y^2=3*x^6+40*x^5+2*x^4+50*x^3+55*x^2+55*x+41', 'y^2=2*x^6+8*x^3+6', 'y^2=2*x^6+28*x^3+59', 'y^2=51*x^6+27*x^5+35*x^4+21*x^3+51*x^2+52*x+31', 'y^2=18*x^6+42*x^5+15*x^4+9*x^3+57*x^2+x+18', 'y^2=20*x^6+15*x^5+16*x^4+50*x^3+46*x^2+22*x+3', 'y^2=33*x^6+26*x^5+23*x^4+4*x^3+37*x^2+32*x+38', 'y^2=35*x^6+4*x^5+15*x^4+34*x^3+9*x^2+60*x+10', 'y^2=28*x^6+26*x^5+25*x^4+15*x^3+49*x^2+30*x+53', 'y^2=46*x^6+55*x^5+6*x^4+45*x^3+6*x^2+55*x+46', 'y^2=2*x^6+35*x^3+59', 'y^2=17*x^6+37*x^5+38*x^4+25*x^3+55*x^2+31*x+44', 'y^2=18*x^6+46*x^5+38*x^4+3*x^3+54*x^2+52*x+7', 'y^2=32*x^6+34*x^5+11*x^4+50*x^3+24*x^2+58*x+17', 'y^2=33*x^6+55*x^5+13*x^4+39*x^3+41*x^2+13*x+21', 'y^2=26*x^5+48*x^4+39*x^3+14*x^2+2*x', 'y^2=59*x^6+53*x^5+16*x^4+46*x^3+57*x^2+30*x+21', 'y^2=38*x^6+2*x^5+60*x^4+12*x^3+12*x^2+44*x+33', 'y^2=32*x^6+17*x^5+48*x^4+18*x^3+9*x^2+28*x+35'], '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': ['2.0.4.1'], 'geometric_splitting_field': '2.0.4.1', 'geometric_splitting_polynomials': [[1, 0, 1]], 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 49, 'is_geometrically_simple': False, 'is_geometrically_squarefree': False, 'is_primitive': True, 'is_simple': False, 'is_squarefree': False, 'is_supersingular': False, 'jacobian_count': 49, 'label': '2.61.au_io', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 12, 'newton_coelevation': 2, 'newton_elevation': 0, 'number_fields': ['2.0.4.1'], 'p': 61, 'p_rank': 2, 'p_rank_deficit': 0, 'poly': [1, -20, 222, -1220, 3721], 'poly_str': '1 -20 222 -1220 3721 ', 'primitive_models': [], 'q': 61, 'real_poly': [1, -20, 100], 'simple_distinct': ['1.61.ak'], 'simple_factors': ['1.61.akA', '1.61.akB'], 'simple_multiplicities': [2], 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '2.0.4.1', 'splitting_polynomials': [[1, 0, 1]], 'twist_count': 16, 'twists': [['2.61.a_w', '2.3721.bs_lsw', 2], ['2.61.u_io', '2.3721.bs_lsw', 2], ['2.61.k_bn', '2.226981.clw_cnaqg', 3], ['2.61.ay_kg', '2.13845841.upg_gkocao', 4], ['2.61.aw_ji', '2.13845841.upg_gkocao', 4], ['2.61.ac_c', '2.13845841.upg_gkocao', 4], ['2.61.a_aw', '2.13845841.upg_gkocao', 4], ['2.61.c_c', '2.13845841.upg_gkocao', 4], ['2.61.w_ji', '2.13845841.upg_gkocao', 4], ['2.61.y_kg', '2.13845841.upg_gkocao', 4], ['2.61.ak_bn', '2.51520374361.abatce_tsgazlgg', 6], ['2.61.a_aeq', '2.191707312997281.admrzyi_ftsiajznsyw', 8], ['2.61.a_eq', '2.191707312997281.admrzyi_ftsiajznsyw', 8], ['2.61.am_df', '2.2654348974297586158321.lxttuvvw_enufrjizegwqykmg', 12], ['2.61.m_df', '2.2654348974297586158321.lxttuvvw_enufrjizegwqykmg', 12]]}
• av_fq_endalg_factors •

  Column	Type
  base_label	text
  extension_degree	smallint
  extension_label	text
  multiplicity	smallint

  
  {'base_label': '2.61.au_io', 'extension_degree': 1, 'extension_label': '1.61.ak', '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': '2.0.4.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.61.ak', 'galois_group': '2T1', 'places': [['50', '1'], ['11', '1']]}