Abelian variety isogeny class data - 2.31.a_abu

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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': 916, 'abvar_counts': [916, 839056, 887538964, 852534595584, 819628336307476, 787725412618193296, 756943935197782027156, 727426208204485983535104, 699053619998995019546996884, 671790609678160980574413490576], 'abvar_counts_str': '916 839056 887538964 852534595584 819628336307476 787725412618193296 756943935197782027156 727426208204485983535104 699053619998995019546996884 671790609678160980574413490576 ', 'all_polarized_product': False, 'all_unpolarized_product': False, 'angle_corank': 1, 'angle_rank': 1, 'angles': [0.116954024640961, 0.883045975359039], 'center_dim': 4, 'cohen_macaulay_max': 1, 'curve_count': 32, 'curve_counts': [32, 870, 29792, 923134, 28629152, 887574246, 27512614112, 852894656254, 26439622160672, 819628385634150], 'curve_counts_str': '32 870 29792 923134 28629152 887574246 27512614112 852894656254 26439622160672 819628385634150 ', 'curves': ['y^2=16*x^6+17*x^5+11*x^4+22*x^2+25*x+4', 'y^2=3*x^6+5*x^5+17*x^4+22*x^3+18*x^2+7*x+7', 'y^2=5*x^6+11*x^5+25*x^4+21*x^3+22*x^2+17*x+13', 'y^2=9*x^6+24*x^5+23*x^4+7*x^3+8*x^2+24*x+22', 'y^2=13*x^6+23*x^5+22*x^4+22*x^3+20*x^2+29*x+10', 'y^2=9*x^6+25*x^5+7*x^4+22*x^3+15*x^2+26*x+22', 'y^2=27*x^6+13*x^5+21*x^4+4*x^3+14*x^2+16*x+4', 'y^2=30*x^6+13*x^5+30*x^4+22*x^3+25*x^2+3*x+1', 'y^2=24*x^6+5*x^5+23*x^4+29*x^3+5*x^2+x+15', 'y^2=28*x^6+14*x^5+21*x^4+5*x^3+9*x^2+23*x+24', 'y^2=21*x^6+12*x^5+17*x^4+13*x^2+8*x+13', 'y^2=28*x^6+26*x^5+12*x^4+24*x^3+7*x^2+11*x+24', 'y^2=x^6+30*x^5+23*x^4+18*x^3+25*x^2+13*x+29', 'y^2=15*x^6+23*x^5+23*x^4+12*x^2+18*x+23', 'y^2=10*x^6+29*x^5+19*x^4+20*x^3+17*x^2+28*x+7', 'y^2=30*x^6+25*x^5+26*x^4+29*x^3+20*x^2+22*x+21', 'y^2=19*x^6+2*x^5+x^4+29*x^3+30*x^2+10*x+6', 'y^2=26*x^6+6*x^5+3*x^4+25*x^3+28*x^2+30*x+18', 'y^2=12*x^5+17*x^4+28*x^3+4*x^2+13*x', 'y^2=24*x^6+7*x^5+15*x^4+20*x^3+11*x^2+21*x+18', 'y^2=10*x^6+21*x^5+14*x^4+29*x^3+2*x^2+x+23', 'y^2=28*x^6+22*x^5+26*x^4+20*x^2+11*x+6', 'y^2=12*x^6+3*x^5+27*x^3+6*x+25', 'y^2=16*x^6+30*x^5+27*x^4+18*x^3+21*x^2+5*x+2', 'y^2=15*x^6+23*x^5+23*x^4+15*x^3+8*x^2+23*x+16', 'y^2=5*x^6+28*x^5+8*x^4+3*x^3+19*x^2+2*x+28', 'y^2=15*x^6+22*x^5+24*x^4+9*x^3+26*x^2+6*x+22', 'y^2=9*x^5+2*x^4+9*x^3+15*x^2+18*x', 'y^2=x^6+x^5+4*x^4+16*x^3+8*x^2+20*x+30', 'y^2=17*x^6+6*x^5+22*x^4+26*x^3+14*x^2+6*x+23', 'y^2=20*x^6+18*x^5+4*x^4+16*x^3+11*x^2+18*x+7', 'y^2=19*x^6+23*x^5+30*x^4+9*x^3+4*x^2+27*x+24', 'y^2=7*x^6+23*x^5+26*x^4+28*x^3+2*x^2+26*x+6', 'y^2=x^6+9*x^5+24*x^4+19*x^3+20*x^2+14*x+30', 'y^2=x^6+16*x^5+14*x^4+26*x^3+17*x^2+16*x+30', 'y^2=8*x^6+9*x^5+27*x^4+14*x^3+9*x^2+22*x+26', 'y^2=24*x^6+27*x^5+19*x^4+11*x^3+27*x^2+4*x+16', 'y^2=20*x^6+6*x^5+23*x^4+27*x^3+25*x^2+x+15', 'y^2=12*x^6+23*x^5+29*x^4+2*x^3+24*x^2+29*x+27', 'y^2=5*x^6+7*x^5+25*x^4+6*x^3+10*x^2+25*x+19'], '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': 14, 'g': 2, 'galois_groups': ['4T2'], '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': 2, 'geometric_galois_groups': ['2T1'], 'geometric_number_fields': ['2.0.3.1'], 'geometric_splitting_field': '2.0.3.1', 'geometric_splitting_polynomials': [[1, -1, 1]], 'group_structure_count': 2, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 40, 'is_geometrically_simple': False, 'is_geometrically_squarefree': False, 'is_primitive': True, 'is_simple': True, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 40, 'label': '2.31.a_abu', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 12, 'newton_coelevation': 2, 'newton_elevation': 0, 'number_fields': ['4.0.144.1'], 'p': 31, 'p_rank': 2, 'p_rank_deficit': 0, 'pic_prime_gens': [[1, 13, 1, 12]], 'poly': [1, 0, -46, 0, 961], 'poly_str': '1 0 -46 0 961 ', 'primitive_models': [], 'principal_polarization_count': 58, 'q': 31, 'real_poly': [1, 0, -108], 'simple_distinct': ['2.31.a_abu'], 'simple_factors': ['2.31.a_abuA'], 'simple_multiplicities': [1], 'singular_primes': ['2,F+1', '3,5*F^2+3*F+5'], 'size': 46, 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '4.0.144.1', 'splitting_polynomials': [[1, 0, -1, 0, 1]], 'twist_count': 24, 'twists': [['2.31.a_an', '2.29791.a_cafa', 3], ['2.31.a_ch', '2.29791.a_cafa', 3], ['2.31.ai_da', '2.923521.aoy_edfzq', 4], ['2.31.a_bu', '2.923521.aoy_edfzq', 4], ['2.31.i_da', '2.923521.aoy_edfzq', 4], ['2.31.aw_hb', '2.787662783788549761.dlgkxbw_tluogrckpisug', 12], ['2.31.as_fj', '2.787662783788549761.dlgkxbw_tluogrckpisug', 12], ['2.31.ap_ec', '2.787662783788549761.dlgkxbw_tluogrckpisug', 12], ['2.31.ao_eh', '2.787662783788549761.dlgkxbw_tluogrckpisug', 12], ['2.31.al_dm', '2.787662783788549761.dlgkxbw_tluogrckpisug', 12], ['2.31.ah_s', '2.787662783788549761.dlgkxbw_tluogrckpisug', 12], ['2.31.ae_ap', '2.787662783788549761.dlgkxbw_tluogrckpisug', 12], ['2.31.ad_bi', '2.787662783788549761.dlgkxbw_tluogrckpisug', 12], ['2.31.a_ach', '2.787662783788549761.dlgkxbw_tluogrckpisug', 12], ['2.31.a_n', '2.787662783788549761.dlgkxbw_tluogrckpisug', 12], ['2.31.d_bi', '2.787662783788549761.dlgkxbw_tluogrckpisug', 12], ['2.31.e_ap', '2.787662783788549761.dlgkxbw_tluogrckpisug', 12], ['2.31.h_s', '2.787662783788549761.dlgkxbw_tluogrckpisug', 12], ['2.31.l_dm', '2.787662783788549761.dlgkxbw_tluogrckpisug', 12], ['2.31.o_eh', '2.787662783788549761.dlgkxbw_tluogrckpisug', 12], ['2.31.p_ec', '2.787662783788549761.dlgkxbw_tluogrckpisug', 12], ['2.31.s_fj', '2.787662783788549761.dlgkxbw_tluogrckpisug', 12], ['2.31.w_hb', '2.787662783788549761.dlgkxbw_tluogrckpisug', 12]], 'weak_equivalence_count': 14, 'zfv_index': 576, 'zfv_index_factorization': [[2, 6], [3, 2]], 'zfv_is_bass': True, 'zfv_is_maximal': False, 'zfv_pic_size': 12, 'zfv_plus_index': 6, 'zfv_plus_index_factorization': [[2, 1], [3, 1]], 'zfv_plus_norm': 256, 'zfv_singular_count': 4, 'zfv_singular_primes': ['2,F+1', '3,5*F^2+3*F+5']}
• av_fq_endalg_factors •

  Column	Type
  base_label	text
  extension_degree	smallint
  extension_label	text
  multiplicity	smallint

  
  
  • id: 20660
    {'base_label': '2.31.a_abu', 'extension_degree': 1, 'extension_label': '2.31.a_abu', 'multiplicity': 1}
  • id: 20661
    {'base_label': '2.31.a_abu', 'extension_degree': 2, 'extension_label': '1.961.abu', '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': '4.0.144.1', 'center_dim': 4, 'divalg_dim': 1, 'extension_label': '2.31.a_abu', 'galois_group': '4T2', 'places': [['25', '0', '1', '0'], ['5', '0', '1', '0']]}
• 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': '2.0.3.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.961.abu', 'galois_group': '2T1', 'places': [['5', '1'], ['25', '1']]}