Abelian variety isogeny class data - 2.113.ax_kl

Formats: - HTML - YAML - JSON - 2025-10-10T05:57:58.620788

• 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': 10419, 'abvar_counts': [10419, 163192797, 2080127938059, 26577705720223269, 339451579345745554224, 4334525812170757661791941, 55347528905342236742029213107, 706732546909881673737458667591525, 9024267959184396094957059690979706211, 115230877658898161132037201996230476676352], 'abvar_counts_str': '10419 163192797 2080127938059 26577705720223269 339451579345745554224 4334525812170757661791941 55347528905342236742029213107 706732546909881673737458667591525 9024267959184396094957059690979706211 115230877658898161132037201996230476676352 ', 'all_polarized_product': False, 'all_unpolarized_product': False, 'angle_corank': 0, 'angle_rank': 2, 'angles': [0.0633394078667105, 0.467616104284846], 'center_dim': 4, 'cohen_macaulay_max': 1, 'curve_count': 91, 'curve_counts': [91, 12783, 1441633, 163006043, 18424071746, 2081953055223, 235260562662629, 26584441712023411, 3004041935992324639, 339456739026584323518], 'curve_counts_str': '91 12783 1441633 163006043 18424071746 2081953055223 235260562662629 26584441712023411 3004041935992324639 339456739026584323518 ', 'curves': ['y^2=83*x^6+40*x^5+69*x^4+86*x^3+62*x^2+83*x', 'y^2=74*x^6+56*x^5+109*x^4+112*x^3+14*x^2+76*x+92', 'y^2=30*x^6+68*x^5+42*x^4+72*x^3+5*x^2+93*x+29', 'y^2=56*x^6+21*x^5+49*x^4+67*x^3+86*x^2+52*x+92', 'y^2=108*x^6+8*x^5+76*x^4+10*x^3+33*x^2+23*x+84', 'y^2=100*x^6+34*x^5+63*x^4+98*x^3+52*x^2+98*x+58', 'y^2=71*x^6+73*x^5+34*x^4+109*x^3+3*x^2+81*x+82', 'y^2=24*x^6+70*x^5+3*x^4+46*x^3+104*x^2+9*x+73', 'y^2=14*x^6+61*x^5+49*x^4+8*x^3+15*x^2+108*x+12', 'y^2=16*x^6+112*x^5+99*x^4+101*x^3+4*x^2+105*x+108', 'y^2=14*x^6+69*x^5+110*x^4+6*x^3+53*x^2+92*x+61', 'y^2=99*x^6+31*x^5+96*x^4+19*x^3+35*x^2+27*x+35', 'y^2=4*x^6+81*x^5+73*x^4+83*x^3+85*x^2+39*x+109', 'y^2=58*x^6+15*x^5+69*x^4+18*x^3+21*x^2+21*x+90', 'y^2=65*x^6+98*x^5+91*x^4+71*x^3+76*x^2+52*x+70', 'y^2=13*x^6+19*x^5+72*x^4+73*x^3+26*x^2+9*x+37', 'y^2=83*x^6+44*x^5+76*x^4+110*x^3+101*x^2+11*x', 'y^2=7*x^6+57*x^5+70*x^4+9*x^3+6*x^2+99*x+66', 'y^2=93*x^6+86*x^5+83*x^4+62*x^3+10*x^2+41*x+75', 'y^2=x^6+17*x^5+89*x^4+2*x^3+19*x^2+56*x+96', 'y^2=71*x^6+80*x^5+33*x^4+105*x^3+30*x^2+98*x+72', 'y^2=103*x^6+31*x^5+95*x^4+21*x^3+111*x^2+83*x+28', 'y^2=110*x^6+63*x^5+101*x^4+56*x^3+11*x^2+28*x+109', 'y^2=20*x^6+46*x^5+104*x^4+22*x^3+90*x^2+55*x+111', 'y^2=78*x^6+24*x^5+15*x^4+60*x^3+92*x^2+51*x+21', 'y^2=17*x^6+61*x^5+103*x^4+46*x^3+58*x^2+59*x+82', 'y^2=5*x^6+63*x^5+14*x^4+103*x^3+15*x^2+15*x+77', 'y^2=93*x^6+18*x^5+91*x^4+x^3+15*x^2+8*x+48', 'y^2=107*x^6+41*x^5+10*x^4+39*x^3+4*x^2+18*x+35', 'y^2=31*x^6+24*x^5+78*x^4+76*x^3+6*x^2+83*x+14', 'y^2=85*x^6+90*x^5+2*x^4+46*x^3+4*x^2+104*x+53', 'y^2=10*x^6+53*x^5+59*x^4+22*x^3+49*x^2+107*x+80', 'y^2=2*x^6+54*x^5+106*x^4+95*x^3+93*x^2+101*x+12', 'y^2=27*x^6+51*x^5+50*x^4+88*x^3+31*x^2+104*x+13', 'y^2=75*x^6+101*x^5+51*x^4+62*x^3+63*x^2+37*x+105', 'y^2=53*x^6+16*x^5+73*x^4+4*x^2+106*x+27', 'y^2=29*x^6+103*x^5+15*x^4+36*x^3+93*x^2+81*x+75', 'y^2=40*x^6+9*x^5+32*x^4+68*x^3+18*x^2+89*x+81', 'y^2=47*x^6+73*x^5+30*x^4+84*x^3+30*x^2+61*x+99', 'y^2=90*x^6+22*x^5+62*x^4+35*x^3+71*x^2+7*x+22', 'y^2=111*x^6+88*x^5+69*x^4+23*x^3+58*x^2+110*x+37', 'y^2=34*x^6+109*x^5+53*x^4+x^3+71*x^2+81*x+50', 'y^2=35*x^6+69*x^5+55*x^4+95*x^2+105*x+51', 'y^2=21*x^6+27*x^5+103*x^4+64*x^3+7*x^2+95*x+43', 'y^2=71*x^6+32*x^5+47*x^4+18*x^3+22*x^2+67*x+15'], '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': 1, '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': ['4.0.962349701.1'], 'geometric_splitting_field': '4.0.962349701.1', 'geometric_splitting_polynomials': [[3259, 967, 73, -1, 1]], 'group_structure_count': 1, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 45, 'is_geometrically_simple': True, 'is_geometrically_squarefree': True, 'is_primitive': True, 'is_simple': True, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 45, 'label': '2.113.ax_kl', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 2, 'newton_coelevation': 2, 'newton_elevation': 0, 'number_fields': ['4.0.962349701.1'], 'p': 113, 'p_rank': 2, 'p_rank_deficit': 0, 'pic_prime_gens': [[1, 3, 1, 9], [1, 23, 1, 45]], 'poly': [1, -23, 271, -2599, 12769], 'poly_str': '1 -23 271 -2599 12769 ', 'primitive_models': [], 'principal_polarization_count': 45, 'q': 113, 'real_poly': [1, -23, 45], 'simple_distinct': ['2.113.ax_kl'], 'simple_factors': ['2.113.ax_klA'], 'simple_multiplicities': [1], 'singular_primes': [], 'size': 45, 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '4.0.962349701.1', 'splitting_polynomials': [[3259, 967, 73, -1, 1]], 'twist_count': 2, 'twists': [['2.113.x_kl', '2.12769.n_abelj', 2]], 'weak_equivalence_count': 1, 'zfv_index': 1, 'zfv_index_factorization': [], 'zfv_is_bass': True, 'zfv_is_maximal': True, 'zfv_pic_size': 45, 'zfv_plus_index': 1, 'zfv_plus_index_factorization': [], 'zfv_plus_norm': 7901, 'zfv_singular_count': 0, 'zfv_singular_primes': []}
• av_fq_endalg_factors •

  Column	Type
  base_label	text
  extension_degree	smallint
  extension_label	text
  multiplicity	smallint

  
  {'base_label': '2.113.ax_kl', 'extension_degree': 1, 'extension_label': '2.113.ax_kl', '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': '4.0.962349701.1', 'center_dim': 4, 'divalg_dim': 1, 'extension_label': '2.113.ax_kl', 'galois_group': '4T3', 'places': [['1585/113', '103/113', '5/113', '1/113'], ['107', '1', '0', '0']]}