Abelian variety isogeny class data - 3.13.ac_t_aci

Formats: - HTML - YAML - JSON - 2025-12-07T08:44:36.389441

• 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': 2064, 'abvar_counts': [2064, 5911296, 10256422608, 23358036885504, 51517536226654224, 112526636764696978176, 247061223911595416446416, 542778217027900696534450176, 1192502589562592095745484489744, 2619994503993061021314778113006336], 'abvar_counts_str': '2064 5911296 10256422608 23358036885504 51517536226654224 112526636764696978176 247061223911595416446416 542778217027900696534450176 1192502589562592095745484489744 2619994503993061021314778113006336 ', 'angle_corank': 0, 'angle_rank': 3, 'angles': [0.207502090325433, 0.518616831924189, 0.651841336648398], 'center_dim': 6, 'curve_count': 12, 'curve_counts': [12, 204, 2124, 28636, 373692, 4829868, 62747676, 815696828, 10604226348, 137858431884], 'curve_counts_str': '12 204 2124 28636 373692 4829868 62747676 815696828 10604226348 137858431884 ', 'curves': ['y^2=2*x^7+6*x^6+8*x^5+2*x^4+4*x^3+5*x+8', 'y^2=2*x^8+5*x^7+5*x^6+2*x^5+11*x^4+8*x^3+x^2+11*x+7', 'y^2=2*x^7+10*x^6+2*x^5+5*x^4+9*x^3+4*x^2+10*x+4', 'y^2=x^7+12*x^5+6*x^4+3*x^2+7*x+11', 'y^2=2*x^8+6*x^7+2*x^6+5*x^5+5*x^4+12*x^3+12*x^2+8*x+12', 'y^2=2*x^7+10*x^6+2*x^5+8*x^4+x^3+8*x^2+5*x+10', 'y^2=2*x^8+8*x^7+5*x^6+10*x^5+5*x^4+12*x^3+8*x^2+6*x+4', 'y^2=2*x^7+5*x^6+2*x^5+7*x^4+8*x^3+9*x^2+8', 'y^2=x^8+3*x^6+x^5+6*x^4+x^3+8*x^2+4*x', 'y^2=2*x^8+x^7+7*x^6+7*x^5+7*x^4+10*x^3+x^2+11*x+2', 'y^2=x^8+6*x^7+12*x^6+8*x^5+7*x^4+10*x^2+8*x+7', 'y^2=2*x^8+8*x^7+x^6+5*x^5+10*x^4+x^2+4*x+8', 'y^2=2*x^8+4*x^7+2*x^6+9*x^5+9*x^4+x^2+2*x+2', 'y^2=x^8+10*x^7+10*x^5+7*x^4+6*x^3+11*x^2+11*x+9', 'y^2=x^8+11*x^7+4*x^6+4*x^5+9*x^4+9*x^3+10*x^2+x+8', 'y^2=x^8+7*x^7+3*x^5+9*x^4+4*x^2+6*x+4', 'y^2=2*x^8+2*x^7+7*x^6+3*x^5+12*x^4+9*x^3+6*x^2+4*x+9', 'y^2=2*x^8+10*x^7+10*x^6+7*x^4+4*x^3+10*x^2+12*x+3', 'y^2=x^8+x^7+5*x^6+11*x^5+6*x^4+x^3+x^2+x+5', 'y^2=x^8+x^6+3*x^5+11*x^4+3*x^3+7*x^2+12*x+2', 'y^2=2*x^8+12*x^6+10*x^5+6*x^4+10*x^3+2*x^2+x+4', 'y^2=x^8+x^7+8*x^6+4*x^4+3*x^3+8*x^2+9*x+11', 'y^2=x^8+2*x^7+6*x^6+6*x^5+5*x^4+12*x^3+3*x^2+3*x+10', 'y^2=x^8+x^7+2*x^6+10*x^5+7*x^4+12*x^3+7*x^2+4*x+4', 'y^2=x^8+x^7+12*x^6+4*x^3+5*x^2+7*x+2', 'y^2=2*x^8+2*x^7+9*x^6+6*x^5+4*x^4+8*x^3+8*x^2+9*x+7', 'y^2=x^8+x^7+6*x^6+11*x^5+2*x^4+5*x^3+7*x^2+6*x+9', 'y^2=x^8+9*x^7+6*x^6+9*x^5+x^4+4*x^3+8*x^2+11*x+2', 'y^2=2*x^8+x^7+8*x^6+12*x^5+11*x^4+8*x^3+3', 'y^2=x^7+6*x^5+6*x^4+7*x^2+4*x', 'y^2=2*x^8+9*x^7+9*x^6+2*x^5+7*x^4+5*x^3+6*x^2+9*x+3', 'y^2=2*x^8+6*x^7+9*x^6+5*x^5+4*x^4+12*x^3+11*x^2+x+6', 'y^2=2*x^8+7*x^7+3*x^6+x^5+12*x^4+x^3+6*x+7', 'y^2=2*x^8+4*x^7+6*x^6+7*x^5+8*x^4+10*x^3+8*x^2+6*x+1', 'y^2=2*x^8+7*x^7+8*x^6+3*x^5+9*x^4+7*x^3+12*x^2+10*x+1', 'y^2=2*x^8+8*x^7+5*x^6+3*x^5+5*x^4+9*x^3+9*x^2+8*x+2', 'y^2=x^8+6*x^5+4*x^4+5*x^2+3*x+6', 'y^2=2*x^8+7*x^7+8*x^6+10*x^5+5*x^4+3*x^3+x^2+10*x+1', 'y^2=2*x^8+4*x^7+2*x^6+12*x^5+10*x^3+9*x^2+11*x+10', 'y^2=2*x^8+6*x^7+7*x^6+6*x^5+3*x^4+7*x^3+3*x+2', 'y^2=2*x^8+8*x^7+x^6+11*x^5+5*x^4+6*x^3+6*x^2+x+12', 'y^2=2*x^8+10*x^7+9*x^6+7*x^5+3*x^4+3*x^3+7*x^2+2*x+7', 'y^2=x^8+7*x^7+3*x^6+10*x^5+8*x^3+8*x^2+6*x+11', 'y^2=x^8+x^7+6*x^6+10*x^5+6*x^4+6*x^2+10*x+7', 'y^2=2*x^8+2*x^7+5*x^6+4*x^5+4*x^4+11*x^3+6*x^2+2*x+8', 'y^2=x^8+6*x^7+11*x^6+12*x^5+6*x^4+4*x^3+8*x^2+7', 'y^2=2*x^8+10*x^7+5*x^6+x^5+4*x^4+7*x^3+4*x^2+8*x+4', 'y^2=2*x^8+10*x^7+10*x^6+10*x^5+8*x^4+3*x^3+9*x^2+6*x+12', 'y^2=x^8+7*x^7+9*x^6+9*x^5+4*x^4+10*x^3+6*x^2+2*x+11', 'y^2=x^8+4*x^7+7*x^6+x^5+8*x^4+7*x^3+2*x^2+7*x+8', 'y^2=2*x^8+4*x^7+5*x^6+5*x^4+8*x^3+9*x^2+6', 'y^2=2*x^8+9*x^7+2*x^6+8*x^5+10*x^4+12*x^3+7*x^2+10*x+6', 'y^2=2*x^8+6*x^6+x^5+3*x^4+9*x^2+2*x+12', 'y^2=2*x^8+5*x^7+x^6+3*x^5+x^4+4*x^3+9*x^2+5*x+10', 'y^2=2*x^8+2*x^5+12*x^4+x^3+7*x+11', 'y^2=x^7+2*x^6+12*x^5+12*x^4+6*x^3+6*x^2+5*x', 'y^2=x^8+10*x^7+9*x^6+10*x^5+x^4+9*x^3+5*x+12', 'y^2=x^8+9*x^7+2*x^6+x^5+4*x^4+7*x^2+2*x+3', 'y^2=2*x^8+9*x^7+4*x^6+x^5+7*x^4+8*x^3+7*x^2+12*x+11', 'y^2=x^8+5*x^7+7*x^5+10*x^2+4*x+10', 'y^2=2*x^8+5*x^7+10*x^6+12*x^5+11*x^4+4*x^3+10*x^2+7*x+2', 'y^2=2*x^8+4*x^6+10*x^5+8*x^4+9*x^3+4*x+7', 'y^2=2*x^8+6*x^7+8*x^6+4*x^5+2*x^4+9*x^3+3*x^2+10*x+9', 'y^2=2*x^8+9*x^7+11*x^6+10*x^5+6*x^2+5*x+2', 'y^2=2*x^8+11*x^7+11*x^6+3*x^5+11*x^4+8*x^3+3*x^2+8*x+4', 'y^2=2*x^8+2*x^7+7*x^6+11*x^5+2*x^4+7*x^3+10*x^2+6*x+6', 'y^2=x^8+9*x^7+12*x^6+6*x^5+10*x^4+5*x^3+4*x^2+8*x+8', 'y^2=2*x^8+3*x^7+10*x^6+3*x^5+4*x^4+3*x^3+9*x^2+5*x+9', 'y^2=x^8+12*x^7+9*x^6+11*x^5+x^4+6*x^3+11*x^2+x+2', 'y^2=2*x^8+10*x^7+2*x^6+3*x^5+10*x^3+5*x^2+6*x+12', 'y^2=2*x^8+12*x^7+4*x^6+12*x^5+8*x^4+11*x^3+4*x^2+8*x+5', 'y^2=2*x^8+9*x^7+11*x^6+10*x^5+5*x^4+3*x^3+4*x^2+8*x+7', 'y^2=2*x^8+4*x^7+4*x^6+3*x^5+12*x^4+10*x^3+7*x^2+9*x+2', 'y^2=2*x^8+9*x^7+11*x^6+6*x^4+6*x^3+5*x^2+10*x+11', 'y^2=2*x^8+4*x^7+x^6+3*x^5+5*x^4+7*x^3+9*x^2+11*x+11', 'y^2=2*x^8+7*x^7+8*x^6+12*x^4+x^3+6*x^2+5*x+10', 'y^2=2*x^8+6*x^7+7*x^6+3*x^5+11*x^4+8*x^3+11*x^2+12*x+7', 'y^2=x^8+2*x^7+7*x^6+2*x^5+10*x^4+x^2+9*x+8', 'y^2=x^8+6*x^7+11*x^6+6*x^5+2*x^4+3*x^3+4*x^2+10*x+1', 'y^2=x^8+9*x^7+12*x^6+2*x^5+6*x^4+8*x^3+4*x^2+9*x+7', 'y^2=2*x^8+11*x^7+2*x^6+8*x^5+10*x^4+6*x^3+9*x^2+3*x+10', 'y^2=2*x^8+4*x^7+4*x^6+4*x^5+11*x^4+2*x^3+x^2+7*x+11', 'y^2=2*x^8+5*x^7+12*x^6+12*x^5+4*x^4+7*x^3+5*x^2+11*x+9', 'y^2=2*x^8+11*x^7+11*x^6+5*x^5+x^4+12*x^3+2*x^2+3*x+12', 'y^2=2*x^8+5*x^7+10*x^6+6*x^5+6*x^4+7*x^3+x^2+9*x+12', 'y^2=2*x^8+5*x^7+7*x^6+8*x^5+10*x^4+3*x^2+x+12', 'y^2=x^8+12*x^7+10*x^5+4*x^3+4*x^2+x+11', 'y^2=2*x^8+5*x^7+3*x^6+6*x^5+3*x^4+4*x^3+x^2+12*x+10', 'y^2=x^8+8*x^7+4*x^6+10*x^5+2*x^4+11*x^3+11*x^2+x+7', 'y^2=2*x^8+5*x^7+x^6+2*x^5+11*x^4+2*x^3+2*x^2+5*x+7', 'y^2=2*x^8+4*x^7+7*x^6+2*x^5+3*x^4+12*x^3+12*x^2+4*x+9', 'y^2=2*x^8+8*x^7+x^6+5*x^4+8*x^3+10*x^2+8*x+8', 'y^2=2*x^8+3*x^7+2*x^6+5*x^5+6*x^4+x^3+4*x^2+12*x+2', 'y^2=x^8+2*x^7+2*x^6+3*x^5+4*x^4+7*x^3+3*x+10', 'y^2=x^8+3*x^7+6*x^6+7*x^5+2*x^4+11*x^3+8*x^2+4*x+11', 'y^2=2*x^8+5*x^7+11*x^6+3*x^5+3*x^4+x^3+10*x^2+3*x+11', 'y^2=x^8+8*x^7+2*x^6+12*x^5+4*x^4+12*x^3+5*x^2+8*x+8', 'y^2=2*x^8+6*x^7+2*x^6+11*x^5+12*x^4+8*x^3+4*x^2+3*x+9', 'y^2=x^8+11*x^7+3*x^6+3*x^5+10*x^4+12*x^3+2*x+2', 'y^2=2*x^8+10*x^7+8*x^6+6*x^5+9*x^4+8*x^3+5*x^2+11*x+4', 'y^2=2*x^8+10*x^6+8*x^5+3*x^4+5*x^3+11*x^2+12*x+4', 'y^2=2*x^8+2*x^7+7*x^6+9*x^5+4*x^4+12*x^3+5*x^2+7*x+10', 'y^2=2*x^8+9*x^7+7*x^6+6*x^5+11*x^4+x^3+6*x^2+5*x+6', 'y^2=2*x^8+11*x^7+12*x^6+6*x^4+10*x^3+6*x^2+7*x+8', 'y^2=2*x^8+8*x^7+7*x^6+2*x^5+3*x^4+5*x^2+4*x+5', 'y^2=x^8+x^7+8*x^6+9*x^5+6*x^4+7*x^3+3*x^2+x+9', 'y^2=x^8+2*x^7+12*x^6+10*x^5+x^4+8*x^3+10*x^2+x+9', 'y^2=x^8+7*x^7+4*x^6+11*x^5+6*x^4+7*x^3+10*x^2+6*x+3', 'y^2=x^8+12*x^7+4*x^5+3*x^4+6*x^2+2*x+4', 'y^2=x^8+7*x^7+3*x^6+7*x^5+6*x^4+8*x^3+3*x^2+8*x+2', 'y^2=x^8+12*x^7+11*x^5+4*x^4+10*x^3+5*x^2+7*x+10', 'y^2=2*x^8+x^7+3*x^6+4*x^5+11*x^4+6*x^3+12*x^2+5*x+4', 'y^2=2*x^8+12*x^7+8*x^6+4*x^5+x^4+10*x^3+4*x^2+3', 'y^2=2*x^8+2*x^7+6*x^5+10*x^4+5*x^3+11*x^2+2*x+12', 'y^2=2*x^8+10*x^7+6*x^6+2*x^5+2*x^3+2*x^2+9*x+4', 'y^2=2*x^8+3*x^7+5*x^6+8*x^5+11*x^4+11*x^3+2*x^2+4*x+9', 'y^2=2*x^8+2*x^6+12*x^5+5*x^4+11*x^3+4*x^2+x+10', 'y^2=2*x^8+x^7+2*x^5+6*x^4+x^3+5*x^2+6*x+2', 'y^2=2*x^8+3*x^7+4*x^6+8*x^5+6*x^4+3*x^3+2*x^2+5*x+9', 'y^2=x^8+5*x^6+4*x^5+4*x^4+9*x^3+5*x^2+4*x+8', 'y^2=x^8+2*x^6+11*x^5+4*x^4+9*x^3+8*x^2+9*x+3', 'y^2=2*x^8+9*x^7+6*x^6+5*x^5+x^4+8*x^2+6*x+12', 'y^2=x^8+8*x^7+5*x^6+7*x^5+10*x^4+11*x^2+11*x+11', 'y^2=x^8+2*x^6+9*x^5+9*x^4+x^3+6*x^2+7*x+2', 'y^2=2*x^8+9*x^7+11*x^6+5*x^5+8*x^4+5*x^3+2*x^2+4*x+7', 'y^2=x^8+11*x^7+8*x^6+2*x^5+9*x^4+10*x^2+5', 'y^2=2*x^8+12*x^7+2*x^6+8*x^5+4*x^4+3*x^3+5*x^2+6', 'y^2=2*x^8+9*x^7+4*x^6+x^5+4*x^4+10*x^3+6*x^2+12*x+6', 'y^2=x^8+8*x^7+4*x^6+8*x^5+8*x^4+6*x^3+12*x^2+6*x+10', 'y^2=2*x^8+12*x^7+3*x^5+9*x^4+9*x^3+2*x^2+11*x+10', 'y^2=x^8+6*x^7+5*x^6+11*x^5+11*x^4+6*x^3+3*x^2+6', 'y^2=2*x^8+12*x^7+8*x^5+10*x^3+x^2+12*x+12', 'y^2=x^8+7*x^7+3*x^6+x^5+8*x^4+3*x^3+7', 'y^2=2*x^8+x^7+10*x^6+x^5+12*x^4+11*x^3+3*x^2+5*x+9', 'y^2=x^8+2*x^7+9*x^6+6*x^5+2*x^4+9*x^3+3*x^2+4*x+9', 'y^2=x^8+10*x^7+10*x^6+9*x^5+9*x^4+7*x^3+11*x^2+7*x+9', 'y^2=x^8+5*x^7+12*x^6+11*x^5+2*x^4+3*x^3+2*x^2+2*x+3', 'y^2=2*x^8+11*x^7+2*x^6+6*x^5+7*x^4+2*x^3+x^2+5'], 'dim1_distinct': 0, 'dim1_factors': 0, 'dim2_distinct': 0, 'dim2_factors': 0, 'dim3_distinct': 1, 'dim3_factors': 1, 'dim4_distinct': 0, 'dim4_factors': 0, 'dim5_distinct': 0, 'dim5_factors': 0, 'g': 3, 'galois_groups': ['6T11'], 'geom_dim1_distinct': 0, 'geom_dim1_factors': 0, 'geom_dim2_distinct': 0, 'geom_dim2_factors': 0, 'geom_dim3_distinct': 1, 'geom_dim3_factors': 1, 'geom_dim4_distinct': 0, 'geom_dim4_factors': 0, 'geom_dim5_distinct': 0, 'geom_dim5_factors': 0, 'geometric_center_dim': 6, 'geometric_extension_degree': 1, 'geometric_galois_groups': ['6T11'], 'geometric_number_fields': ['6.0.25951344.1'], 'geometric_splitting_field': '6.0.25951344.1', 'geometric_splitting_polynomials': [[29, 12, 21, -2, 5, -2, 1]], 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 138, 'is_cyclic': False, 'is_geometrically_simple': True, 'is_geometrically_squarefree': True, 'is_primitive': True, 'is_simple': True, 'is_squarefree': True, 'is_supersingular': False, 'label': '3.13.ac_t_aci', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 2, 'newton_coelevation': 4, 'newton_elevation': 0, 'noncyclic_primes': [2], 'number_fields': ['6.0.25951344.1'], 'p': 13, 'p_rank': 3, 'p_rank_deficit': 0, 'poly': [1, -2, 19, -60, 247, -338, 2197], 'poly_str': '1 -2 19 -60 247 -338 2197 ', 'primitive_models': [], 'q': 13, 'real_poly': [1, -2, -20, -8], 'simple_distinct': ['3.13.ac_t_aci'], 'simple_factors': ['3.13.ac_t_aciA'], 'simple_multiplicities': [1], 'slopes': ['0A', '0B', '0C', '1A', '1B', '1C'], 'splitting_field': '6.0.25951344.1', 'splitting_polynomials': [[29, 12, 21, -2, 5, -2, 1]], 'twist_count': 2, 'twists': [['3.13.c_t_ci', '3.169.bi_xr_nbo', 2]]}
• av_fq_endalg_factors •

  Column	Type
  base_label	text
  extension_degree	smallint
  extension_label	text
  multiplicity	smallint

  
  {'base_label': '3.13.ac_t_aci', 'extension_degree': 1, 'extension_label': '3.13.ac_t_aci', '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': '6.0.25951344.1', 'center_dim': 6, 'divalg_dim': 1, 'extension_label': '3.13.ac_t_aci', 'galois_group': '6T11', 'places': [['9', '6', '2', '3', '0', '0'], ['1', '12', '6', '1', '0', '0']]}