Abelian variety isogeny class data - 2.37.aq_fi

Formats: - HTML - YAML - JSON - 2025-11-10T12:46:00.074754

• 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': 900, 'abvar_counts': [900, 1904400, 2604060900, 3522378240000, 4809582006322500, 6582746395262595600, 9011949910299512820900, 12337489359044385546240000, 16890052776273987134543856900, 23122484502999502322011284810000], 'abvar_counts_str': '900 1904400 2604060900 3522378240000 4809582006322500 6582746395262595600 9011949910299512820900 12337489359044385546240000 16890052776273987134543856900 23122484502999502322011284810000 ', 'angle_corank': 1, 'angle_rank': 1, 'angles': [0.271573428245867, 0.271573428245867], 'center_dim': 2, 'curve_count': 22, 'curve_counts': [22, 1390, 51406, 1879438, 69358342, 2565646270, 94930703806, 3512473032478, 129961731836662, 4808584546343950], 'curve_counts_str': '22 1390 51406 1879438 69358342 2565646270 94930703806 3512473032478 129961731836662 4808584546343950 ', 'curves': ['y^2=27*x^6+26*x^5+20*x^4+8*x^3+20*x^2+26*x+27', 'y^2=6*x^6+19*x^5+5*x^4+17*x^3+35*x^2+6*x+23', 'y^2=19*x^6+27*x^5+29*x^4+12*x^3+29*x^2+27*x+19', 'y^2=36*x^6+19*x^5+22*x^4+22*x^3+22*x^2+19*x+36', 'y^2=19*x^6+24*x^4+24*x^2+19', 'y^2=28*x^6+11*x^5+15*x^4+13*x^3+15*x^2+11*x+28', 'y^2=24*x^6+29*x^5+27*x^4+3*x^3+9*x^2+32*x+5', 'y^2=17*x^6+5*x^4+5*x^2+17', 'y^2=x^6+4*x^3+27', 'y^2=11*x^6+25*x^5+18*x^4+2*x^3+18*x^2+25*x+11', 'y^2=27*x^6+3*x^5+25*x^4+23*x^3+11*x+2', 'y^2=23*x^6+5*x^5+21*x^4+28*x^3+22*x^2+4*x+14', 'y^2=23*x^6+7*x^5+6*x^4+6*x^3+24*x^2+x+29', 'y^2=36*x^6+10*x^5+10*x^4+30*x^3+10*x^2+10*x+36', 'y^2=23*x^6+17*x^5+24*x^4+23*x^3+4*x^2+35*x+22', 'y^2=6*x^6+7*x^5+5*x^4+19*x^3+5*x^2+7*x+6', 'y^2=x^6+9*x^3+26', 'y^2=15*x^6+35*x^5+31*x^4+15*x^3+30*x^2+36*x+15'], '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': ['2.0.84.1'], 'geometric_splitting_field': '2.0.84.1', 'geometric_splitting_polynomials': [[21, 0, 1]], 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 18, 'is_geometrically_simple': False, 'is_geometrically_squarefree': False, 'is_primitive': True, 'is_simple': False, 'is_squarefree': False, 'is_supersingular': False, 'jacobian_count': 18, 'label': '2.37.aq_fi', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 6, 'newton_coelevation': 2, 'newton_elevation': 0, 'number_fields': ['2.0.84.1'], 'p': 37, 'p_rank': 2, 'p_rank_deficit': 0, 'poly': [1, -16, 138, -592, 1369], 'poly_str': '1 -16 138 -592 1369 ', 'primitive_models': [], 'q': 37, 'real_poly': [1, -16, 64], 'simple_distinct': ['1.37.ai'], 'simple_factors': ['1.37.aiA', '1.37.aiB'], 'simple_multiplicities': [2], 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '2.0.84.1', 'splitting_polynomials': [[21, 0, 1]], 'twist_count': 6, 'twists': [['2.37.a_k', '2.1369.u_efe', 2], ['2.37.q_fi', '2.1369.u_efe', 2], ['2.37.i_bb', '2.50653.bcy_nuzy', 3], ['2.37.a_ak', '2.1874161.huy_xlfhu', 4], ['2.37.ai_bb', '2.2565726409.aeooi_vvasbso', 6]]}
• av_fq_endalg_factors •

  Column	Type
  base_label	text
  extension_degree	smallint
  extension_label	text
  multiplicity	smallint

  
  {'base_label': '2.37.aq_fi', 'extension_degree': 1, 'extension_label': '1.37.ai', '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': '2.0.84.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.37.ai', 'galois_group': '2T1', 'places': [['33', '1'], ['4', '1']]}