Abelian variety isogeny class data - 2.59.b_acg

Formats: - HTML - YAML - JSON - 2026-02-18T02:34:12.210237

• 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': 3484, 'abvar_counts': [3484, 11720176, 42253269136, 146911984233664, 511128985948200724, 1779229457282983403776, 6193382755330598920150084, 21559180493130496612713517824, 75047494769657936416648080892816, 261240334923417143944286448352433776], 'abvar_counts_str': '3484 11720176 42253269136 146911984233664 511128985948200724 1779229457282983403776 6193382755330598920150084 21559180493130496612713517824 75047494769657936416648080892816 261240334923417143944286448352433776 ', 'angle_corank': 1, 'angle_rank': 1, 'angles': [0.1874015362731, 0.854068202939767], 'center_dim': 4, 'cohen_macaulay_max': 1, 'curve_count': 61, 'curve_counts': [61, 3365, 205732, 12124089, 714941411, 42181293206, 2488650095489, 146830458622129, 8662995612678268, 511116752163579125], 'curve_counts_str': '61 3365 205732 12124089 714941411 42181293206 2488650095489 146830458622129 8662995612678268 511116752163579125 ', 'curves': ['y^2=55*x^6+13*x^5+4*x^4+41*x^3+26*x^2+31*x+30', 'y^2=11*x^6+36*x^5+32*x^4+11*x^3+4*x^2+51*x+3', 'y^2=34*x^6+25*x^5+49*x^4+49*x^3+16*x^2+14*x+12', 'y^2=51*x^6+8*x^5+46*x^4+42*x^3+26*x^2+55*x+18', 'y^2=11*x^6+12*x^5+8*x^4+x^3+49*x^2+38*x+38', 'y^2=18*x^6+52*x^5+55*x^4+42*x^3+41*x^2+30*x+16', 'y^2=14*x^6+14*x^5+20*x^4+28*x^3+x^2+42*x+25', 'y^2=58*x^6+x^5+3*x^4+53*x^3+51*x^2+24*x+46', 'y^2=36*x^6+19*x^5+57*x^4+29*x^3+14*x^2+24*x+47', 'y^2=9*x^6+30*x^5+39*x^4+5*x^3+35*x^2+55*x+13', 'y^2=21*x^6+31*x^5+55*x^4+32*x^3+5*x^2+3*x+54', 'y^2=16*x^6+48*x^5+9*x^4+5*x^3+12*x^2+55*x+40', 'y^2=14*x^6+57*x^5+43*x^4+22*x^3+56*x^2+36*x+24', 'y^2=52*x^6+13*x^5+48*x^4+48*x^3+26*x^2+33*x+46', 'y^2=47*x^6+35*x^5+46*x^4+16*x^3+10*x^2+17*x+35', 'y^2=55*x^6+29*x^5+12*x^4+11*x^3+53*x^2+15*x+13', 'y^2=52*x^6+58*x^4+18*x^3+11*x^2+24*x+20', 'y^2=10*x^5+7*x^4+50*x^3+57*x^2+19*x+34', 'y^2=58*x^6+36*x^5+28*x^4+14*x^3+30*x^2+22*x+34', 'y^2=49*x^6+50*x^5+28*x^4+53*x^3+12*x^2+21*x+54', 'y^2=53*x^6+47*x^5+19*x^4+35*x^3+13*x^2+3*x+45', 'y^2=56*x^6+42*x^5+52*x^4+17*x^3+35*x^2+11*x+29'], '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': 4, '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': 3, 'geometric_galois_groups': ['2T1'], 'geometric_number_fields': ['2.0.235.1'], 'geometric_splitting_field': '2.0.235.1', 'geometric_splitting_polynomials': [[59, -1, 1]], 'group_structure_count': 2, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 22, 'is_cyclic': False, 'is_geometrically_simple': False, 'is_geometrically_squarefree': False, 'is_primitive': True, 'is_simple': True, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 22, 'label': '2.59.b_acg', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 12, 'newton_coelevation': 2, 'newton_elevation': 0, 'noncyclic_primes': [2], 'number_fields': ['4.0.497025.3'], 'p': 59, 'p_rank': 2, 'p_rank_deficit': 0, 'poly': [1, 1, -58, 59, 3481], 'poly_str': '1 1 -58 59 3481 ', 'primitive_models': [], 'q': 59, 'real_poly': [1, 1, -176], 'simple_distinct': ['2.59.b_acg'], 'simple_factors': ['2.59.b_acgA'], 'simple_multiplicities': [1], 'singular_primes': ['2,64*F-67*V-69', '29,-9*F-6*V+14'], 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '4.0.497025.3', 'splitting_polynomials': [[3481, -59, -58, -1, 1]], 'twist_count': 6, 'twists': [['2.59.ab_acg', '2.3481.aen_pcq', 2], ['2.59.ac_ep', '2.205379.no_zdlu', 3], ['2.59.a_en', '2.42180533641.brfqa_bclzvcpfy', 6], ['2.59.c_ep', '2.42180533641.brfqa_bclzvcpfy', 6], ['2.59.a_aen', '2.1779197418239532716881.aoxqniroe_egszrfwueeiuweqg', 12]], 'weak_equivalence_count': 4, 'zfv_index': 58, 'zfv_index_factorization': [[2, 1], [29, 1]], 'zfv_is_bass': True, 'zfv_is_maximal': False, 'zfv_plus_index': 1, 'zfv_plus_index_factorization': [], 'zfv_plus_norm': 3364, 'zfv_singular_count': 4, 'zfv_singular_primes': ['2,64*F-67*V-69', '29,-9*F-6*V+14']}
• av_fq_endalg_factors •

  Column	Type
  base_label	text
  extension_degree	smallint
  extension_label	text
  multiplicity	smallint

  
  
  • id: 49132
    {'base_label': '2.59.b_acg', 'extension_degree': 1, 'extension_label': '2.59.b_acg', 'multiplicity': 1}
  • id: 49133
    {'base_label': '2.59.b_acg', 'extension_degree': 3, 'extension_label': '1.205379.gu', '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': '4.0.497025.3', 'center_dim': 4, 'divalg_dim': 1, 'extension_label': '2.59.b_acg', 'galois_group': '4T2', 'places': [['0', '3364/59', '58/59', '1/59'], ['0', '1', '0', '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': '2.0.235.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.205379.gu', 'galois_group': '2T1', 'places': [['0', '1'], ['58', '1']]}