Abelian variety isogeny class data - 2.53.aq_gk

Formats: - HTML - YAML - JSON - 2025-10-01T14:30:59.327353

• 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': 2112, 'abvar_counts': [2112, 8110080, 22362804288, 62309420236800, 174883181334430272, 491252316267439964160, 1379944569027551944093248, 3876269043125149150740480000, 10888439808640562344982220858432, 30585627266122935712037388205670400], 'abvar_counts_str': '2112 8110080 22362804288 62309420236800 174883181334430272 491252316267439964160 1379944569027551944093248 3876269043125149150740480000 10888439808640562344982220858432 30585627266122935712037388205670400 ', 'angle_corank': 0, 'angle_rank': 2, 'angles': [0.259013587977068, 0.364801829573176], 'center_dim': 4, 'cohen_macaulay_max': 3, 'curve_count': 38, 'curve_counts': [38, 2886, 150206, 7896782, 418185238, 22164063894, 1174709698606, 62259690299038, 3299763606002438, 174887470224134886], 'curve_counts_str': '38 2886 150206 7896782 418185238 22164063894 1174709698606 62259690299038 3299763606002438 174887470224134886 ', 'curves': ['y^2=14*x^6+x^5+46*x^4+23*x^3+42*x^2+36*x+50', 'y^2=52*x^6+22*x^5+18*x^4+8*x^3+14*x^2+12*x+6', 'y^2=5*x^6+52*x^5+28*x^3+8*x+44', 'y^2=21*x^6+11*x^5+24*x^4+31*x^3+15*x^2+25*x+22', 'y^2=52*x^6+46*x^4+43*x^3+20*x^2+x+5', 'y^2=39*x^6+6*x^5+18*x^4+32*x^3+2*x^2+4*x+50', 'y^2=49*x^6+45*x^5+27*x^4+12*x^3+27*x^2+45*x+49', 'y^2=25*x^6+9*x^5+49*x^4+24*x^3+37*x^2+38*x+10', 'y^2=22*x^6+34*x^5+x^4+17*x^3+36*x^2+21*x+34', 'y^2=34*x^6+24*x^5+46*x^4+49*x^3+46*x^2+24*x+34', 'y^2=34*x^6+15*x^5+23*x^4+20*x^3+30*x^2+15*x+19', 'y^2=32*x^6+11*x^5+31*x^4+19*x^3+23*x^2+6*x+33', 'y^2=27*x^6+6*x^5+44*x^4+28*x^3+44*x^2+6*x+27', 'y^2=32*x^6+32*x^5+31*x^4+24*x^3+31*x^2+32*x+32', 'y^2=45*x^6+42*x^5+5*x^4+39*x^3+5*x^2+42*x+45', 'y^2=49*x^5+34*x^4+32*x^3+34*x^2+49*x', 'y^2=5*x^6+48*x^5+45*x^4+7*x^3+35*x^2+31*x+23', 'y^2=18*x^6+28*x^5+41*x^4+8*x^3+41*x^2+28*x+18', 'y^2=45*x^6+6*x^5+43*x^4+24*x^3+40*x^2+37*x+40', 'y^2=28*x^6+21*x^5+9*x^4+40*x^3+24*x^2+8*x+52', 'y^2=51*x^6+52*x^5+50*x^4+7*x^3+50*x^2+52*x+51', 'y^2=40*x^6+2*x^5+33*x^4+28*x^3+33*x^2+2*x+40', 'y^2=22*x^6+41*x^5+51*x^4+49*x^3+8*x^2+20*x+23', 'y^2=19*x^6+48*x^5+31*x^4+40*x^3+52*x^2+31*x+33', 'y^2=39*x^6+8*x^5+3*x^4+7*x^3+3*x^2+8*x+39', 'y^2=21*x^6+20*x^5+40*x^4+9*x^3+31*x^2+40*x+30', 'y^2=26*x^6+33*x^5+45*x^4+16*x^3+5*x^2+22*x+51', 'y^2=41*x^6+17*x^5+3*x^4+27*x^3+3*x^2+17*x+41', 'y^2=42*x^6+30*x^5+37*x^4+18*x^3+37*x^2+30*x+42', 'y^2=32*x^6+3*x^5+33*x^4+x^3+33*x^2+3*x+32', 'y^2=35*x^6+16*x^5+19*x^4+34*x^3+8*x^2+46*x+34', 'y^2=50*x^6+10*x^5+22*x^4+24*x^3+22*x^2+10*x+50', 'y^2=34*x^6+33*x^4+7*x^3+8*x^2+26*x+30', 'y^2=27*x^6+18*x^5+9*x^4+43*x^3+9*x^2+18*x+27', 'y^2=20*x^6+20*x^5+7*x^4+42*x^3+37*x^2+45*x+41', 'y^2=45*x^6+12*x^5+19*x^4+24*x^3+19*x^2+12*x+45', 'y^2=33*x^6+52*x^5+22*x^4+26*x^3+22*x^2+52*x+33', 'y^2=50*x^6+34*x^5+47*x^4+28*x^3+47*x^2+34*x+50', 'y^2=41*x^6+7*x^5+17*x^4+35*x^3+17*x^2+7*x+41', 'y^2=32*x^6+12*x^5+9*x^4+7*x^3+49*x^2+22*x+23', 'y^2=20*x^6+48*x^5+50*x^4+25*x^3+50*x^2+48*x+20', 'y^2=19*x^6+11*x^5+9*x^4+46*x^3+7*x^2+51*x+37', 'y^2=5*x^6+10*x^4+4*x^3+20*x^2+9*x+5', 'y^2=6*x^6+32*x^5+46*x^4+6*x^3+17*x^2+11*x+6', 'y^2=34*x^6+25*x^5+24*x^4+12*x^3+24*x^2+25*x+34', 'y^2=24*x^6+6*x^5+10*x^4+7*x^3+4*x^2+37*x+38', 'y^2=15*x^6+48*x^5+16*x^4+9*x^3+52*x^2+30*x+52', 'y^2=21*x^6+24*x^5+51*x^4+30*x^3+32*x^2+4*x+38', 'y^2=3*x^6+47*x^5+28*x^4+29*x^3+35*x^2+30*x+19', 'y^2=32*x^6+42*x^5+11*x^4+36*x^3+15*x^2+47*x+33', 'y^2=2*x^6+52*x^5+22*x^4+11*x^3+22*x^2+52*x+2', 'y^2=45*x^6+35*x^5+51*x^4+23*x^3+51*x^2+35*x+45', 'y^2=3*x^6+8*x^5+37*x^4+32*x^3+37*x^2+8*x+3', 'y^2=2*x^6+23*x^5+39*x^4+33*x^3+39*x^2+23*x+2', 'y^2=16*x^6+22*x^5+33*x^4+21*x^3+33*x^2+22*x+16', 'y^2=35*x^5+36*x^4+15*x^3+10*x^2+31*x', 'y^2=35*x^6+41*x^5+2*x^4+51*x^3+2*x^2+41*x+35', 'y^2=10*x^6+26*x^4+32*x^3+26*x^2+10', 'y^2=50*x^6+23*x^5+46*x^4+47*x^3+6*x^2+48*x+23', 'y^2=23*x^6+6*x^5+24*x^4+6*x^2+7*x+31', 'y^2=32*x^6+41*x^5+20*x^4+37*x^3+20*x^2+41*x+32', 'y^2=26*x^6+48*x^5+16*x^4+43*x^3+16*x^2+48*x+26', 'y^2=14*x^6+26*x^5+31*x^4+49*x^3+22*x^2+26*x+39', 'y^2=22*x^6+21*x^5+36*x^4+43*x^3+x^2+22*x+12', 'y^2=28*x^6+36*x^5+46*x^4+44*x^3+46*x^2+36*x+28', 'y^2=24*x^6+48*x^5+44*x^4+8*x^3+44*x^2+48*x+24', 'y^2=23*x^6+46*x^5+43*x^4+21*x^3+29*x^2+x+31', 'y^2=39*x^6+6*x^5+41*x^4+14*x^3+41*x^2+6*x+39', 'y^2=51*x^6+21*x^5+42*x^4+21*x^3+43*x^2+34*x+20', 'y^2=17*x^6+3*x^5+32*x^3+48*x+28', 'y^2=10*x^6+29*x^5+51*x^4+28*x^3+21*x^2+4*x+44', 'y^2=9*x^6+34*x^5+35*x^4+39*x^3+35*x^2+34*x+9', 'y^2=12*x^6+10*x^5+6*x^4+4*x^3+6*x^2+10*x+12', 'y^2=22*x^6+30*x^5+4*x^4+43*x^3+4*x^2+30*x+22', 'y^2=14*x^6+11*x^5+52*x^4+47*x^3+4*x^2+17*x+5', 'y^2=36*x^6+47*x^5+44*x^4+9*x^3+23*x^2+18*x+33', 'y^2=49*x^6+20*x^5+33*x^4+11*x^3+33*x^2+20*x+49', 'y^2=28*x^6+41*x^5+21*x^4+46*x^3+29*x^2+52*x+40', 'y^2=45*x^6+14*x^5+12*x^4+24*x^3+20*x^2+33*x+14', 'y^2=30*x^6+52*x^5+21*x^4+20*x^3+40*x^2+48*x+31', 'y^2=5*x^6+10*x^5+51*x^4+13*x^3+23*x^2+7*x+24', 'y^2=x^6+31*x^5+14*x^4+45*x^3+14*x^2+31*x+1', 'y^2=31*x^6+19*x^5+12*x^4+31*x^3+x^2+23*x+34', 'y^2=7*x^6+44*x^5+28*x^4+35*x^3+13*x^2+13*x+38', 'y^2=45*x^6+47*x^5+45*x^4+x^3+14*x^2+28*x+23', 'y^2=46*x^6+11*x^5+47*x^4+8*x^3+49*x^2+31*x+32', 'y^2=42*x^5+29*x^4+6*x^3+15*x^2+28*x', 'y^2=8*x^6+14*x^5+50*x^4+48*x^3+5*x^2+33*x+14', 'y^2=19*x^6+32*x^5+30*x^4+39*x^3+12*x^2+3*x+8', 'y^2=34*x^6+13*x^5+51*x^4+44*x^3+44*x^2+24*x+11', 'y^2=41*x^6+10*x^5+4*x^4+24*x^3+5*x^2+39*x+23', 'y^2=33*x^6+7*x^5+52*x^4+45*x^3+52*x^2+7*x+33', 'y^2=22*x^6+13*x^5+46*x^4+28*x^3+4*x^2+27*x+24', 'y^2=48*x^6+37*x^5+8*x^4+23*x^3+19*x^2+7*x+14', 'y^2=46*x^6+44*x^5+45*x^4+38*x^3+45*x^2+44*x+46', 'y^2=39*x^6+25*x^5+3*x^4+43*x^3+3*x^2+25*x+39'], 'dim1_distinct': 2, '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, 'endomorphism_ring_count': 29, 'g': 2, 'galois_groups': ['2T1', '2T1'], 'geom_dim1_distinct': 2, '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': 4, 'geometric_extension_degree': 1, 'geometric_galois_groups': ['2T1', '2T1'], 'geometric_number_fields': ['2.0.7.1', '2.0.11.1'], 'geometric_splitting_field': '4.0.5929.1', 'geometric_splitting_polynomials': [[1, 0, 9, 0, 1]], 'group_structure_count': 9, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 96, 'is_geometrically_simple': False, 'is_geometrically_squarefree': True, 'is_primitive': True, 'is_simple': False, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 96, 'label': '2.53.aq_gk', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 2, 'newton_coelevation': 2, 'newton_elevation': 0, 'number_fields': ['2.0.7.1', '2.0.11.1'], 'p': 53, 'p_rank': 2, 'p_rank_deficit': 0, 'poly': [1, -16, 166, -848, 2809], 'poly_str': '1 -16 166 -848 2809 ', 'primitive_models': [], 'q': 53, 'real_poly': [1, -16, 60], 'simple_distinct': ['1.53.ak', '1.53.ag'], 'simple_factors': ['1.53.akA', '1.53.agA'], 'simple_multiplicities': [1, 1], 'singular_primes': ['2,15*F+9'], 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '4.0.5929.1', 'splitting_polynomials': [[1, 0, 9, 0, 1]], 'twist_count': 4, 'twists': [['2.53.ae_bu', '2.2809.cy_iyg', 2], ['2.53.e_bu', '2.2809.cy_iyg', 2], ['2.53.q_gk', '2.2809.cy_iyg', 2]], 'weak_equivalence_count': 57, 'zfv_index': 256, 'zfv_index_factorization': [[2, 8]], 'zfv_is_bass': False, 'zfv_is_maximal': False, 'zfv_plus_index': 1, 'zfv_plus_index_factorization': [], 'zfv_plus_norm': 19712, 'zfv_singular_count': 2, 'zfv_singular_primes': ['2,15*F+9']}
• av_fq_endalg_factors •

  Column	Type
  base_label	text
  extension_degree	smallint
  extension_label	text
  multiplicity	smallint

  
  
  • id: 46971
    {'base_label': '2.53.aq_gk', 'extension_degree': 1, 'extension_label': '1.53.ak', 'multiplicity': 1}
  • id: 46972
    {'base_label': '2.53.aq_gk', 'extension_degree': 1, 'extension_label': '1.53.ag', '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': '2.0.7.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.53.ak', 'galois_group': '2T1', 'places': [['38', '1'], ['14', '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': '2.0.11.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.53.ag', 'galois_group': '2T1', 'places': [['12', '1'], ['40', '1']]}