Abelian variety isogeny class data - 2.89.ac_gx

Formats: - HTML - YAML - JSON - 2026-03-03T04:54:55.676503

• 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': 7921, 'abvar_counts': [7921, 65593801, 497357815696, 3934645792830025, 31181282587963643521, 246991734664847897460736, 1956411413429676648257041681, 15496730524781210518679078966025, 122749609237833855425420593490209936, 972299658391693040706424956173155779241], 'abvar_counts_str': '7921 65593801 497357815696 3934645792830025 31181282587963643521 246991734664847897460736 1956411413429676648257041681 15496730524781210518679078966025 122749609237833855425420593490209936 972299658391693040706424956173155779241 ', 'angle_corank': 1, 'angle_rank': 1, 'angles': [0.483121701649934, 0.483121701649934], 'center_dim': 2, 'curve_count': 88, 'curve_counts': [88, 8276, 705502, 62711268, 5583981128, 496983969326, 44231344544552, 3936588576976708, 350356402619996878, 31181719949235253556], 'curve_counts_str': '88 8276 705502 62711268 5583981128 496983969326 44231344544552 3936588576976708 350356402619996878 31181719949235253556 ', 'curves': ['y^2=67*x^6+66*x^5+35*x^4+53*x^3+45*x^2+55*x+47', 'y^2=20*x^6+39*x^5+66*x^4+51*x^3+12*x^2+80*x+58', 'y^2=43*x^6+27*x^5+47*x^4+69*x^3+53*x^2+71*x+83', 'y^2=65*x^6+65*x^5+3*x^4+41*x^3+85*x^2+45*x+51', 'y^2=36*x^6+78*x^5+8*x^4+5*x^3+69*x^2+87*x+16', 'y^2=59*x^6+82*x^5+34*x^4+12*x^3+10*x^2+78*x+1', 'y^2=4*x^6+7*x^5+44*x^4+33*x^3+10*x^2+41*x+40', 'y^2=4*x^6+70*x^5+44*x^4+68*x^3+54*x^2+60*x+38', 'y^2=63*x^6+64*x^5+82*x^4+2*x^3+62*x^2+44*x+28', 'y^2=35*x^6+15*x^5+19*x^4+72*x^3+73*x^2+77', 'y^2=35*x^6+23*x^5+2*x^4+23*x^3+28*x^2+53*x+19', 'y^2=66*x^6+25*x^5+34*x^4+9*x^3+50*x^2+67*x+35', 'y^2=41*x^6+81*x^5+35*x^4+62*x^3+75*x^2+45*x+70', 'y^2=17*x^6+38*x^5+37*x^4+9*x^3+62*x^2+19*x+84', 'y^2=54*x^6+80*x^5+52*x^4+20*x^3+17*x^2+30*x+54', 'y^2=59*x^6+18*x^5+67*x^4+26*x^3+65*x^2+4*x+75', 'y^2=62*x^6+67*x^5+42*x^4+45*x^3+64*x^2+25*x+56', 'y^2=4*x^6+62*x^5+30*x^4+72*x^3+77*x^2+54*x+84', 'y^2=79*x^6+56*x^5+61*x^4+59*x^3+66*x^2+6*x+72', 'y^2=87*x^6+86*x^5+42*x^4+72*x^3+11*x^2+6*x+18', 'y^2=64*x^6+10*x^5+40*x^4+23*x^3+88*x^2+84*x+72', 'y^2=16*x^6+87*x^5+x^4+68*x^3+19*x^2+60*x+29', 'y^2=18*x^6+2*x^5+18*x^4+31*x^3+16*x^2+73*x+50', 'y^2=84*x^6+17*x^5+11*x^4+57*x^3+3*x+59', 'y^2=32*x^6+10*x^5+78*x^4+4*x^3+9*x^2+11*x+43', 'y^2=51*x^6+61*x^5+67*x^4+6*x^3+23*x^2+64*x+10', 'y^2=37*x^6+31*x^5+42*x^4+69*x^3+55*x^2+4*x+75', 'y^2=54*x^6+36*x^5+68*x^4+88*x^3+38*x^2+41*x+26', 'y^2=59*x^6+58*x^5+44*x^4+5*x^3+88*x^2+54*x+27', 'y^2=51*x^6+76*x^5+21*x^4+21*x^3+47*x^2+73*x+32', 'y^2=47*x^6+76*x^5+44*x^4+73*x^3+84*x^2+24*x+49', 'y^2=45*x^6+73*x^5+38*x^4+75*x^3+83*x^2+63*x+70', 'y^2=37*x^6+22*x^5+33*x^4+46*x^3+62*x^2+39*x+46', 'y^2=15*x^6+20*x^5+18*x^4+27*x^3+15*x^2+23*x+6', 'y^2=86*x^6+47*x^5+30*x^4+25*x^3+56*x^2+25*x+21', 'y^2=37*x^6+11*x^5+86*x^4+38*x^3+12*x^2+36*x+23', 'y^2=56*x^6+31*x^5+40*x^4+x^3+64*x^2+45*x+70', 'y^2=24*x^6+35*x^5+81*x^4+3*x^3+24*x^2+18*x+78', 'y^2=24*x^6+52*x^5+67*x^4+33*x^3+2*x^2+5*x+52', 'y^2=40*x^6+30*x^5+71*x^4+18*x^3+29*x^2+5*x+79', 'y^2=57*x^6+26*x^5+88*x^4+52*x^3+64*x^2+77*x+67', 'y^2=27*x^6+40*x^5+28*x^4+67*x^3+9*x^2+34*x+70', 'y^2=44*x^6+67*x^5+13*x^4+2*x^3+13*x^2+67*x+44', 'y^2=12*x^6+70*x^5+58*x^4+32*x^3+36*x^2+59*x+54', 'y^2=35*x^6+35*x^5+50*x^4+87*x^3+88*x^2+19*x+43', 'y^2=26*x^6+16*x^5+51*x^4+74*x^3+74*x^2+2*x+37', 'y^2=39*x^6+10*x^5+42*x^4+3*x^3+40*x^2+68*x+11', 'y^2=78*x^6+43*x^5+55*x^4+65*x^3+47*x^2+19*x+15', 'y^2=88*x^6+14*x^5+20*x^4+36*x^3+17*x^2+7*x+73', 'y^2=62*x^6+61*x^5+28*x^4+76*x^3+31*x^2+7*x+48', 'y^2=52*x^6+72*x^5+77*x^4+13*x^3+4*x^2+11*x+71', 'y^2=56*x^6+44*x^5+37*x^4+25*x^3+30*x^2+17*x+73', 'y^2=7*x^6+19*x^5+69*x^4+35*x^3+19*x^2+72*x+3', 'y^2=17*x^6+80*x^5+53*x^4+26*x^3+78*x^2+69*x+50', 'y^2=80*x^6+9*x^5+33*x^4+47*x^3+37*x^2+37*x+40', 'y^2=71*x^6+21*x^5+8*x^4+60*x^3+16*x^2+44*x+60', 'y^2=75*x^6+80*x^5+28*x^4+4*x^3+31*x^2+69*x+15', 'y^2=22*x^6+54*x^5+62*x^4+63*x^3+60*x^2+71*x+67', 'y^2=67*x^6+21*x^5+56*x^4+32*x^3+55*x^2+58*x+29', 'y^2=59*x^6+80*x^5+77*x^4+13*x^3+11*x^2+55*x+19', 'y^2=54*x^6+80*x^5+29*x^4+62*x^3+12*x^2+21*x+43', 'y^2=63*x^6+87*x^5+72*x^4+44*x^3+21*x^2+42*x+85', 'y^2=56*x^6+67*x^5+73*x^4+70*x^3+74*x^2+35*x+31', 'y^2=81*x^6+63*x^5+62*x^4+61*x^3+26*x^2+43*x+70', 'y^2=39*x^6+86*x^5+11*x^4+83*x^3+49*x^2+28*x+21', 'y^2=28*x^6+10*x^5+18*x^4+68*x^3+76*x^2+85*x+55'], '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': ['2.0.355.1'], 'geometric_splitting_field': '2.0.355.1', 'geometric_splitting_polynomials': [[89, -1, 1]], 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 66, 'is_cyclic': False, 'is_geometrically_simple': False, 'is_geometrically_squarefree': False, 'is_primitive': True, 'is_simple': False, 'is_squarefree': False, 'is_supersingular': False, 'jacobian_count': 66, 'label': '2.89.ac_gx', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 6, 'newton_coelevation': 2, 'newton_elevation': 0, 'noncyclic_primes': [89], 'number_fields': ['2.0.355.1'], 'p': 89, 'p_rank': 2, 'p_rank_deficit': 0, 'poly': [1, -2, 179, -178, 7921], 'poly_str': '1 -2 179 -178 7921 ', 'primitive_models': [], 'q': 89, 'real_poly': [1, -2, 1], 'simple_distinct': ['1.89.ab'], 'simple_factors': ['1.89.abA', '1.89.abB'], 'simple_multiplicities': [2], 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '2.0.355.1', 'splitting_polynomials': [[89, -1, 1]], 'twist_count': 6, 'twists': [['2.89.a_gv', '2.7921.nq_cruh', 2], ['2.89.c_gx', '2.7921.nq_cruh', 2], ['2.89.b_adk', '2.704969.um_dggju', 3], ['2.89.a_agv', '2.62742241.abtvi_betlvlj', 4], ['2.89.ab_adk', '2.496981290961.fwkca_njbcallzy', 6]]}
• av_fq_endalg_factors •

  Column	Type
  base_label	text
  extension_degree	smallint
  extension_label	text
  multiplicity	smallint

  
  {'base_label': '2.89.ac_gx', 'extension_degree': 1, 'extension_label': '1.89.ab', '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': '2.0.355.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.89.ab', 'galois_group': '2T1', 'places': [['88', '1'], ['0', '1']]}