Abelian variety isogeny class data - 2.89.au_ks

Formats: - HTML - YAML - JSON - 2025-10-26T14:36:19.743236

• 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': 6400, 'abvar_counts': [6400, 64000000, 499340089600, 3937813504000000, 31181149811270560000, 246989032931527744000000, 1956410168699731825668409600, 15496731663467893210497024000000, 122749610407542487907462327184390400, 972299658324807092786782195240000000000], 'abvar_counts_str': '6400 64000000 499340089600 3937813504000000 31181149811270560000 246989032931527744000000 1956410168699731825668409600 15496731663467893210497024000000 122749610407542487907462327184390400 972299658324807092786782195240000000000 ', 'angle_corank': 1, 'angle_rank': 1, 'angles': [0.322192315510647, 0.322192315510647], 'center_dim': 2, 'curve_count': 70, 'curve_counts': [70, 8078, 708310, 62761758, 5583957350, 496978533038, 44231316403190, 3936588866233918, 350356405958621830, 31181719947090216398], 'curve_counts_str': '70 8078 708310 62761758 5583957350 496978533038 44231316403190 3936588866233918 350356405958621830 31181719947090216398 ', 'curves': ['y^2=11*x^6+73*x^5+15*x^4+35*x^3+60*x^2+11*x+81', 'y^2=76*x^6+73*x^4+73*x^2+76', 'y^2=61*x^6+60*x^5+15*x^4+13*x^3+82*x^2+19*x+52', 'y^2=75*x^6+30*x^5+35*x^4+51*x^3+75*x^2+24*x+75', 'y^2=35*x^6+78*x^5+29*x^4+58*x^3+88*x^2+39*x+67', 'y^2=33*x^6+65*x^5+52*x^4+14*x^3+52*x^2+65*x+33', 'y^2=32*x^6+52*x^5+57*x^4+32*x^3+80*x^2+65*x+16', 'y^2=81*x^6+78*x^5+85*x^4+75*x^3+8*x^2+45*x+64', 'y^2=22*x^6+26*x^5+46*x^3+70*x+44', 'y^2=61*x^6+56*x^5+67*x^4+41*x^3+67*x^2+56*x+61', 'y^2=24*x^6+72*x^5+3*x^4+21*x^3+23*x^2+49*x+56', 'y^2=25*x^6+24*x^5+54*x^3+75*x+69', 'y^2=6*x^6+19*x^5+27*x^4+56*x^3+59*x^2+47*x+53', 'y^2=29*x^6+86*x^5+87*x^4+77*x^3+32*x^2+33*x+31', 'y^2=58*x^6+20*x^5+33*x^4+32*x^3+33*x^2+20*x+58', 'y^2=24*x^6+43*x^5+53*x^4+28*x^3+8*x^2+51*x+61', 'y^2=68*x^6+19*x^5+64*x^4+36*x^3+21*x^2+51*x+11', 'y^2=55*x^6+64*x^5+80*x^4+6*x^3+80*x^2+64*x+55', 'y^2=25*x^6+44*x^5+50*x^4+36*x^3+68*x^2+84*x+82', 'y^2=77*x^6+36*x^5+73*x^4+42*x^3+73*x^2+36*x+77', 'y^2=15*x^6+53*x^5+68*x^4+43*x^3+73*x^2+79*x+6', 'y^2=66*x^6+3*x^5+69*x^4+86*x^3+69*x^2+84*x+7', 'y^2=40*x^6+17*x^5+8*x^4+32*x^3+63*x^2+19*x+27', 'y^2=54*x^6+39*x^5+59*x^4+82*x^3+12*x^2+81*x+77', 'y^2=3*x^6+10*x^5+18*x^4+18*x^3+29*x^2+42*x', 'y^2=67*x^6+62*x^5+35*x^4+23*x^3+46*x^2+47*x+62', 'y^2=74*x^6+65*x^5+60*x^4+23*x^3+19*x^2+86*x+30', 'y^2=13*x^5+9*x^4+35*x^3+57*x^2+36*x+69', 'y^2=25*x^6+43*x^5+65*x^4+70*x^3+80*x^2+70*x+59', 'y^2=69*x^6+19*x^4+19*x^2+69', 'y^2=24*x^6+37*x^5+13*x^4+48*x^3+13*x^2+37*x+24', 'y^2=74*x^6+81*x^5+85*x^4+64*x^3+32*x^2+56*x+59', 'y^2=68*x^6+19*x^5+72*x^4+10*x^3+32*x^2+51*x+78', 'y^2=17*x^6+55*x^5+85*x^4+84*x^3+9*x^2+17*x+8', 'y^2=59*x^6+62*x^5+32*x^4+83*x^3+47*x^2+28*x+14', 'y^2=74*x^6+17*x^5+77*x^4+22*x^3+33*x^2+34*x+38', 'y^2=81*x^6+64*x^4+64*x^2+81', 'y^2=11*x^6+68*x^5+x^4+74*x^3+x^2+68*x+11', 'y^2=7*x^6+82*x^5+31*x^4+43*x^3+35*x^2+66*x+3', 'y^2=80*x^6+x^5+60*x^4+19*x^3+83*x^2+81*x+64', 'y^2=11*x^6+72*x^5+8*x^4+43*x^3+8*x^2+72*x+11', 'y^2=76*x^6+7*x^5+32*x^4+40*x^3+32*x^2+7*x+76', 'y^2=74*x^6+7*x^5+51*x^4+29*x^3+5*x^2+83*x+62', 'y^2=68*x^6+74*x^5+36*x^4+72*x^3+36*x^2+74*x+68', 'y^2=41*x^6+66*x^5+13*x^4+19*x^3+56*x^2+24*x+58', 'y^2=32*x^6+79*x^5+44*x^4+49*x^3+25*x^2+9*x+16', 'y^2=81*x^6+77*x^5+85*x^4+71*x^3+81*x^2+43*x+79', 'y^2=55*x^6+51*x^5+73*x^4+51*x^3+30*x^2+19*x+59', 'y^2=51*x^6+50*x^5+12*x^4+80*x^3+52*x^2+85*x+3', 'y^2=3*x^6+82*x^4+82*x^2+3', 'y^2=56*x^6+51*x^5+39*x^4+35*x^3+39*x^2+51*x+56', 'y^2=11*x^6+61*x^5+66*x^4+24*x^3+64*x^2+47*x+68', 'y^2=14*x^6+43*x^5+71*x^4+18*x^3+58*x^2+19*x+18', 'y^2=49*x^6+78*x^5+41*x^4+48*x^3+3*x^2+48*x+52', 'y^2=57*x^6+21*x^5+5*x^4+18*x^3+5*x^2+21*x+57', 'y^2=49*x^6+17*x^5+15*x^4+7*x^3+43*x^2+42*x+57', 'y^2=65*x^5+7*x^4+5*x^3+7*x^2+65*x', 'y^2=61*x^6+41*x^5+7*x^4+19*x^3+48*x^2+72*x+84', 'y^2=29*x^6+56*x^4+7*x^3+56*x^2+29', 'y^2=27*x^6+30*x^5+76*x^4+14*x^3+43*x^2+37*x+48', 'y^2=28*x^6+40*x^5+55*x^4+12*x^3+55*x^2+40*x+28', 'y^2=51*x^5+74*x^4+59*x^3+74*x^2+51*x', 'y^2=31*x^6+47*x^4+47*x^2+31', 'y^2=2*x^6+79*x^5+39*x^4+14*x^3+39*x^2+79*x+2', 'y^2=63*x^6+49*x^4+49*x^2+63', 'y^2=29*x^6+83*x^5+16*x^4+36*x^3+16*x^2+83*x+29', 'y^2=27*x^6+64*x^5+45*x^4+54*x^3+44*x^2+20*x+50', 'y^2=72*x^6+62*x^5+70*x^4+41*x^3+62*x^2+84*x+26', 'y^2=59*x^6+66*x^5+24*x^4+72*x^3+41*x^2+86*x+62', 'y^2=3*x^6+39*x^5+35*x^4+87*x^3+54*x^2+57*x+12', 'y^2=82*x^6+18*x^5+15*x^4+77*x^3+19*x^2+64*x+5', 'y^2=46*x^5+66*x^4+84*x^3+53*x^2+18*x+85', 'y^2=70*x^6+43*x^5+27*x^4+8*x^3+63*x^2+66*x+52', 'y^2=73*x^6+42*x^5+80*x^4+72*x^3+26*x^2+47*x+64', 'y^2=51*x^6+43*x^5+54*x^4+61*x^3+22*x^2+12*x+45', 'y^2=46*x^6+45*x^4+45*x^2+46', 'y^2=35*x^6+85*x^5+43*x^4+79*x^3+59*x^2+2*x+6', 'y^2=12*x^6+71*x^5+71*x^4+14*x^3+81*x^2+36*x+19', 'y^2=69*x^6+28*x^5+80*x^4+87*x^3+60*x^2+13*x+52', 'y^2=51*x^6+62*x^5+26*x^4+31*x^3+40*x^2+76*x+57'], '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': ['2.0.4.1'], 'geometric_splitting_field': '2.0.4.1', 'geometric_splitting_polynomials': [[1, 0, 1]], 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 80, 'is_geometrically_simple': False, 'is_geometrically_squarefree': False, 'is_primitive': True, 'is_simple': False, 'is_squarefree': False, 'is_supersingular': False, 'jacobian_count': 80, 'label': '2.89.au_ks', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 12, 'newton_coelevation': 2, 'newton_elevation': 0, 'number_fields': ['2.0.4.1'], 'p': 89, 'p_rank': 2, 'p_rank_deficit': 0, 'poly': [1, -20, 278, -1780, 7921], 'poly_str': '1 -20 278 -1780 7921 ', 'primitive_models': [], 'q': 89, 'real_poly': [1, -20, 100], 'simple_distinct': ['1.89.ak'], 'simple_factors': ['1.89.akA', '1.89.akB'], 'simple_multiplicities': [2], 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '2.0.4.1', 'splitting_polynomials': [[1, 0, 1]], 'twist_count': 16, 'twists': [['2.89.a_da', '2.7921.ga_bgli', 2], ['2.89.u_ks', '2.7921.ga_bgli', 2], ['2.89.k_l', '2.704969.eym_jexhu', 3], ['2.89.abg_qs', '2.62742241.bcwq_sozbus', 4], ['2.89.aba_na', '2.62742241.bcwq_sozbus', 4], ['2.89.ag_s', '2.62742241.bcwq_sozbus', 4], ['2.89.a_ada', '2.62742241.bcwq_sozbus', 4], ['2.89.g_s', '2.62742241.bcwq_sozbus', 4], ['2.89.ba_na', '2.62742241.bcwq_sozbus', 4], ['2.89.bg_qs', '2.62742241.bcwq_sozbus', 4], ['2.89.ak_l', '2.496981290961.agaxua_nwncqhtzy', 6], ['2.89.a_age', '2.3936588805702081.fcmado_ckgulfbhtksc', 8], ['2.89.a_ge', '2.3936588805702081.fcmado_ckgulfbhtksc', 8], ['2.89.aq_gl', '2.246990403565262140303521.airzwmjwae_befpvymugjpqvbdwag', 12], ['2.89.q_gl', '2.246990403565262140303521.airzwmjwae_befpvymugjpqvbdwag', 12]]}
• av_fq_endalg_factors •

  Column	Type
  base_label	text
  extension_degree	smallint
  extension_label	text
  multiplicity	smallint

  
  {'base_label': '2.89.au_ks', 'extension_degree': 1, 'extension_label': '1.89.ak', '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': '2.0.4.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.89.ak', 'galois_group': '2T1', 'places': [['55', '1'], ['34', '1']]}