Abelian variety isogeny class data - 2.89.ah_gw

Formats: - HTML - YAML - JSON - 2025-09-28T07:05:24.006175

• 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': 7470, 'abvar_counts': [7470, 65213100, 498058485120, 3935544850195200, 31180930316039656350, 246990647682170859801600, 1956411258842686009194646110, 15496731422665806411882120268800, 122749609733132642089020471705747840, 972299657863824819270828996767796427500], 'abvar_counts_str': '7470 65213100 498058485120 3935544850195200 31180930316039656350 246990647682170859801600 1956411258842686009194646110 15496731422665806411882120268800 122749609733132642089020471705747840 972299657863824819270828996767796427500 ', 'angle_corank': 1, 'angle_rank': 1, 'angles': [0.379015237148192, 0.5], 'center_dim': 4, 'cohen_macaulay_max': 1, 'curve_count': 83, 'curve_counts': [83, 8229, 706496, 62725601, 5583918043, 496981782162, 44231341049587, 3936588805063681, 350356404033696704, 31181719932306481749], 'curve_counts_str': '83 8229 706496 62725601 5583918043 496981782162 44231341049587 3936588805063681 350356404033696704 31181719932306481749 ', 'curves': ['y^2=8*x^6+9*x^5+45*x^4+86*x^3+31*x^2+33*x+11', 'y^2=76*x^6+11*x^5+32*x^4+42*x^3+24*x^2+70*x+49', 'y^2=58*x^6+47*x^5+21*x^4+45*x^3+9*x^2+57*x+56', 'y^2=66*x^6+13*x^5+27*x^4+49*x^3+31*x^2+58*x+23', 'y^2=83*x^6+24*x^5+81*x^4+42*x^3+81*x^2+27*x+72', 'y^2=x^6+85*x^5+48*x^4+88*x^3+75*x^2+69*x+35', 'y^2=78*x^6+30*x^5+54*x^4+6*x^3+2*x^2+47*x+41', 'y^2=25*x^6+67*x^5+35*x^4+29*x^3+7*x^2+33*x+69', 'y^2=26*x^6+55*x^5+78*x^4+40*x^3+43*x^2+31*x+80', 'y^2=21*x^6+6*x^5+60*x^4+39*x^3+40*x^2+27*x+64', 'y^2=2*x^6+52*x^5+67*x^4+8*x^3+43*x^2+88*x+41', 'y^2=50*x^6+87*x^5+53*x^4+84*x^3+7*x^2+85*x+57', 'y^2=5*x^6+58*x^5+35*x^4+49*x^3+72*x^2+56*x+33', 'y^2=85*x^6+61*x^5+50*x^4+10*x^3+55*x^2+55*x+55', 'y^2=73*x^6+79*x^5+88*x^4+49*x^3+13*x^2+86*x+81', 'y^2=83*x^6+4*x^5+26*x^4+9*x^3+84*x^2+84*x+49', 'y^2=87*x^6+3*x^5+37*x^4+10*x^3+30*x^2+48*x+68', 'y^2=4*x^6+49*x^5+29*x^4+76*x^3+36*x^2+9*x+88', 'y^2=47*x^6+14*x^5+31*x^4+4*x^3+18*x^2+19*x+38', 'y^2=34*x^6+11*x^5+19*x^4+2*x^3+40*x^2+23*x+74', 'y^2=20*x^6+57*x^5+65*x^4+36*x^3+6*x^2+26*x+88', 'y^2=37*x^6+80*x^5+27*x^4+46*x^3+26*x^2+7', 'y^2=62*x^6+40*x^5+43*x^4+33*x^3+40*x^2+16*x+72', 'y^2=47*x^6+52*x^5+73*x^4+54*x^3+43*x^2+25*x+60', 'y^2=15*x^6+46*x^5+9*x^4+31*x^3+4*x^2+57*x+57', 'y^2=63*x^6+17*x^5+56*x^4+48*x^3+18*x^2+5*x+65', 'y^2=37*x^6+34*x^5+86*x^4+81*x^3+16*x^2+13*x+61', 'y^2=12*x^6+82*x^5+37*x^4+50*x^3+53*x^2+68*x+87', 'y^2=15*x^6+38*x^5+49*x^4+64*x^3+54*x^2+48*x+66', 'y^2=62*x^6+26*x^5+49*x^4+64*x^3+81*x^2+28*x+31', 'y^2=63*x^6+10*x^5+23*x^4+10*x^3+61*x^2+78*x+21', 'y^2=38*x^6+22*x^5+31*x^4+72*x^3+4*x^2+30*x+71', 'y^2=42*x^6+19*x^5+56*x^4+82*x^3+21*x^2+43*x+3', 'y^2=36*x^6+11*x^5+31*x^4+71*x^3+88*x^2+18*x+31', 'y^2=48*x^6+25*x^5+31*x^4+28*x^3+52*x^2+31*x+30', 'y^2=33*x^6+18*x^5+15*x^4+63*x^3+15*x^2+42*x+18', 'y^2=55*x^6+16*x^5+61*x^4+16*x^3+47*x^2+14*x+66', 'y^2=44*x^6+17*x^5+27*x^4+59*x^3+81*x^2+2*x+46', 'y^2=38*x^6+58*x^5+27*x^4+64*x^3+28*x^2+48*x+71', 'y^2=22*x^6+41*x^5+24*x^4+78*x^3+60*x^2+4*x+60', 'y^2=60*x^6+8*x^5+56*x^4+12*x^3+5*x^2+37*x+23', 'y^2=19*x^6+81*x^5+54*x^4+69*x^3+72*x^2+81*x+79', 'y^2=85*x^6+66*x^5+85*x^4+85*x^3+47*x^2+60*x+56', 'y^2=87*x^6+29*x^5+50*x^4+17*x^3+7*x^2+25*x+57', 'y^2=83*x^6+32*x^5+77*x^4+15*x^3+60*x^2+8*x+29', 'y^2=77*x^6+41*x^5+46*x^4+3*x^3+41*x^2+62*x+60', 'y^2=11*x^6+69*x^5+14*x^4+82*x^3+59*x^2+85*x+85', 'y^2=26*x^6+81*x^5+80*x^4+62*x^3+80*x^2+8*x+5', 'y^2=31*x^6+25*x^5+60*x^4+46*x^3+71*x^2+82*x+12', 'y^2=30*x^6+12*x^5+18*x^4+37*x^3+60*x^2+46*x+58', 'y^2=11*x^6+39*x^5+73*x^4+43*x^2+11*x+27', 'y^2=2*x^6+8*x^5+30*x^4+85*x^3+29*x^2+65*x+81', 'y^2=72*x^6+12*x^5+69*x^4+19*x^3+48*x^2+83*x+62', 'y^2=83*x^6+34*x^5+72*x^4+5*x^3+64*x^2+54*x+82', 'y^2=29*x^6+19*x^5+73*x^4+32*x^3+40*x^2+82*x+46', 'y^2=74*x^6+82*x^5+85*x^4+2*x^3+29*x^2+11*x+37', 'y^2=50*x^6+5*x^5+20*x^4+78*x^3+30*x^2+13*x+68', 'y^2=11*x^6+79*x^5+81*x^4+22*x^3+36*x^2+81*x+15', 'y^2=64*x^6+50*x^5+56*x^4+58*x^3+50*x^2+21*x+49', 'y^2=2*x^6+64*x^5+60*x^4+82*x^3+21*x^2+68*x+73', 'y^2=49*x^6+56*x^5+12*x^4+62*x^3+18*x^2+30*x+50', 'y^2=62*x^6+82*x^5+31*x^4+2*x^3+80*x^2+24*x+1', 'y^2=45*x^6+39*x^5+68*x^4+84*x^3+64*x^2+69*x+15', 'y^2=87*x^6+60*x^5+48*x^4+78*x^3+49*x^2+63*x+48', 'y^2=81*x^6+46*x^5+76*x^4+46*x^3+9*x^2+73*x+22', 'y^2=78*x^6+69*x^5+83*x^4+22*x^3+30*x^2+8*x+72', 'y^2=34*x^6+44*x^5+6*x^4+81*x^3+88*x^2+75*x+57', 'y^2=69*x^6+24*x^5+24*x^4+20*x^3+8*x^2+44*x+76', 'y^2=53*x^6+57*x^5+69*x^4+46*x^3+63*x^2+74*x+61', 'y^2=32*x^6+14*x^5+84*x^4+39*x^3+45*x^2+49*x+41', 'y^2=42*x^6+53*x^5+14*x^4+86*x^3+83*x^2+34*x+14', 'y^2=14*x^6+6*x^5+81*x^4+23*x^3+49*x^2+28*x+6', 'y^2=30*x^6+60*x^5+7*x^4+52*x^3+28*x^2+86*x+35', 'y^2=30*x^6+55*x^5+35*x^4+8*x^3+32*x^2+47*x+28', 'y^2=27*x^6+8*x^5+44*x^4+28*x^3+12*x^2+x+65', 'y^2=73*x^6+16*x^5+10*x^4+15*x^3+29*x^2+16*x+57', 'y^2=86*x^6+86*x^5+60*x^4+77*x^3+24*x^2+51*x+73', 'y^2=33*x^6+30*x^5+59*x^4+53*x^3+43*x^2+40*x+3', 'y^2=11*x^6+24*x^5+63*x^4+25*x^3+56*x^2+39*x+71', 'y^2=52*x^6+59*x^5+2*x^4+27*x^3+30*x^2+82*x+70', 'y^2=24*x^6+47*x^5+16*x^4+42*x^3+42*x^2+87*x+29', 'y^2=87*x^6+7*x^5+74*x^4+73*x^3+15*x^2+45*x+81', 'y^2=62*x^6+28*x^5+13*x^4+40*x^3+44*x^2+82*x+76', 'y^2=58*x^6+71*x^5+55*x^4+32*x^3+46*x^2+51*x+16', 'y^2=70*x^6+71*x^5+59*x^4+86*x^3+44*x^2+27*x+5', 'y^2=38*x^6+24*x^5+34*x^4+19*x^3+64*x^2+7*x+11', 'y^2=5*x^6+47*x^5+31*x^4+64*x^3+35*x^2+83*x+28', 'y^2=50*x^6+2*x^5+47*x^4+75*x^3+75*x^2+46*x+65', 'y^2=40*x^6+7*x^5+82*x^4+33*x^3+37*x^2+52*x+82', 'y^2=26*x^6+26*x^5+33*x^4+84*x^3+73*x^2+55*x+86', 'y^2=60*x^6+78*x^5+80*x^4+18*x^3+64*x^2+29*x+80', 'y^2=5*x^6+14*x^5+4*x^4+11*x^3+33*x^2+56*x+56', 'y^2=73*x^6+77*x^5+44*x^4+4*x^3+63*x^2+38*x+8', 'y^2=44*x^6+71*x^5+81*x^4+56*x^3+74*x^2+60*x+77', 'y^2=13*x^6+13*x^5+5*x^4+48*x^3+76*x^2+60*x+9', 'y^2=84*x^6+62*x^5+54*x^4+74*x^3+80*x^2+10*x+66', 'y^2=30*x^6+51*x^5+46*x^4+82*x^3+51*x^2+33*x+20', 'y^2=28*x^6+19*x^5+50*x^4+16*x^3+59*x^2+57*x+30', 'y^2=31*x^6+27*x^5+73*x^4+x^3+49*x^2+8*x+1', 'y^2=23*x^6+82*x^5+44*x^4+19*x^3+87*x^2+84*x+15', 'y^2=58*x^6+34*x^5+69*x^4+18*x^3+58*x^2+30*x+61', 'y^2=60*x^6+84*x^5+9*x^4+38*x^3+68*x^2+10*x+53', 'y^2=63*x^6+30*x^5+22*x^4+21*x^3+31*x^2+70*x+5', 'y^2=60*x^6+17*x^5+20*x^4+50*x^3+72*x^2+11*x+61', 'y^2=74*x^6+42*x^5+45*x^4+44*x^3+30*x^2+66*x+24', 'y^2=54*x^6+85*x^5+71*x^4+27*x^3+11*x^2+42*x+37', 'y^2=45*x^6+25*x^5+74*x^4+22*x^3+61*x^2+10*x+83', 'y^2=50*x^6+88*x^5+11*x^4+33*x^3+34*x^2+45*x+13'], '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': 4, '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': 3, 'geometric_extension_degree': 2, 'geometric_galois_groups': ['1T1', '2T1'], 'geometric_number_fields': ['1.1.1.1', '2.0.307.1'], 'geometric_splitting_field': '2.0.307.1', 'geometric_splitting_polynomials': [[77, -1, 1]], 'group_structure_count': 1, 'has_geom_ss_factor': True, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 108, 'is_geometrically_simple': False, 'is_geometrically_squarefree': True, 'is_primitive': True, 'is_simple': False, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 108, 'label': '2.89.ah_gw', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 4, 'max_twist_degree': 2, 'newton_coelevation': 1, 'newton_elevation': 1, 'number_fields': ['2.0.307.1', '2.0.356.1'], 'p': 89, 'p_rank': 1, 'p_rank_deficit': 1, 'poly': [1, -7, 178, -623, 7921], 'poly_str': '1 -7 178 -623 7921 ', 'primitive_models': [], 'q': 89, 'real_poly': [1, -7], 'simple_distinct': ['1.89.ah', '1.89.a'], 'simple_factors': ['1.89.ahA', '1.89.aA'], 'simple_multiplicities': [1, 1], 'singular_primes': ['7,18*F+V-12', '7,-11*F+12'], 'slopes': ['0A', '1/2A', '1/2B', '1A'], 'splitting_polynomials': [[233, -332, 333, -2, 1]], 'twist_count': 2, 'twists': [['2.89.h_gw', '2.7921.lv_cfkm', 2]], 'weak_equivalence_count': 4, 'zfv_index': 49, 'zfv_index_factorization': [[7, 2]], 'zfv_is_bass': True, 'zfv_is_maximal': False, 'zfv_plus_index': 1, 'zfv_plus_index_factorization': [], 'zfv_plus_norm': 109292, 'zfv_singular_count': 4, 'zfv_singular_primes': ['7,18*F+V-12', '7,-11*F+12']}
• av_fq_endalg_factors •

  Column	Type
  base_label	text
  extension_degree	smallint
  extension_label	text
  multiplicity	smallint

  
  
  • id: 119052
    {'base_label': '2.89.ah_gw', 'extension_degree': 1, 'extension_label': '1.89.ah', 'multiplicity': 1}
  • id: 119053
    {'base_label': '2.89.ah_gw', 'extension_degree': 1, 'extension_label': '1.89.a', 'multiplicity': 1}
  • id: 119054
    {'base_label': '2.89.ah_gw', 'extension_degree': 2, 'extension_label': '1.7921.ez', 'multiplicity': 1}
  • id: 119055
    {'base_label': '2.89.ah_gw', 'extension_degree': 2, 'extension_label': '1.7921.gw', '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': '2.0.307.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.89.ah', 'galois_group': '2T1', 'places': [['85', '1'], ['3', '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'], 'center': '2.0.356.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.89.a', 'galois_group': '2T1', 'places': [['0', '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': '2.0.307.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.7921.ez', 'galois_group': '2T1', 'places': [['85', '1'], ['3', '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': ['1/2'], 'center': '1.1.1.1', 'center_dim': 1, 'divalg_dim': 4, 'extension_label': '1.7921.gw', 'galois_group': '1T1', 'places': [['0']]}