Abelian variety isogeny class data - 2.73.as_ha

Formats: - HTML - YAML - JSON - 2025-12-10T13:59:43.818521

• 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': 4180, 'abvar_counts': [4180, 28607920, 151355797780, 806214669638400, 4297590717905204500, 22902218467608248684080, 122045143370526156004967380, 650377903670960447798211686400, 3465863719884589665047947263205780, 18469587787132686780987211779741598000], 'abvar_counts_str': '4180 28607920 151355797780 806214669638400 4297590717905204500 22902218467608248684080 122045143370526156004967380 650377903670960447798211686400 3465863719884589665047947263205780 18469587787132686780987211779741598000 ', 'all_polarized_product': False, 'all_unpolarized_product': False, 'angle_corank': 0, 'angle_rank': 2, 'angles': [0.128793700061317, 0.457180132592647], 'center_dim': 4, 'cohen_macaulay_max': 1, 'curve_count': 56, 'curve_counts': [56, 5370, 389072, 28389598, 2073054656, 151335352410, 11047410225992, 806460121471678, 58871586679994216, 4297625833193273850], 'curve_counts_str': '56 5370 389072 28389598 2073054656 151335352410 11047410225992 806460121471678 58871586679994216 4297625833193273850 ', 'curves': ['y^2=72*x^6+4*x^5+41*x^4+8*x^3+25*x^2+32*x+60', 'y^2=11*x^6+29*x^5+58*x^4+29*x^3+52*x^2+56*x+24', 'y^2=31*x^6+32*x^5+67*x^4+5*x^3+62*x^2+4*x+52', 'y^2=54*x^6+63*x^5+33*x^4+19*x^3+58*x+69', 'y^2=24*x^6+18*x^5+62*x^4+52*x^3+59*x^2+23*x+60', 'y^2=60*x^6+30*x^5+20*x^4+8*x^3+38*x^2+7*x+41', 'y^2=40*x^6+9*x^5+29*x^4+46*x^3+17*x^2+71*x+70', 'y^2=45*x^6+17*x^5+62*x^4+64*x^3+36*x^2+10*x+16', 'y^2=19*x^6+9*x^5+39*x^4+20*x^3+31*x^2+28*x+4', 'y^2=33*x^6+13*x^5+26*x^4+18*x^3+29*x^2+2*x+15', 'y^2=72*x^6+28*x^5+66*x^4+22*x^3+65*x^2+2*x+63', 'y^2=26*x^6+21*x^5+57*x^4+70*x^3+45*x^2+49*x+12', 'y^2=47*x^6+49*x^5+19*x^4+58*x^3+51*x^2+11*x+5', 'y^2=14*x^6+5*x^5+13*x^3+44*x^2+65*x+4', 'y^2=18*x^6+31*x^5+66*x^4+4*x^3+22*x^2+4*x+53', 'y^2=67*x^6+12*x^5+21*x^4+51*x^3+7*x+30', 'y^2=23*x^6+32*x^5+42*x^4+6*x^3+14*x^2+26*x+29', 'y^2=7*x^6+59*x^5+70*x^4+40*x^3+30*x+45', 'y^2=14*x^6+50*x^5+49*x^4+27*x^3+51*x^2+15*x+38', 'y^2=44*x^6+63*x^5+17*x^4+65*x^3+54*x^2+8*x+37', 'y^2=25*x^6+12*x^5+3*x^4+41*x^3+63*x^2+41*x+63', 'y^2=49*x^6+69*x^5+51*x^4+22*x^3+60*x^2+6*x+65', 'y^2=22*x^6+66*x^5+3*x^4+29*x^3+40*x^2+65*x+50', 'y^2=20*x^6+54*x^5+19*x^4+60*x^3+24*x^2+14*x+43', 'y^2=43*x^6+69*x^5+10*x^4+49*x^3+57*x+61', 'y^2=17*x^6+42*x^5+50*x^4+20*x^3+8*x^2+69*x+22', 'y^2=24*x^6+10*x^5+58*x^4+70*x^3+23*x^2+20*x+21', 'y^2=25*x^6+48*x^5+27*x^4+33*x^3+71*x^2+55*x+18', 'y^2=37*x^6+2*x^5+11*x^4+54*x^3+70*x^2+14*x+70', 'y^2=30*x^6+49*x^5+x^4+14*x^3+31*x^2+47*x+49', 'y^2=4*x^6+15*x^5+9*x^4+41*x^3+51*x^2+43*x+56', 'y^2=28*x^6+49*x^5+24*x^4+60*x^3+15*x^2+29*x+11', 'y^2=56*x^6+60*x^5+32*x^4+53*x^3+26*x^2+54*x+43', 'y^2=10*x^6+22*x^5+50*x^4+66*x^3+35*x^2+70*x+34', 'y^2=47*x^6+32*x^5+11*x^4+7*x^3+60*x^2+56*x+5', 'y^2=23*x^6+71*x^5+52*x^4+63*x^3+59*x^2+45*x+69', 'y^2=70*x^6+41*x^5+24*x^4+49*x^3+37*x^2+x+23', 'y^2=36*x^6+5*x^5+3*x^4+31*x^3+25*x^2+30*x+41', 'y^2=51*x^6+60*x^5+24*x^4+49*x^3+57*x^2+24*x+22', 'y^2=5*x^6+72*x^5+14*x^4+51*x^3+13*x^2+60*x+18', 'y^2=39*x^6+22*x^5+26*x^4+43*x^3+61*x^2+69*x+61', 'y^2=36*x^6+2*x^5+30*x^4+42*x^3+35*x^2+21*x+27', 'y^2=40*x^6+50*x^5+13*x^4+64*x^3+53*x^2+23*x+6', 'y^2=44*x^6+24*x^5+59*x^4+57*x^3+68*x^2+24*x+16', 'y^2=39*x^6+28*x^5+17*x^4+37*x^3+29*x^2+8*x+36', 'y^2=10*x^6+15*x^5+67*x^4+58*x^3+15*x^2+49*x+61', 'y^2=54*x^6+35*x^4+8*x^3+8*x^2+66*x+4', 'y^2=72*x^6+30*x^5+62*x^4+68*x^3+20*x^2+59*x+37', 'y^2=52*x^6+11*x^5+5*x^4+32*x^3+49*x^2+63*x+11', 'y^2=65*x^6+67*x^5+22*x^4+x^3+43*x^2+9*x+7', 'y^2=45*x^6+54*x^5+72*x^4+28*x^3+10*x^2+41*x+16', 'y^2=11*x^6+28*x^5+69*x^4+70*x^3+21*x^2+6*x', 'y^2=46*x^6+16*x^5+61*x^4+29*x^3+57*x^2+32*x+23', 'y^2=9*x^6+53*x^5+20*x^4+33*x^3+30*x^2+50*x+62', 'y^2=24*x^6+50*x^5+55*x^4+22*x^3+68*x^2+55*x+10', 'y^2=61*x^6+22*x^5+31*x^4+53*x^3+37*x^2+9*x+58', 'y^2=19*x^6+37*x^5+33*x^4+3*x^3+58*x^2+55*x+49', 'y^2=28*x^6+49*x^5+69*x^4+9*x^3+58*x^2+12*x+39', 'y^2=54*x^6+6*x^5+5*x^4+18*x^3+26*x^2+49*x+32', 'y^2=71*x^6+62*x^5+60*x^4+57*x^3+58*x^2+3*x+5', 'y^2=26*x^6+68*x^5+11*x^4+44*x^3+56*x^2+41*x', 'y^2=66*x^6+4*x^5+x^4+69*x^3+46*x^2+57*x+10', 'y^2=10*x^6+71*x^5+5*x^4+57*x^3+34*x^2+30*x+28', 'y^2=55*x^6+21*x^5+24*x^4+2*x^3+59*x^2+57', 'y^2=67*x^6+34*x^5+44*x^4+40*x^3+64*x^2+46*x+59', 'y^2=x^6+34*x^5+50*x^4+39*x^3+35*x^2+3*x+47', 'y^2=62*x^6+62*x^5+10*x^4+50*x^3+53*x^2+44', 'y^2=46*x^6+15*x^5+18*x^4+33*x^3+49*x^2+19*x+34', 'y^2=42*x^6+40*x^5+58*x^4+29*x^3+64*x^2+52*x+34', 'y^2=29*x^6+56*x^5+65*x^4+42*x^3+53*x^2+2*x+23', 'y^2=16*x^6+72*x^5+56*x^4+53*x^3+12*x^2+52*x+59', 'y^2=25*x^6+37*x^5+19*x^4+62*x^3+44*x^2+8*x+9', 'y^2=29*x^6+69*x^5+18*x^4+64*x^3+50*x^2+49*x+35', 'y^2=70*x^6+38*x^5+11*x^4+67*x^3+65*x^2+45*x+12', 'y^2=20*x^6+53*x^5+15*x^4+65*x^3+46*x^2+30*x+28', 'y^2=12*x^6+x^5+48*x^4+60*x^3+69*x^2+67*x+25', 'y^2=29*x^6+63*x^5+24*x^4+70*x^3+37*x^2+41*x+11', 'y^2=71*x^6+6*x^5+57*x^4+68*x^3+35*x^2+57*x+43', 'y^2=52*x^6+27*x^5+50*x^4+20*x^3+8*x^2+48*x+14', 'y^2=63*x^6+41*x^5+54*x^4+71*x^3+54*x^2+30*x+13', 'y^2=28*x^6+4*x^5+15*x^4+26*x^3+16*x^2+71*x+59', 'y^2=15*x^6+41*x^5+32*x^4+32*x^3+53*x^2+17*x+18', 'y^2=12*x^6+31*x^5+29*x^4+71*x^3+6*x^2+16*x+33', 'y^2=68*x^6+40*x^5+x^4+38*x^3+23*x^2+50*x+51', 'y^2=52*x^6+27*x^5+48*x^4+2*x^3+50*x^2+40*x+47', 'y^2=38*x^6+61*x^5+44*x^4+46*x^3+2*x^2+14', 'y^2=14*x^6+15*x^5+72*x^4+40*x^3+53*x^2+17*x+64', 'y^2=11*x^6+28*x^5+50*x^4+58*x^3+18*x^2+42*x', 'y^2=17*x^6+15*x^5+22*x^4+25*x^3+12*x^2+62*x+66', 'y^2=42*x^6+52*x^5+59*x^4+x^3+61*x^2+52*x+30', 'y^2=39*x^6+43*x^5+7*x^4+4*x^3+34*x^2+68*x+56', 'y^2=26*x^6+60*x^5+45*x^4+19*x^3+51*x^2+x+38', 'y^2=37*x^6+6*x^5+69*x^4+21*x^3+26*x^2+30*x+66', 'y^2=2*x^6+3*x^5+45*x^4+40*x^3+33*x^2+72*x+13', 'y^2=41*x^6+38*x^5+68*x^4+30*x^3+24*x^2+35*x+15', 'y^2=21*x^6+24*x^5+69*x^4+40*x^3+18*x^2+45*x+14', 'y^2=31*x^6+13*x^5+8*x^4+4*x^3+66*x^2+32*x+64', 'y^2=5*x^6+29*x^5+53*x^4+36*x^3+38*x^2+47*x+58', 'y^2=52*x^6+36*x^5+62*x^4+45*x^3+31*x^2+33*x+2', 'y^2=72*x^6+28*x^5+72*x^4+10*x^3+44*x^2+71*x+69', 'y^2=4*x^6+43*x^5+33*x^4+3*x^3+46*x^2+18*x+63', 'y^2=40*x^6+14*x^5+32*x^4+29*x^3+51*x^2+x+39', 'y^2=2*x^6+17*x^5+23*x^4+32*x^3+64*x^2+35*x+28', 'y^2=11*x^6+62*x^5+x^4+69*x^3+26*x^2+44*x+60', 'y^2=51*x^6+39*x^5+13*x^4+42*x^3+41*x^2+19*x+23', 'y^2=61*x^6+38*x^5+34*x^4+5*x^3+x^2+11*x+58', 'y^2=38*x^6+4*x^5+24*x^4+4*x^3+34*x^2+46*x+40', 'y^2=12*x^6+16*x^4+45*x^3+3*x^2+56*x+61', 'y^2=10*x^6+31*x^5+35*x^4+23*x^3+72*x^2+11*x+54', 'y^2=13*x^6+38*x^5+2*x^4+72*x^3+65*x^2+50*x+67', 'y^2=37*x^6+70*x^4+59*x^3+19*x^2+4*x+66', 'y^2=20*x^6+35*x^5+56*x^3+61*x^2+24*x+33', 'y^2=60*x^6+72*x^5+48*x^4+69*x^3+9*x^2+51*x+40', 'y^2=22*x^6+31*x^5+40*x^4+35*x^3+34*x^2+64*x+26', 'y^2=56*x^6+43*x^5+60*x^4+24*x^3+70*x^2+67*x+7', 'y^2=56*x^6+43*x^5+64*x^4+21*x^3+51*x^2+42*x+40', 'y^2=54*x^6+46*x^5+31*x^4+8*x^3+x^2+7*x+71', 'y^2=59*x^6+8*x^5+35*x^4+51*x^3+37*x^2+52*x+23', 'y^2=2*x^6+12*x^5+60*x^4+42*x^3+42*x^2+38*x+51', 'y^2=17*x^6+10*x^5+6*x^4+24*x^3+31*x^2+42*x+11', 'y^2=x^6+61*x^5+18*x^4+8*x^3+15*x^2+19*x+35', 'y^2=8*x^6+19*x^5+66*x^4+60*x^3+55*x^2+20*x+8', 'y^2=14*x^6+46*x^5+54*x^4+52*x^3+67*x^2+10*x+39', 'y^2=49*x^6+62*x^5+62*x^4+9*x^3+26*x^2+41*x+39', 'y^2=17*x^6+27*x^5+20*x^4+27*x^3+62*x^2+6*x+17', 'y^2=33*x^6+12*x^5+72*x^4+42*x^3+62*x^2+12*x+25', 'y^2=43*x^6+39*x^5+52*x^4+29*x^3+6*x^2+16*x+32', 'y^2=19*x^6+2*x^5+53*x^4+23*x^3+25*x^2+71*x+19', 'y^2=33*x^6+69*x^5+33*x^4+21*x^3+51*x^2+8*x+20', 'y^2=3*x^6+57*x^5+72*x^4+44*x^3+67*x^2+14*x+42', 'y^2=52*x^6+54*x^5+22*x^4+42*x^3+11*x^2+61*x+47', 'y^2=64*x^6+29*x^5+18*x^4+64*x^3+51*x^2+57*x+58', 'y^2=58*x^6+70*x^5+25*x^4+45*x^3+71*x^2+29*x+19', 'y^2=30*x^6+62*x^5+21*x^4+3*x^3+63*x^2+37*x+68', 'y^2=11*x^6+55*x^5+64*x^4+37*x^3+14*x^2+64*x+69', 'y^2=16*x^6+50*x^5+8*x^4+32*x^3+50*x^2+69*x+56', 'y^2=65*x^6+53*x^5+27*x^4+40*x^3+44*x^2+40*x+33', 'y^2=7*x^5+51*x^4+x^3+32*x^2+9*x+21', 'y^2=68*x^6+35*x^5+48*x^4+63*x^3+71*x^2+23*x+66', 'y^2=42*x^6+70*x^5+22*x^4+41*x^3+62*x^2+25*x+38', 'y^2=63*x^6+8*x^5+6*x^4+43*x^3+40*x^2+15*x+58', 'y^2=13*x^6+69*x^5+56*x^4+34*x^3+32*x^2+8*x+13', 'y^2=8*x^6+7*x^5+64*x^4+12*x^3+5*x^2+12*x+36', 'y^2=45*x^6+16*x^5+49*x^4+54*x^3+53*x^2+6*x+42', 'y^2=11*x^6+30*x^5+32*x^4+23*x^3+62*x^2+48*x+42', 'y^2=33*x^6+24*x^5+69*x^4+2*x^3+23*x^2+20*x+70', 'y^2=54*x^6+54*x^5+10*x^4+33*x^3+x^2+4*x+52', 'y^2=17*x^6+31*x^5+22*x^4+38*x^3+40*x^2+57*x+5', 'y^2=52*x^6+45*x^5+42*x^4+29*x^3+55*x^2+6*x+12', 'y^2=48*x^6+22*x^5+60*x^4+64*x^3+57*x^2+10*x+65', 'y^2=56*x^5+59*x^4+23*x^3+44*x^2+19*x+47', 'y^2=10*x^6+39*x^5+72*x^4+47*x^3+42*x^2+33*x+6', 'y^2=65*x^6+67*x^5+7*x^4+15*x^3+26*x^2+12*x+9', 'y^2=59*x^6+10*x^5+37*x^4+59*x^3+2*x^2+5*x+62', 'y^2=70*x^6+66*x^5+64*x^4+53*x^3+40*x^2+31*x+37', 'y^2=64*x^6+2*x^5+45*x^4+55*x^3+72*x^2+71*x+13', 'y^2=11*x^6+6*x^5+45*x^4+69*x^3+72*x^2+4*x+6', 'y^2=32*x^6+23*x^5+28*x^4+72*x^3+54*x^2+9*x+31', 'y^2=55*x^6+32*x^5+32*x^4+45*x^3+x^2+9*x+17', 'y^2=44*x^6+7*x^5+20*x^4+26*x^3+18*x+60', 'y^2=57*x^6+35*x^5+39*x^4+45*x^3+50*x^2+46*x+7', 'y^2=28*x^6+48*x^5+15*x^4+43*x^3+47*x^2+38*x+22'], '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': 6, 'g': 2, 'galois_groups': ['4T3'], 'geom_dim1_distinct': 0, 'geom_dim1_factors': 0, 'geom_dim2_distinct': 1, 'geom_dim2_factors': 1, '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': ['4T3'], 'geometric_number_fields': ['4.0.324400.1'], 'geometric_splitting_field': '4.0.324400.1', 'geometric_splitting_polynomials': [[811, 0, 57, 0, 1]], 'group_structure_count': 2, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 162, 'is_cyclic': False, 'is_geometrically_simple': True, 'is_geometrically_squarefree': True, 'is_primitive': True, 'is_simple': True, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 162, 'label': '2.73.as_ha', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 2, 'newton_coelevation': 2, 'newton_elevation': 0, 'noncyclic_primes': [2], 'number_fields': ['4.0.324400.1'], 'p': 73, 'p_rank': 2, 'p_rank_deficit': 0, 'pic_prime_gens': [[1, 5, 1, 18], [1, 11, 1, 18], [1, 19, 1, 6]], 'poly': [1, -18, 182, -1314, 5329], 'poly_str': '1 -18 182 -1314 5329 ', 'primitive_models': [], 'principal_polarization_count': 162, 'q': 73, 'real_poly': [1, -18, 36], 'simple_distinct': ['2.73.as_ha'], 'simple_factors': ['2.73.as_haA'], 'simple_multiplicities': [1], 'singular_primes': ['2,F^2-F+2', '3,20*F+8*V-135'], 'size': 216, 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '4.0.324400.1', 'splitting_polynomials': [[811, 0, 57, 0, 1]], 'twist_count': 2, 'twists': [['2.73.s_ha', '2.5329.bo_affm', 2]], 'weak_equivalence_count': 6, 'zfv_index': 36, 'zfv_index_factorization': [[2, 2], [3, 2]], 'zfv_is_bass': True, 'zfv_is_maximal': False, 'zfv_pic_size': 72, 'zfv_plus_index': 6, 'zfv_plus_index_factorization': [[2, 1], [3, 1]], 'zfv_plus_norm': 12976, 'zfv_singular_count': 4, 'zfv_singular_primes': ['2,F^2-F+2', '3,20*F+8*V-135']}
• av_fq_endalg_factors •

  Column	Type
  base_label	text
  extension_degree	smallint
  extension_label	text
  multiplicity	smallint

  
  {'base_label': '2.73.as_ha', 'extension_degree': 1, 'extension_label': '2.73.as_ha', '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': '4.0.324400.1', 'center_dim': 4, 'divalg_dim': 1, 'extension_label': '2.73.as_ha', 'galois_group': '4T3', 'places': [['54', '1', '67', '0'], ['19', '1', '6', '0']]}