Abelian variety isogeny class data - 2.113.az_ma

Formats: - HTML - YAML - JSON - 2025-10-25T22:05:26.194964

• 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': 10232, 'abvar_counts': [10232, 163016224, 2080941922304, 26578452721579136, 339449671022827141432, 4334522905715198808457216, 55347530762527468905298752248, 706732552076274418853259319038464, 9024267956286328751314764058765285376, 115230877646539712516570215906829312398624], 'abvar_counts_str': '10232 163016224 2080941922304 26578452721579136 339449671022827141432 4334522905715198808457216 55347530762527468905298752248 706732552076274418853259319038464 9024267956286328751314764058765285376 115230877646539712516570215906829312398624 ', 'angle_corank': 0, 'angle_rank': 2, 'angles': [0.0601744223070752, 0.437945754369735], 'center_dim': 4, 'cohen_macaulay_max': 1, 'curve_count': 89, 'curve_counts': [89, 12769, 1442198, 163010625, 18423968169, 2081951659198, 235260570556793, 26584441906362369, 3004041935027601974, 339456738990177773889], 'curve_counts_str': '89 12769 1442198 163010625 18423968169 2081951659198 235260570556793 26584441906362369 3004041935027601974 339456738990177773889 ', 'curves': ['y^2=83*x^6+99*x^5+73*x^4+93*x^3+68*x^2+39*x+4', 'y^2=34*x^6+17*x^5+31*x^4+22*x^3+5*x+31', 'y^2=101*x^6+25*x^5+67*x^4+108*x^3+49*x^2+10*x+51', 'y^2=22*x^6+68*x^5+88*x^4+64*x^3+29*x^2+54*x+18', 'y^2=67*x^6+15*x^5+30*x^4+112*x^3+85*x^2+27*x+75', 'y^2=108*x^6+87*x^5+44*x^4+48*x^3+19*x^2+90*x+42', 'y^2=42*x^6+72*x^5+87*x^4+4*x^3+74*x^2+36*x+63', 'y^2=33*x^6+40*x^5+45*x^4+112*x^3+43*x+75', 'y^2=84*x^6+103*x^5+13*x^4+38*x^3+50*x^2+22*x+76', 'y^2=12*x^6+17*x^5+4*x^4+31*x^3+33*x^2+95*x+57', 'y^2=41*x^6+3*x^5+23*x^4+42*x^3+86*x^2+3*x+13', 'y^2=33*x^6+6*x^5+68*x^4+8*x^3+26*x^2+107*x', 'y^2=110*x^6+x^5+76*x^4+83*x^3+37*x^2+6*x+73', 'y^2=45*x^6+47*x^5+44*x^4+90*x^3+102*x^2+5', 'y^2=79*x^6+38*x^5+107*x^4+48*x^3+20*x^2+63*x+13', 'y^2=107*x^6+84*x^5+65*x^4+18*x^3+17*x^2+88*x+28', 'y^2=29*x^6+21*x^5+72*x^4+42*x^3+27*x^2+93*x+76', 'y^2=74*x^6+85*x^5+103*x^4+37*x^3+100*x^2+27*x+108', 'y^2=14*x^6+80*x^5+95*x^4+94*x^3+52*x^2+4*x+20', 'y^2=48*x^6+44*x^5+3*x^4+2*x^3+18*x^2+81*x+10', 'y^2=24*x^6+64*x^5+7*x^4+24*x^3+15*x^2+75*x+8', 'y^2=101*x^6+59*x^5+42*x^4+102*x^3+22*x^2+71*x+97', 'y^2=64*x^6+11*x^5+5*x^4+21*x^3+102*x^2+92*x+81', 'y^2=46*x^6+85*x^5+28*x^4+58*x^3+39*x^2+87*x+112', 'y^2=16*x^6+79*x^5+12*x^4+60*x^3+44*x^2+60*x+67', 'y^2=40*x^6+39*x^5+5*x^4+83*x^3+96*x^2+60*x+3', 'y^2=65*x^6+44*x^5+25*x^4+30*x^3+25*x^2+64*x+28', 'y^2=96*x^6+106*x^5+25*x^4+61*x^3+96*x^2+87*x+67', 'y^2=8*x^6+12*x^5+41*x^4+67*x^3+44*x^2+6*x+58', 'y^2=64*x^6+43*x^5+93*x^4+79*x^3+74*x^2+96*x+86', 'y^2=24*x^6+96*x^5+24*x^4+99*x^3+12*x^2+102*x+18', 'y^2=51*x^6+56*x^5+54*x^4+95*x^3+23*x^2+103', 'y^2=5*x^6+33*x^5+42*x^4+17*x^3+15*x^2+19*x+45', 'y^2=2*x^6+38*x^5+66*x^4+29*x^3+49*x^2+77*x+61', 'y^2=53*x^6+74*x^5+76*x^4+36*x^3+83*x^2+6*x+95', 'y^2=93*x^6+12*x^5+71*x^4+49*x^3+100*x^2+55*x+84', 'y^2=13*x^6+16*x^5+27*x^4+34*x^3+50*x^2+86*x+86', 'y^2=8*x^6+63*x^5+19*x^4+69*x^3+25*x^2+72*x+53', 'y^2=78*x^6+90*x^5+71*x^4+2*x^3+8*x^2+61*x+108', 'y^2=76*x^6+73*x^5+44*x^4+70*x^3+17*x^2+99*x+67', 'y^2=78*x^6+14*x^5+66*x^4+89*x^3+111*x^2+55*x+29', 'y^2=86*x^6+59*x^5+8*x^4+64*x^3+40*x^2+33*x+59', 'y^2=48*x^6+42*x^5+52*x^4+53*x^3+19*x^2+71*x+101', 'y^2=51*x^6+44*x^5+42*x^4+80*x^3+42*x^2+110*x+80', 'y^2=53*x^6+53*x^5+66*x^4+64*x^3+67*x^2+18*x+104', 'y^2=53*x^6+3*x^5+12*x^4+29*x^3+112*x^2+13*x+26', 'y^2=50*x^6+26*x^5+41*x^4+47*x^3+81*x^2+95*x+72', 'y^2=69*x^6+10*x^5+56*x^4+99*x^3+112*x^2+102*x+108', 'y^2=54*x^6+13*x^5+99*x^4+9*x^3+90*x^2+31*x+91', 'y^2=50*x^6+95*x^5+111*x^4+63*x^3+40*x^2+36*x+47', 'y^2=71*x^6+2*x^5+30*x^4+42*x^3+5*x^2+47*x+92', 'y^2=56*x^6+51*x^5+100*x^4+100*x^3+43*x^2+23*x+40', 'y^2=80*x^6+11*x^5+42*x^4+50*x^3+93*x^2+79*x+77', 'y^2=88*x^6+65*x^5+78*x^4+21*x^3+64*x^2+103*x+5', 'y^2=74*x^6+46*x^5+5*x^4+4*x^3+83*x^2+76*x+102', 'y^2=78*x^6+56*x^5+53*x^4+36*x^3+35*x^2+85*x+112', 'y^2=48*x^6+49*x^5+110*x^4+108*x^3+7*x^2+32*x+70', 'y^2=112*x^6+12*x^5+91*x^4+27*x^3+28*x^2+4*x+55', 'y^2=42*x^6+19*x^5+52*x^4+29*x^3+67*x^2+54', 'y^2=34*x^6+20*x^5+32*x^4+41*x^3+110*x^2+56*x+19', 'y^2=55*x^6+43*x^5+76*x^4+8*x^3+88*x^2+94*x', 'y^2=94*x^6+30*x^5+62*x^4+36*x^3+68*x^2+100*x+13', 'y^2=87*x^6+29*x^5+94*x^4+47*x^3+32*x^2+33*x+73', 'y^2=98*x^6+109*x^5+41*x^4+64*x^3+91*x^2+94*x+31', 'y^2=83*x^6+56*x^5+70*x^4+32*x^3+4*x^2+8*x+13', 'y^2=47*x^6+84*x^5+27*x^4+86*x^3+7*x^2+33*x+52', 'y^2=71*x^6+81*x^5+43*x^4+77*x^3+57*x^2+11*x+27', 'y^2=87*x^6+107*x^5+79*x^4+37*x^3+3*x^2+71*x+38', 'y^2=76*x^6+57*x^5+47*x^4+42*x^3+84*x^2+66*x+24', 'y^2=84*x^6+44*x^5+37*x^3+31*x^2+23*x+24', 'y^2=47*x^6+103*x^5+69*x^4+8*x^3+53*x^2+5*x+109', 'y^2=26*x^6+33*x^5+72*x^4+73*x^3+94*x^2+17*x+30'], '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': 2, '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': ['4.0.137076296.1'], 'geometric_splitting_field': '4.0.137076296.1', 'geometric_splitting_polynomials': [[2947, -917, 78, -1, 1]], 'group_structure_count': 2, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 72, 'is_geometrically_simple': True, 'is_geometrically_squarefree': True, 'is_primitive': True, 'is_simple': True, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 72, 'label': '2.113.az_ma', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 2, 'newton_coelevation': 2, 'newton_elevation': 0, 'number_fields': ['4.0.137076296.1'], 'p': 113, 'p_rank': 2, 'p_rank_deficit': 0, 'poly': [1, -25, 312, -2825, 12769], 'poly_str': '1 -25 312 -2825 12769 ', 'primitive_models': [], 'q': 113, 'real_poly': [1, -25, 86], 'simple_distinct': ['2.113.az_ma'], 'simple_factors': ['2.113.az_maA'], 'simple_multiplicities': [1], 'singular_primes': ['2,-11*F-4*V+99'], 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '4.0.137076296.1', 'splitting_polynomials': [[2947, -917, 78, -1, 1]], 'twist_count': 2, 'twists': [['2.113.z_ma', '2.12769.ab_abbem', 2]], 'weak_equivalence_count': 2, 'zfv_index': 2, 'zfv_index_factorization': [[2, 1]], 'zfv_is_bass': True, 'zfv_is_maximal': False, 'zfv_plus_index': 1, 'zfv_plus_index_factorization': [], 'zfv_plus_norm': 6944, 'zfv_singular_count': 2, 'zfv_singular_primes': ['2,-11*F-4*V+99']}
• av_fq_endalg_factors •

  Column	Type
  base_label	text
  extension_degree	smallint
  extension_label	text
  multiplicity	smallint

  
  {'base_label': '2.113.az_ma', 'extension_degree': 1, 'extension_label': '2.113.az_ma', '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': '4.0.137076296.1', 'center_dim': 4, 'divalg_dim': 1, 'extension_label': '2.113.az_ma', 'galois_group': '4T3', 'places': [['11132/113', '120/113', '12762/113', '1/113'], ['6', '1', '0', '0']]}