Abelian variety isogeny class data - 2.113.ax_kz

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• 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': 10433, 'abvar_counts': [10433, 163558141, 2081521977209, 26579997215609141, 339454130356384853248, 4334529789094991520615517, 55347536572622023193580148049, 706732556674873312328903838583973, 9024267965649009393947791141198145753, 115230877661667966584206032299374544982016], 'abvar_counts_str': '10433 163558141 2081521977209 26579997215609141 339454130356384853248 4334529789094991520615517 55347536572622023193580148049 706732556674873312328903838583973 9024267965649009393947791141198145753 115230877661667966584206032299374544982016 ', 'angle_corank': 0, 'angle_rank': 2, 'angles': [0.107532636921407, 0.455819855075615], 'center_dim': 4, 'cohen_macaulay_max': 1, 'curve_count': 91, 'curve_counts': [91, 12811, 1442599, 163020099, 18424210206, 2081954965411, 235260595253215, 26584442079343203, 3004041938144296363, 339456739034743847646], 'curve_counts_str': '91 12811 1442599 163020099 18424210206 2081954965411 235260595253215 26584442079343203 3004041938144296363 339456739034743847646 ', 'curves': ['y^2=78*x^6+67*x^5+60*x^4+83*x^3+x^2+87*x+31', 'y^2=61*x^6+99*x^5+84*x^4+104*x^3+98*x^2+15*x+106', 'y^2=80*x^6+105*x^5+62*x^4+50*x^3+100*x^2+90*x+97', 'y^2=61*x^6+100*x^5+82*x^4+81*x^3+82*x^2+42*x+94', 'y^2=90*x^6+60*x^5+52*x^4+46*x^3+95*x^2+27*x+36', 'y^2=31*x^6+45*x^5+6*x^4+103*x^3+95*x^2+69*x+68', 'y^2=5*x^6+82*x^5+37*x^4+60*x^3+82*x^2+97*x+56', 'y^2=96*x^6+58*x^5+22*x^4+42*x^3+104*x^2+84*x+33', 'y^2=61*x^6+81*x^5+19*x^4+60*x^3+26*x^2+x+85', 'y^2=40*x^6+75*x^5+33*x^4+98*x^3+101*x^2+79*x+56', 'y^2=71*x^6+22*x^5+85*x^4+51*x^3+96*x^2+42*x+58', 'y^2=54*x^6+103*x^5+7*x^4+72*x^3+5*x^2+40*x+10', 'y^2=34*x^6+22*x^5+79*x^4+111*x^3+51*x^2+26*x+95', 'y^2=74*x^6+109*x^5+11*x^4+75*x^3+50*x^2+90*x+73', 'y^2=x^6+23*x^5+69*x^4+30*x^3+11*x^2+27*x+38', 'y^2=42*x^6+76*x^5+86*x^4+27*x^3+21*x^2+10*x+92', 'y^2=24*x^6+6*x^5+63*x^4+79*x^3+78*x^2+18*x+71', 'y^2=105*x^6+92*x^5+105*x^4+100*x^3+109*x^2+10*x+76', 'y^2=66*x^6+70*x^5+32*x^4+41*x^3+26*x^2+75*x+72', 'y^2=32*x^6+82*x^5+52*x^4+44*x^3+28*x^2+94*x+107', 'y^2=11*x^6+11*x^5+71*x^4+15*x^3+21*x^2+52*x+16', 'y^2=76*x^6+57*x^5+109*x^4+64*x^3+26*x^2+x+73', 'y^2=102*x^6+108*x^5+38*x^4+101*x^3+92*x^2+79*x+64', 'y^2=101*x^6+43*x^4+47*x^3+73*x^2+16*x+80', 'y^2=73*x^6+71*x^5+90*x^4+111*x^3+87*x^2+66*x+59', 'y^2=38*x^6+106*x^5+45*x^4+40*x^3+41*x^2+62*x+6', 'y^2=87*x^6+7*x^5+98*x^4+48*x^3+37*x^2+67*x+18', 'y^2=100*x^6+50*x^5+80*x^4+91*x^3+80*x^2+49*x+68', 'y^2=23*x^6+84*x^5+58*x^4+104*x^3+2*x^2+100*x+29', 'y^2=29*x^6+56*x^4+57*x^3+104*x^2+76*x+61', 'y^2=108*x^6+91*x^5+24*x^4+20*x^3+112*x^2+55*x+65', 'y^2=102*x^6+84*x^5+42*x^4+43*x^3+4*x^2+53*x+20', 'y^2=86*x^6+109*x^5+66*x^4+35*x^3+82*x^2+5*x+18', 'y^2=109*x^6+104*x^5+94*x^4+75*x^3+15*x^2+100*x+56', 'y^2=65*x^5+19*x^4+102*x^3+68*x^2+59*x+104', 'y^2=17*x^6+44*x^5+88*x^4+4*x^3+28*x^2+24*x+89', 'y^2=16*x^6+32*x^5+50*x^4+51*x^3+96*x^2+87*x+103', 'y^2=33*x^6+11*x^5+111*x^4+105*x^3+63*x^2+48*x+24', 'y^2=86*x^6+10*x^5+47*x^4+19*x^2+74*x+58', 'y^2=98*x^6+45*x^5+77*x^4+85*x^3+90*x^2+9*x+52', 'y^2=69*x^6+90*x^5+23*x^4+88*x^3+89*x^2+18*x+86', 'y^2=97*x^6+78*x^5+12*x^4+112*x^3+69*x^2+47*x+20', 'y^2=74*x^6+77*x^5+6*x^4+85*x^3+86*x^2+35*x+10', 'y^2=59*x^6+13*x^5+89*x^4+100*x^3+73*x^2+26*x+10', 'y^2=67*x^6+20*x^5+90*x^4+49*x^3+108*x^2+104*x+107', 'y^2=39*x^6+60*x^5+15*x^4+71*x^3+81*x^2+104*x+76', 'y^2=107*x^6+66*x^5+23*x^4+34*x^3+35*x^2+62*x+86', 'y^2=40*x^6+83*x^5+73*x^4+x^3+17*x^2+48*x+35', 'y^2=68*x^6+96*x^5+77*x^4+3*x^3+27*x^2+81*x+79', 'y^2=41*x^6+13*x^5+26*x^4+26*x^3+3*x^2+67*x+85', 'y^2=58*x^6+56*x^5+81*x^4+58*x^3+41*x^2+92*x', 'y^2=101*x^6+54*x^5+5*x^4+58*x^3+105*x^2+84*x+108', 'y^2=69*x^6+83*x^5+39*x^4+11*x^3+38*x^2+50*x+81', 'y^2=64*x^6+108*x^5+30*x^4+40*x^3+105*x^2+76*x+8', 'y^2=6*x^6+94*x^5+91*x^4+64*x^3+3*x^2+109*x+88', 'y^2=84*x^6+80*x^5+66*x^4+61*x^3+46*x^2+6*x+65', 'y^2=38*x^6+106*x^5+51*x^4+82*x^3+25*x^2+64*x+110', 'y^2=111*x^6+50*x^5+79*x^4+86*x^3+89*x^2+89*x+15', 'y^2=27*x^6+102*x^5+57*x^4+86*x^3+49*x^2+33*x+22', 'y^2=5*x^6+42*x^5+111*x^4+35*x^3+29*x^2+42', 'y^2=41*x^6+53*x^5+28*x^4+39*x^3+112*x^2+84*x+36', 'y^2=59*x^6+42*x^5+100*x^4+83*x^3+97*x^2+4*x+19', 'y^2=16*x^6+109*x^5+83*x^4+82*x^3+93*x^2+69*x+6', 'y^2=9*x^6+75*x^5+34*x^4+95*x^3+73*x^2+32*x+31', 'y^2=97*x^6+34*x^5+97*x^4+9*x^3+36*x^2+21*x+77', 'y^2=59*x^6+36*x^5+101*x^4+40*x^3+7*x^2+4*x+73', 'y^2=111*x^6+16*x^5+92*x^4+37*x^3+24*x^2+36*x+15', 'y^2=9*x^6+28*x^5+8*x^4+35*x^3+6*x^2+59*x+104', 'y^2=23*x^6+35*x^5+53*x^4+32*x^3+80*x^2+53*x+43', 'y^2=14*x^6+112*x^5+77*x^4+40*x^3+83*x^2+62*x+110', 'y^2=54*x^6+24*x^5+53*x^4+103*x^3+9*x^2+40*x+93', 'y^2=30*x^6+26*x^5+42*x^4+58*x^3+40*x^2+11*x+36', 'y^2=36*x^6+8*x^5+82*x^4+9*x^3+11*x^2+81*x+65', 'y^2=37*x^6+105*x^5+52*x^4+110*x^3+101*x^2+9*x+48', 'y^2=65*x^6+6*x^5+34*x^4+23*x^3+73*x^2+56*x+47', 'y^2=x^6+28*x^5+104*x^4+3*x^3+106*x^2+36*x+62', 'y^2=47*x^6+92*x^5+39*x^4+64*x^3+103*x^2+44*x+71', 'y^2=84*x^6+101*x^5+90*x^4+42*x^3+26*x^2+87*x+7', 'y^2=26*x^6+3*x^5+21*x^4+58*x^3+90*x^2+85*x+111', 'y^2=45*x^6+70*x^5+58*x^4+35*x^3+87*x^2+96*x+35', 'y^2=24*x^6+62*x^5+8*x^4+22*x^3+27*x^2+97*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': 1, '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': ['4.0.1889794037.1'], 'geometric_splitting_field': '4.0.1889794037.1', 'geometric_splitting_polynomials': [[3763, 799, 87, -1, 1]], 'group_structure_count': 1, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 81, 'is_geometrically_simple': True, 'is_geometrically_squarefree': True, 'is_primitive': True, 'is_simple': True, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 81, 'label': '2.113.ax_kz', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 2, 'newton_coelevation': 2, 'newton_elevation': 0, 'number_fields': ['4.0.1889794037.1'], 'p': 113, 'p_rank': 2, 'p_rank_deficit': 0, 'poly': [1, -23, 285, -2599, 12769], 'poly_str': '1 -23 285 -2599 12769 ', 'primitive_models': [], 'q': 113, 'real_poly': [1, -23, 59], 'simple_distinct': ['2.113.ax_kz'], 'simple_factors': ['2.113.ax_kzA'], 'simple_multiplicities': [1], 'singular_primes': [], 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '4.0.1889794037.1', 'splitting_polynomials': [[3763, 799, 87, -1, 1]], 'twist_count': 2, 'twists': [['2.113.x_kz', '2.12769.bp_asxz', 2]], 'weak_equivalence_count': 1, 'zfv_index': 1, 'zfv_index_factorization': [], 'zfv_is_bass': True, 'zfv_is_maximal': True, 'zfv_plus_index': 1, 'zfv_plus_index_factorization': [], 'zfv_plus_norm': 22013, 'zfv_singular_count': 0, 'zfv_singular_primes': []}
• av_fq_endalg_factors •

  Column	Type
  base_label	text
  extension_degree	smallint
  extension_label	text
  multiplicity	smallint

  
  {'base_label': '2.113.ax_kz', 'extension_degree': 1, 'extension_label': '2.113.ax_kz', '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': '4.0.1889794037.1', 'center_dim': 4, 'divalg_dim': 1, 'extension_label': '2.113.ax_kz', 'galois_group': '4T3', 'places': [['1501/113', '117/113', '5/113', '1/113'], ['107', '1', '0', '0']]}