Abelian variety isogeny class data - 2.97.abc_pa

Formats: - HTML - YAML - JSON - 2025-10-30T08:43:53.099506

• 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': 7056, 'abvar_counts': [7056, 88510464, 835403312016, 7840765305225216, 73744720761342926736, 693842455032982711013376, 6528360795824404696553863056, 61425362573258679843953845469184, 577951260583274376046278449742754704, 5437943429136960821825249151610865946624], 'abvar_counts_str': '7056 88510464 835403312016 7840765305225216 73744720761342926736 693842455032982711013376 6528360795824404696553863056 61425362573258679843953845469184 577951260583274376046278449742754704 5437943429136960821825249151610865946624 ', 'angle_corank': 1, 'angle_rank': 1, 'angles': [0.248359198325529, 0.248359198325529], 'center_dim': 2, 'curve_count': 70, 'curve_counts': [70, 9406, 915334, 88566910, 8587609030, 832972117822, 80798259987718, 7837433240560894, 760231056076708678, 73742412687722993086], 'curve_counts_str': '70 9406 915334 88566910 8587609030 832972117822 80798259987718 7837433240560894 760231056076708678 73742412687722993086 ', 'curves': ['y^2=64*x^6+43*x^5+93*x^4+78*x^3+93*x^2+43*x+64', 'y^2=91*x^6+91*x^5+73*x^4+4*x^3+66*x^2+88*x+49', 'y^2=6*x^6+82*x^5+65*x^4+40*x^3+79*x^2+7*x+93', 'y^2=x^6+36*x^5+44*x^4+35*x^3+44*x^2+36*x+1', 'y^2=22*x^6+78*x^5+28*x^4+68*x^3+74*x^2+41*x+8', 'y^2=81*x^6+31*x^5+79*x^4+11*x^3+79*x^2+31*x+81', 'y^2=59*x^6+37*x^5+40*x^4+62*x^3+83*x^2+46*x+5', 'y^2=43*x^6+33*x^5+63*x^4+51*x^3+63*x^2+33*x+43', 'y^2=73*x^6+50*x^5+34*x^4+25*x^3+82*x^2+68*x+37', 'y^2=41*x^6+94*x^4+94*x^2+41', 'y^2=59*x^6+88*x^5+92*x^4+69*x^3+92*x^2+88*x+59', 'y^2=50*x^6+3*x^5+22*x^4+16*x^3+22*x^2+3*x+50', 'y^2=62*x^6+86*x^4+86*x^2+62', 'y^2=87*x^6+44*x^5+43*x^4+46*x^3+43*x^2+44*x+87', 'y^2=5*x^6+4*x^5+36*x^4+79*x^3+36*x^2+4*x+5', 'y^2=20*x^6+25*x^5+49*x^4+90*x^3+49*x^2+25*x+20', 'y^2=15*x^6+62*x^4+62*x^2+15', 'y^2=52*x^6+57*x^5+43*x^4+10*x^3+49*x^2+63*x+63', 'y^2=85*x^6+88*x^5+8*x^4+44*x^3+8*x^2+88*x+85', 'y^2=34*x^6+61*x^5+78*x^4+52*x^3+78*x^2+61*x+34', 'y^2=91*x^6+45*x^5+x^4+3*x^3+81*x^2+74*x+35', 'y^2=48*x^6+58*x^5+9*x^4+92*x^3+64*x^2+90*x+48', 'y^2=15*x^6+50*x^5+8*x^4+63*x^3+11*x^2+43*x+82', 'y^2=26*x^6+26*x^5+41*x^4+30*x^3+41*x^2+26*x+26', 'y^2=33*x^6+22*x^5+46*x^4+96*x^3+2*x^2+30*x+5', 'y^2=18*x^6+44*x^5+58*x^4+50*x^3+85*x^2+81*x+5', 'y^2=50*x^6+81*x^4+81*x^2+50', 'y^2=47*x^6+81*x^5+18*x^4+65*x^3+35*x^2+67*x+1', 'y^2=x^6+44*x^3+18', 'y^2=58*x^6+69*x^5+25*x^4+44*x^3+25*x^2+69*x+58', 'y^2=82*x^6+30*x^5+29*x^4+5*x^3+29*x^2+30*x+82', 'y^2=82*x^6+30*x^5+78*x^4+83*x^3+79*x^2+50*x+45', 'y^2=37*x^6+56*x^5+34*x^3+5*x^2+45*x+36', 'y^2=74*x^6+45*x^5+55*x^4+6*x^3+55*x^2+45*x+74', 'y^2=90*x^6+39*x^5+71*x^4+17*x^3+35*x^2+85*x+20', 'y^2=68*x^6+81*x^5+9*x^4+59*x^3+65*x^2+54*x+77', 'y^2=76*x^6+48*x^4+48*x^2+76', 'y^2=20*x^6+71*x^5+36*x^4+80*x^3+65*x^2+37*x+21', 'y^2=21*x^6+68*x^5+58*x^4+53*x^3+4*x^2+4*x+34', 'y^2=x^6+x^3+27', 'y^2=82*x^6+59*x^5+78*x^4+64*x^3+79*x^2+48*x+55', 'y^2=16*x^6+25*x^4+25*x^2+16', 'y^2=50*x^6+30*x^5+61*x^4+54*x^3+61*x^2+30*x+50', 'y^2=73*x^6+13*x^5+83*x^4+81*x^3+21*x^2+5*x+81', 'y^2=62*x^6+78*x^5+51*x^4+19*x^3+84*x^2+76*x+48', 'y^2=91*x^6+85*x^5+27*x^4+46*x^3+27*x^2+85*x+91', 'y^2=78*x^6+36*x^5+18*x^4+47*x^3+16*x^2+50*x+46', 'y^2=52*x^6+20*x^5+39*x^4+46*x^3+39*x^2+20*x+52', 'y^2=62*x^6+57*x^5+34*x^4+87*x^3+77*x^2+60*x+49', 'y^2=x^6+96', 'y^2=8*x^6+27*x^5+24*x^4+58*x^3+74*x^2+24*x+74', 'y^2=78*x^6+62*x^5+46*x^4+20*x^3+46*x^2+62*x+78', 'y^2=73*x^6+29*x^5+34*x^4+6*x^3+34*x^2+29*x+73', 'y^2=x^6+9*x^3+50', 'y^2=65*x^6+64*x^5+12*x^4+79*x^3+40*x^2+47*x+34', 'y^2=6*x^6+x^5+5*x^4+77*x^3+91*x^2+53*x+16', 'y^2=23*x^6+58*x^5+51*x^4+85*x^3+85*x+2', 'y^2=84*x^6+74*x^5+69*x^4+12*x^3+69*x^2+74*x+84', 'y^2=23*x^6+12*x^5+59*x^4+19*x^3+84*x^2+30*x+20', 'y^2=20*x^6+72*x^5+56*x^4+91*x^3+76*x^2+95*x+77', 'y^2=67*x^6+27*x^5+58*x^4+90*x^3+28*x^2+65*x+77', 'y^2=48*x^6+48*x^5+23*x^4+90*x^3+23*x^2+48*x+48'], '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': ['2.0.3.1'], 'geometric_splitting_field': '2.0.3.1', 'geometric_splitting_polynomials': [[1, -1, 1]], 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 62, 'is_geometrically_simple': False, 'is_geometrically_squarefree': False, 'is_primitive': True, 'is_simple': False, 'is_squarefree': False, 'is_supersingular': False, 'jacobian_count': 62, 'label': '2.97.abc_pa', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 12, 'newton_coelevation': 2, 'newton_elevation': 0, 'number_fields': ['2.0.3.1'], 'p': 97, 'p_rank': 2, 'p_rank_deficit': 0, 'poly': [1, -28, 390, -2716, 9409], 'poly_str': '1 -28 390 -2716 9409 ', 'primitive_models': [], 'q': 97, 'real_poly': [1, -28, 196], 'simple_distinct': ['1.97.ao'], 'simple_factors': ['1.97.aoA', '1.97.aoB'], 'simple_multiplicities': [2], 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '2.0.3.1', 'splitting_polynomials': [[1, -1, 1]], 'twist_count': 24, 'twists': [['2.97.a_ac', '2.9409.ae_bbvy', 2], ['2.97.bc_pa', '2.9409.ae_bbvy', 2], ['2.97.at_ke', '2.912673.dyi_hwmyg', 3], ['2.97.ak_il', '2.912673.dyi_hwmyg', 3], ['2.97.f_acu', '2.912673.dyi_hwmyg', 3], ['2.97.o_dv', '2.912673.dyi_hwmyg', 3], ['2.97.bm_vj', '2.912673.dyi_hwmyg', 3], ['2.97.a_c', '2.88529281.cdrg_bssbceo', 4], ['2.97.abm_vj', '2.832972004929.glaa_hzvexkqty', 6], ['2.97.abh_rs', '2.832972004929.glaa_hzvexkqty', 6], ['2.97.ay_ld', '2.832972004929.glaa_hzvexkqty', 6], ['2.97.ao_dv', '2.832972004929.glaa_hzvexkqty', 6], ['2.97.aj_eu', '2.832972004929.glaa_hzvexkqty', 6], ['2.97.af_acu', '2.832972004929.glaa_hzvexkqty', 6], ['2.97.a_agl', '2.832972004929.glaa_hzvexkqty', 6], ['2.97.a_gn', '2.832972004929.glaa_hzvexkqty', 6], ['2.97.j_eu', '2.832972004929.glaa_hzvexkqty', 6], ['2.97.k_il', '2.832972004929.glaa_hzvexkqty', 6], ['2.97.t_ke', '2.832972004929.glaa_hzvexkqty', 6], ['2.97.y_ld', '2.832972004929.glaa_hzvexkqty', 6], ['2.97.bh_rs', '2.832972004929.glaa_hzvexkqty', 6], ['2.97.a_agn', '2.693842360995438000295041.pybddvhnw_drftcjjzkwzevujfkg', 12], ['2.97.a_gl', '2.693842360995438000295041.pybddvhnw_drftcjjzkwzevujfkg', 12]]}
• av_fq_endalg_factors •

  Column	Type
  base_label	text
  extension_degree	smallint
  extension_label	text
  multiplicity	smallint

  
  {'base_label': '2.97.abc_pa', 'extension_degree': 1, 'extension_label': '1.97.ao', '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': '2.0.3.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.97.ao', 'galois_group': '2T1', 'places': [['35', '1'], ['61', '1']]}