Abelian variety isogeny class data - 2.61.ay_kc

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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': 2496, 'abvar_counts': [2496, 13658112, 51667761600, 191830914662400, 713391542560721856, 2654358551939349964800, 9876832628316327858565056, 36751694451781971901847961600, 136753054296555381088572946814400, 508858110709178338057023579214374912], 'abvar_counts_str': '2496 13658112 51667761600 191830914662400 713391542560721856 2654358551939349964800 9876832628316327858565056 36751694451781971901847961600 136753054296555381088572946814400 508858110709178338057023579214374912 ', 'angle_corank': 0, 'angle_rank': 2, 'angles': [0.146275019398249, 0.278857938376305], 'center_dim': 4, 'cohen_macaulay_max': 3, 'curve_count': 38, 'curve_counts': [38, 3670, 227630, 13854766, 844653878, 51520560262, 3142742866238, 191707316101726, 11694146217341510, 713342913190197430], 'curve_counts_str': '38 3670 227630 13854766 844653878 51520560262 3142742866238 191707316101726 11694146217341510 713342913190197430 ', 'curves': ['y^2=50*x^6+39*x^5+8*x^4+25*x^3+37*x^2+46*x+53', 'y^2=25*x^6+5*x^5+56*x^4+4*x^3+16*x^2+18*x+31', 'y^2=40*x^6+52*x^5+13*x^3+49*x^2+28*x+54', 'y^2=32*x^6+45*x^5+37*x^4+18*x^3+18*x^2+52*x+17', 'y^2=55*x^6+20*x^5+55*x^4+43*x^3+55*x^2+20*x+55', 'y^2=18*x^6+41*x^5+21*x^4+28*x^3+21*x^2+41*x+18', 'y^2=54*x^6+34*x^5+17*x^4+30*x^3+44*x^2+38*x+32', 'y^2=25*x^6+39*x^5+40*x^4+5*x^3+31*x^2+41*x+19', 'y^2=10*x^6+x^5+23*x^4+13*x^3+53*x^2+9*x+35', 'y^2=10*x^6+57*x^5+26*x^4+24*x^3+49*x^2+19*x+39', 'y^2=37*x^6+4*x^5+6*x^4+5*x^3+6*x^2+4*x+37', 'y^2=29*x^6+49*x^5+39*x^4+16*x^3+39*x^2+49*x+29', 'y^2=37*x^6+59*x^5+15*x^4+33*x^3+15*x^2+59*x+37', 'y^2=54*x^6+55*x^5+22*x^4+18*x^2+4*x+55', 'y^2=21*x^6+19*x^5+44*x^4+37*x^3+49*x^2+40*x+54', 'y^2=10*x^6+46*x^5+38*x^4+59*x^3+31*x^2+4*x+31', 'y^2=31*x^6+37*x^5+x^4+52*x^3+46*x^2+55*x+26', 'y^2=50*x^6+24*x^5+36*x^4+13*x^3+9*x^2+44*x+23', 'y^2=34*x^6+24*x^5+4*x^4+27*x^3+4*x^2+24*x+34', 'y^2=15*x^6+35*x^5+43*x^4+47*x^3+39*x^2+30*x+33', 'y^2=38*x^6+4*x^5+49*x^4+14*x^3+25*x^2+36*x+50', 'y^2=59*x^6+17*x^5+29*x^4+31*x^3+29*x^2+17*x+59', 'y^2=10*x^6+26*x^5+21*x^4+54*x^3+21*x^2+26*x+10', 'y^2=2*x^6+24*x^5+13*x^4+38*x^3+13*x^2+24*x+2', 'y^2=33*x^6+48*x^5+26*x^4+52*x^3+17*x^2+5*x+37', 'y^2=51*x^6+50*x^5+51*x^4+34*x^3+29*x^2+24*x+31', 'y^2=29*x^6+50*x^5+37*x^4+31*x^3+24*x^2+26*x+33', 'y^2=45*x^6+27*x^5+16*x^4+41*x^3+40*x^2+55*x+30', 'y^2=32*x^6+50*x^5+36*x^4+4*x^3+20*x^2+32*x+29', 'y^2=24*x^6+37*x^5+30*x^4+26*x^3+5*x^2+5*x+39', 'y^2=29*x^6+12*x^4+15*x^3+12*x^2+29', 'y^2=21*x^6+4*x^5+53*x^4+39*x^3+53*x^2+4*x+21', 'y^2=54*x^6+41*x^5+56*x^4+3*x^3+60*x^2+22*x+19', 'y^2=2*x^5+51*x^4+52*x^3+10*x^2+2*x', 'y^2=8*x^6+8*x^5+44*x^4+6*x^3+44*x^2+8*x+8', 'y^2=54*x^6+58*x^5+37*x^4+37*x^2+58*x+54', 'y^2=55*x^6+53*x^5+32*x^4+10*x^3+59*x+8', 'y^2=58*x^6+x^5+2*x^4+54*x^3+8*x^2+3*x+57', 'y^2=21*x^6+6*x^5+54*x^4+2*x^3+24*x^2+16*x+53', 'y^2=13*x^6+43*x^5+20*x^4+58*x^3+51*x^2+53*x+2', 'y^2=58*x^6+4*x^5+6*x^4+10*x^3+6*x^2+4*x+58', 'y^2=55*x^6+46*x^5+17*x^4+43*x^3+17*x^2+46*x+55', 'y^2=29*x^5+31*x^4+7*x^3+35*x^2+31*x', 'y^2=18*x^6+31*x^5+27*x^4+56*x^3+48*x+31', 'y^2=35*x^6+9*x^5+50*x^4+9*x^3+50*x^2+9*x+35', 'y^2=8*x^6+50*x^5+10*x^4+50*x^3+10*x^2+50*x+8', 'y^2=6*x^6+44*x^5+5*x^4+27*x^3+5*x^2+44*x+6', 'y^2=48*x^6+10*x^5+51*x^4+16*x^3+22*x^2+45*x+49', 'y^2=18*x^6+41*x^5+3*x^4+35*x^3+3*x^2+41*x+18', 'y^2=53*x^6+36*x^5+21*x^4+57*x^3+21*x^2+36*x+53', 'y^2=40*x^6+57*x^5+55*x^4+54*x^3+53*x^2+20*x+18', 'y^2=55*x^5+48*x^4+58*x^3+48*x^2+55*x', 'y^2=15*x^6+11*x^5+36*x^4+56*x^3+20*x^2+29*x+46', 'y^2=50*x^6+60*x^5+10*x^4+24*x^3+10*x^2+60*x+50', 'y^2=26*x^6+54*x^5+25*x^4+37*x^3+25*x^2+54*x+26', 'y^2=60*x^6+35*x^5+59*x^4+57*x^3+59*x^2+35*x+60', 'y^2=40*x^6+22*x^5+59*x^4+7*x^3+46*x^2+21*x+59', 'y^2=54*x^6+50*x^5+23*x^4+50*x^3+50*x^2+33*x+43', 'y^2=44*x^6+9*x^5+58*x^4+31*x^3+58*x^2+9*x+44', 'y^2=52*x^6+44*x^5+60*x^4+6*x^3+52*x^2+26*x+27'], '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': 36, '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': 4, 'geometric_extension_degree': 1, 'geometric_galois_groups': ['2T1', '2T1'], 'geometric_number_fields': ['2.0.3.1', '2.0.4.1'], 'geometric_splitting_field': '4.0.144.1', 'geometric_splitting_polynomials': [[1, 0, -1, 0, 1]], 'group_structure_count': 9, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 60, 'is_geometrically_simple': False, 'is_geometrically_squarefree': True, 'is_primitive': True, 'is_simple': False, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 60, 'label': '2.61.ay_kc', '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', '2.0.4.1'], 'p': 61, 'p_rank': 2, 'p_rank_deficit': 0, 'poly': [1, -24, 262, -1464, 3721], 'poly_str': '1 -24 262 -1464 3721 ', 'primitive_models': [], 'q': 61, 'real_poly': [1, -24, 140], 'simple_distinct': ['1.61.ao', '1.61.ak'], 'simple_factors': ['1.61.aoA', '1.61.akA'], 'simple_multiplicities': [1, 1], 'singular_primes': ['2,3*F+1', '3,-3*F+V-14'], 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '4.0.144.1', 'splitting_polynomials': [[1, 0, -1, 0, 1]], 'twist_count': 24, 'twists': [['2.61.ae_as', '2.3721.aca_ipq', 2], ['2.61.e_as', '2.3721.aca_ipq', 2], ['2.61.y_kc', '2.3721.aca_ipq', 2], ['2.61.aj_ei', '2.226981.yy_rgcc', 3], ['2.61.d_ai', '2.226981.yy_rgcc', 3], ['2.61.aba_le', '2.13845841.nfg_dmnvwo', 4], ['2.61.ac_abu', '2.13845841.nfg_dmnvwo', 4], ['2.61.c_abu', '2.13845841.nfg_dmnvwo', 4], ['2.61.ba_le', '2.13845841.nfg_dmnvwo', 4], ['2.61.ax_js', '2.51520374361.kpaa_nmzagxy', 6], ['2.61.al_fc', '2.51520374361.kpaa_nmzagxy', 6], ['2.61.ad_ai', '2.51520374361.kpaa_nmzagxy', 6], ['2.61.j_ei', '2.51520374361.kpaa_nmzagxy', 6], ['2.61.l_fc', '2.51520374361.kpaa_nmzagxy', 6], ['2.61.x_js', '2.51520374361.kpaa_nmzagxy', 6], ['2.61.az_ks', '2.2654348974297586158321.adgwszmee_bbjkscvgltlvdamg', 12], ['2.61.an_fe', '2.2654348974297586158321.adgwszmee_bbjkscvgltlvdamg', 12], ['2.61.al_eg', '2.2654348974297586158321.adgwszmee_bbjkscvgltlvdamg', 12], ['2.61.ab_abi', '2.2654348974297586158321.adgwszmee_bbjkscvgltlvdamg', 12], ['2.61.b_abi', '2.2654348974297586158321.adgwszmee_bbjkscvgltlvdamg', 12], ['2.61.l_eg', '2.2654348974297586158321.adgwszmee_bbjkscvgltlvdamg', 12], ['2.61.n_fe', '2.2654348974297586158321.adgwszmee_bbjkscvgltlvdamg', 12], ['2.61.z_ks', '2.2654348974297586158321.adgwszmee_bbjkscvgltlvdamg', 12]], 'weak_equivalence_count': 62, 'zfv_index': 384, 'zfv_index_factorization': [[2, 7], [3, 1]], 'zfv_is_bass': False, 'zfv_is_maximal': False, 'zfv_plus_index': 1, 'zfv_plus_index_factorization': [], 'zfv_plus_norm': 6912, 'zfv_singular_count': 4, 'zfv_singular_primes': ['2,3*F+1', '3,-3*F+V-14']}
• av_fq_endalg_factors •

  Column	Type
  base_label	text
  extension_degree	smallint
  extension_label	text
  multiplicity	smallint

  
  
  • id: 58785
    {'base_label': '2.61.ay_kc', 'extension_degree': 1, 'extension_label': '1.61.ao', 'multiplicity': 1}
  • id: 58786
    {'base_label': '2.61.ay_kc', 'extension_degree': 1, 'extension_label': '1.61.ak', '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': '2.0.3.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.61.ao', 'galois_group': '2T1', 'places': [['13', '1'], ['47', '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': '2.0.4.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.61.ak', 'galois_group': '2T1', 'places': [['50', '1'], ['11', '1']]}