Abelian variety isogeny class data - 2.61.aq_he

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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': 2916, 'abvar_counts': [2916, 14288400, 51953908356, 191820284006400, 713299927426289316, 2654302364946880880400, 9876819544993997025708996, 36751698097816430477706854400, 136753057858358162634808539418596, 508858111105703527015772321150250000], 'abvar_counts_str': '2916 14288400 51953908356 191820284006400 713299927426289316 2654302364946880880400 9876819544993997025708996 36751698097816430477706854400 136753057858358162634808539418596 508858111105703527015772321150250000 ', 'angle_corank': 1, 'angle_rank': 1, 'angles': [0.328850104904971, 0.328850104904971], 'center_dim': 2, 'curve_count': 46, 'curve_counts': [46, 3838, 228886, 13853998, 844545406, 51519469678, 3142738703206, 191707335120478, 11694146521921486, 713342913746066398], 'curve_counts_str': '46 3838 228886 13853998 844545406 51519469678 3142738703206 191707335120478 11694146521921486 713342913746066398 ', 'curves': ['y^2=50*x^6+2*x^5+24*x^4+30*x^3+24*x^2+2*x+50', 'y^2=16*x^6+58*x^4+58*x^2+16', 'y^2=52*x^6+50*x^5+6*x^4+47*x^3+60*x^2+50*x+49', 'y^2=37*x^6+3*x^5+35*x^4+24*x^3+36*x^2+44*x+50', 'y^2=7*x^6+42*x^5+51*x^4+55*x^3+26*x^2+57*x+18', 'y^2=49*x^6+54*x^5+10*x^4+34*x^3+7*x^2+13*x+37', 'y^2=52*x^6+25*x^5+40*x^4+26*x^3+7*x^2+57*x+41', 'y^2=29*x^6+10*x^5+27*x^4+34*x^3+27*x^2+10*x+29', 'y^2=27*x^6+x^5+9*x^4+35*x^3+9*x^2+x+27', 'y^2=39*x^6+60*x^5+15*x^4+10*x^3+2*x^2+56*x+7', 'y^2=x^6+16*x^3+9', 'y^2=38*x^6+59*x^5+42*x^4+2*x^3+42*x^2+59*x+38', 'y^2=x^6+x^3+20', 'y^2=32*x^6+44*x^5+19*x^4+38*x^3+22*x^2+31*x+5', 'y^2=60*x^6+24*x^5+9*x^4+3*x^3+9*x^2+24*x+60', 'y^2=58*x^6+10*x^5+56*x^4+3*x^3+56*x^2+10*x+58', 'y^2=9*x^6+3*x^5+46*x^4+4*x^3+46*x^2+3*x+9', 'y^2=42*x^6+50*x^5+41*x^4+13*x^3+32*x^2+23*x+11', 'y^2=11*x^6+15*x^5+47*x^4+30*x^3+55*x^2+60*x+45', 'y^2=58*x^6+23*x^4+23*x^2+58', 'y^2=38*x^6+45*x^5+29*x^4+3*x^3+29*x^2+45*x+38', 'y^2=6*x^6+48*x^5+27*x^4+33*x^3+22*x^2+19*x+26', 'y^2=7*x^6+12*x^5+5*x^4+42*x^3+39*x^2+5*x+29', 'y^2=4*x^6+56*x^5+28*x^4+53*x^3+20*x^2+54*x+53', 'y^2=27*x^6+53*x^5+47*x^4+2*x^3+47*x^2+53*x+27', 'y^2=35*x^6+18*x^5+59*x^4+38*x^3+20*x^2+50*x+24', 'y^2=31*x^5+60*x^4+2*x^3+4*x^2+8*x', 'y^2=37*x^6+51*x^5+46*x^4+33*x^3+53*x^2+44*x+31', 'y^2=12*x^6+19*x^5+44*x^4+21*x^3+13*x^2+20*x+21', 'y^2=x^6+39*x^3+27', 'y^2=28*x^6+48*x^5+12*x^4+23*x^3+16*x^2+34*x+21', 'y^2=24*x^5+20*x^4+45*x^3+25*x^2+7*x', 'y^2=38*x^6+51*x^5+28*x^4+40*x^3+47*x^2+23*x+56', 'y^2=10*x^6+2*x^5+8*x^4+13*x^3+8*x^2+2*x+10', 'y^2=11*x^6+46*x^5+47*x^4+15*x^3+49*x^2+45*x+24', 'y^2=55*x^6+56*x^5+40*x^4+31*x^3+7*x^2+13*x+7', 'y^2=17*x^6+14*x^5+14*x^4+2*x^3+47*x^2+14*x+44', 'y^2=43*x^6+39*x^5+37*x^4+8*x^3+24*x^2+39*x+18', 'y^2=50*x^6+24*x^5+38*x^4+11*x^3+51*x^2+40*x+19', 'y^2=35*x^6+x^5+6*x^4+38*x^3+5*x^2+7*x+18', 'y^2=35*x^6+24*x^4+24*x^2+35', 'y^2=10*x^6+7*x^5+47*x^4+56*x^3+32*x^2+22*x+33', 'y^2=x^6+36*x^3+52', 'y^2=21*x^6+24*x^5+27*x^4+34*x^3+3*x^2+50*x+54', 'y^2=32*x^6+39*x^5+27*x^4+13*x^3+27*x^2+39*x+32', 'y^2=24*x^6+17*x^5+14*x^4+22*x^3+14*x^2+17*x+24', 'y^2=3*x^6+20*x^5+47*x^4+17*x^3+12*x^2+x+60', 'y^2=31*x^6+56*x^5+46*x^4+18*x^3+22*x^2+15*x+51', 'y^2=11*x^6+4*x^5+20*x^4+9*x^3+20*x^2+4*x+11', 'y^2=x^6+25*x^3+9', 'y^2=49*x^6+45*x^5+57*x^4+8*x^3+31*x^2+40*x+24', 'y^2=x^6+56*x^3+58', 'y^2=60*x^6+21*x^5+13*x^4+2*x^3+4*x^2+5*x+4'], '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': ['2.0.20.1'], 'geometric_splitting_field': '2.0.20.1', 'geometric_splitting_polynomials': [[5, 0, 1]], 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 53, 'is_geometrically_simple': False, 'is_geometrically_squarefree': False, 'is_primitive': True, 'is_simple': False, 'is_squarefree': False, 'is_supersingular': False, 'jacobian_count': 53, 'label': '2.61.aq_he', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 6, 'newton_coelevation': 2, 'newton_elevation': 0, 'number_fields': ['2.0.20.1'], 'p': 61, 'p_rank': 2, 'p_rank_deficit': 0, 'poly': [1, -16, 186, -976, 3721], 'poly_str': '1 -16 186 -976 3721 ', 'primitive_models': [], 'q': 61, 'real_poly': [1, -16, 64], 'simple_distinct': ['1.61.ai'], 'simple_factors': ['1.61.aiA', '1.61.aiB'], 'simple_multiplicities': [2], 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '2.0.20.1', 'splitting_polynomials': [[5, 0, 1]], 'twist_count': 6, 'twists': [['2.61.a_cg', '2.3721.em_pzq', 2], ['2.61.q_he', '2.3721.em_pzq', 2], ['2.61.i_d', '2.226981.cvg_czkfy', 3], ['2.61.a_acg', '2.13845841.mbs_dszsti', 4], ['2.61.ai_d', '2.51520374361.abzmho_bmhxuyfhm', 6]]}
• av_fq_endalg_factors •

  Column	Type
  base_label	text
  extension_degree	smallint
  extension_label	text
  multiplicity	smallint

  
  {'base_label': '2.61.aq_he', 'extension_degree': 1, 'extension_label': '1.61.ai', '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': '2.0.20.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.61.ai', 'galois_group': '2T1', 'places': [['19', '1'], ['42', '1']]}