Abelian variety isogeny class data - 2.61.ax_ji

Formats: - HTML - YAML - JSON - 2025-10-26T06:17:24.843185

• 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': 2538, 'abvar_counts': [2538, 13679820, 51593316768, 191719941336000, 713313755584881858, 2654328609401237556480, 9876830468887493757016578, 36751699363122152194506336000, 136753057442086524684236978386848, 508858111508917098061503113556235500], 'abvar_counts_str': '2538 13679820 51593316768 191719941336000 713313755584881858 2654328609401237556480 9876830468887493757016578 36751699363122152194506336000 136753057442086524684236978386848 508858111508917098061503113556235500 ', 'angle_corank': 0, 'angle_rank': 2, 'angles': [0.0900194921158871, 0.328850104904971], 'center_dim': 4, 'cohen_macaulay_max': 1, 'curve_count': 39, 'curve_counts': [39, 3677, 227304, 13846753, 844561779, 51519979082, 3142742179119, 191707341720673, 11694146486324904, 713342914311311477], 'curve_counts_str': '39 3677 227304 13846753 844561779 51519979082 3142742179119 191707341720673 11694146486324904 713342914311311477 ', 'curves': ['y^2=31*x^6+19*x^5+8*x^4+43*x^3+48*x^2+10*x+31', 'y^2=13*x^6+28*x^5+13*x^4+42*x^3+32*x^2+16*x+4', 'y^2=43*x^6+27*x^5+15*x^4+49*x^3+58*x^2+56*x+6', 'y^2=32*x^6+2*x^5+36*x^4+59*x^3+41*x^2+45*x+31', 'y^2=35*x^6+5*x^5+36*x^4+46*x^3+18*x^2+37*x+8', 'y^2=46*x^6+19*x^5+28*x^4+53*x^3+27*x^2+53*x+47', 'y^2=23*x^6+8*x^5+13*x^4+32*x^3+21*x^2+35*x', 'y^2=21*x^6+x^5+42*x^4+19*x^3+28*x^2+15*x+23', 'y^2=40*x^6+41*x^5+58*x^4+52*x^3+49*x^2+36*x+44', 'y^2=21*x^6+5*x^5+57*x^4+53*x^3+46*x^2+48*x+50', 'y^2=8*x^6+51*x^5+4*x^4+32*x^3+42*x^2+32*x+26', 'y^2=40*x^6+22*x^5+14*x^4+x^3+58*x^2+49*x+10', 'y^2=7*x^6+23*x^5+27*x^4+24*x^3+10*x^2+40*x+59', 'y^2=30*x^6+30*x^5+45*x^4+56*x^3+22*x^2+8*x+20', 'y^2=12*x^6+57*x^5+27*x^4+27*x^3+3*x^2+9*x+23', 'y^2=43*x^6+54*x^5+34*x^4+13*x^3+18*x^2+2*x+50', 'y^2=16*x^6+60*x^5+19*x^4+43*x^3+19*x^2+31*x+2', 'y^2=11*x^6+44*x^5+14*x^4+23*x^3+34*x^2+30*x+56'], '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': 8, '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': ['2.0.19.1', '2.0.20.1'], 'geometric_splitting_field': '4.0.144400.1', 'geometric_splitting_polynomials': [[5, -20, 21, -2, 1]], 'group_structure_count': 2, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 18, 'is_geometrically_simple': False, 'is_geometrically_squarefree': True, 'is_primitive': True, 'is_simple': False, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 18, 'label': '2.61.ax_ji', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 2, 'newton_coelevation': 2, 'newton_elevation': 0, 'number_fields': ['2.0.19.1', '2.0.20.1'], 'p': 61, 'p_rank': 2, 'p_rank_deficit': 0, 'poly': [1, -23, 242, -1403, 3721], 'poly_str': '1 -23 242 -1403 3721 ', 'primitive_models': [], 'q': 61, 'real_poly': [1, -23, 120], 'simple_distinct': ['1.61.ap', '1.61.ai'], 'simple_factors': ['1.61.apA', '1.61.aiA'], 'simple_multiplicities': [1, 1], 'singular_primes': ['7,37*F+V', '7,F-3*V+37', '3,5*F+V'], 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '4.0.144400.1', 'splitting_polynomials': [[5, -20, 21, -2, 1]], 'twist_count': 4, 'twists': [['2.61.ah_c', '2.3721.abt_cem', 2], ['2.61.h_c', '2.3721.abt_cem', 2], ['2.61.x_ji', '2.3721.abt_cem', 2]], 'weak_equivalence_count': 8, 'zfv_index': 147, 'zfv_index_factorization': [[3, 1], [7, 2]], 'zfv_is_bass': True, 'zfv_is_maximal': False, 'zfv_plus_index': 1, 'zfv_plus_index_factorization': [], 'zfv_plus_norm': 3420, 'zfv_singular_count': 6, 'zfv_singular_primes': ['7,37*F+V', '7,F-3*V+37', '3,5*F+V']}
• av_fq_endalg_factors •

  Column	Type
  base_label	text
  extension_degree	smallint
  extension_label	text
  multiplicity	smallint

  
  
  • id: 58760
    {'base_label': '2.61.ax_ji', 'extension_degree': 1, 'extension_label': '1.61.ap', 'multiplicity': 1}
  • id: 58761
    {'base_label': '2.61.ax_ji', 'extension_degree': 1, 'extension_label': '1.61.ai', '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': '2.0.19.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.61.ap', 'galois_group': '2T1', 'places': [['53', '1'], ['7', '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': '2.0.20.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.61.ai', 'galois_group': '2T1', 'places': [['19', '1'], ['42', '1']]}