Abelian variety isogeny class data - 4.5.a_a_a_by

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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_cyclic	boolean
  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
  noncyclic_primes	integer[]
  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': 676, 'abvar_counts': [676, 456976, 244171876, 208827064576, 95367451171876, 59619905029359376, 37252902996826171876, 22986704741655040229376, 14551915228374481201171876, 9094950743020153045693359376], 'abvar_counts_str': '676 456976 244171876 208827064576 95367451171876 59619905029359376 37252902996826171876 22986704741655040229376 14551915228374481201171876 9094950743020153045693359376 ', 'angle_corank': 4, 'angle_rank': 0, 'angles': [0.25, 0.25, 0.75, 0.75], 'center_dim': 4, 'curve_count': 6, 'curve_counts': [6, 26, 126, 826, 3126, 15626, 78126, 385626, 1953126, 9765626], 'curve_counts_str': '6 26 126 826 3126 15626 78126 385626 1953126 9765626 ', 'curves': ['y^2=x^10+x^9+4*x^8+2*x^7+3*x^6+4*x^4+2*x^3+3*x^2+4*x+3', 'y^2=x^10+2*x^8+2*x^6+3*x^4+3*x^2+4'], 'dim1_distinct': 0, 'dim1_factors': 0, 'dim2_distinct': 1, 'dim2_factors': 2, 'dim3_distinct': 0, 'dim3_factors': 0, 'dim4_distinct': 0, 'dim4_factors': 0, 'dim5_distinct': 0, 'dim5_factors': 0, 'g': 4, 'galois_groups': ['4T2'], 'geom_dim1_distinct': 1, 'geom_dim1_factors': 4, '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': 1, 'geometric_extension_degree': 4, 'geometric_galois_groups': ['1T1'], 'geometric_number_fields': ['1.1.1.1'], 'geometric_splitting_field': '1.1.1.1', 'geometric_splitting_polynomials': [[0, 1]], 'has_geom_ss_factor': True, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 2, 'is_cyclic': False, 'is_geometrically_simple': False, 'is_geometrically_squarefree': False, 'is_primitive': True, 'is_simple': False, 'is_squarefree': False, 'is_supersingular': True, 'label': '4.5.a_a_a_by', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 4, 'max_twist_degree': 120, 'newton_coelevation': 0, 'newton_elevation': 6, 'noncyclic_primes': [2, 13], 'number_fields': ['4.0.6400.3'], 'p': 5, 'p_rank': 0, 'p_rank_deficit': 4, 'poly': [1, 0, 0, 0, 50, 0, 0, 0, 625], 'poly_str': '1 0 0 0 50 0 0 0 625 ', 'primitive_models': [], 'q': 5, 'real_poly': [1, 0, -20, 0, 100], 'simple_distinct': ['2.5.a_a'], 'simple_factors': ['2.5.a_aA', '2.5.a_aB'], 'simple_multiplicities': [2], 'slopes': ['1/2A', '1/2B', '1/2C', '1/2D', '1/2E', '1/2F', '1/2G', '1/2H'], 'splitting_field': '4.0.6400.3', 'splitting_polynomials': [[25, 0, 0, 0, 1]], 'twist_count': 33, 'twists': [['4.5.a_a_a_az', '4.125.a_a_a_bufy', 3], ['4.5.a_au_a_fu', '4.390625.ahki_xyhtc_absgsdvee_bzdwgucoos', 8], ['4.5.a_ak_a_by', '4.390625.ahki_xyhtc_absgsdvee_bzdwgucoos', 8], ['4.5.a_a_a_aby', '4.390625.ahki_xyhtc_absgsdvee_bzdwgucoos', 8], ['4.5.a_k_a_by', '4.390625.ahki_xyhtc_absgsdvee_bzdwgucoos', 8], ['4.5.a_u_a_fu', '4.390625.ahki_xyhtc_absgsdvee_bzdwgucoos', 8], ['4.5.a_a_a_a', '4.152587890625.agvuui_ulyncvvlc_abizktkgcmdpege_bljsnxoyiqcwgmrlas', 16], ['4.5.a_ap_a_dw', '4.59604644775390625.agikaoei_rmsjsdbgbupdc_abbqsulljfxtuxwtrcbie_bbiaogoorycxyqfdcriolzgpms', 24], ['4.5.a_ak_a_cx', '4.59604644775390625.agikaoei_rmsjsdbgbupdc_abbqsulljfxtuxwtrcbie_bbiaogoorycxyqfdcriolzgpms', 24], ['4.5.a_af_a_a', '4.59604644775390625.agikaoei_rmsjsdbgbupdc_abbqsulljfxtuxwtrcbie_bbiaogoorycxyqfdcriolzgpms', 24], ['4.5.a_af_a_by', '4.59604644775390625.agikaoei_rmsjsdbgbupdc_abbqsulljfxtuxwtrcbie_bbiaogoorycxyqfdcriolzgpms', 24], ['4.5.a_a_a_z', '4.59604644775390625.agikaoei_rmsjsdbgbupdc_abbqsulljfxtuxwtrcbie_bbiaogoorycxyqfdcriolzgpms', 24], ['4.5.a_f_a_a', '4.59604644775390625.agikaoei_rmsjsdbgbupdc_abbqsulljfxtuxwtrcbie_bbiaogoorycxyqfdcriolzgpms', 24], ['4.5.a_f_a_by', '4.59604644775390625.agikaoei_rmsjsdbgbupdc_abbqsulljfxtuxwtrcbie_bbiaogoorycxyqfdcriolzgpms', 24], ['4.5.a_k_a_cx', '4.59604644775390625.agikaoei_rmsjsdbgbupdc_abbqsulljfxtuxwtrcbie_bbiaogoorycxyqfdcriolzgpms', 24], ['4.5.a_p_a_dw', '4.59604644775390625.agikaoei_rmsjsdbgbupdc_abbqsulljfxtuxwtrcbie_bbiaogoorycxyqfdcriolzgpms', 24], ['4.5.ak_cd_ahs_uf', '4.9094947017729282379150390625.afknlsxfpsyi_mugmurlzkpcnxzagudunc_argxsmzgbgvkbmlntexuzzkjtpjfilme_opcgepyndcozqwjknwycixpggqpgxuhfsrogapwks', 40], ['4.5.af_f_z_adw', '4.9094947017729282379150390625.afknlsxfpsyi_mugmurlzkpcnxzagudunc_argxsmzgbgvkbmlntexuzzkjtpjfilme_opcgepyndcozqwjknwycixpggqpgxuhfsrogapwks', 40], ['4.5.af_p_az_by', '4.9094947017729282379150390625.afknlsxfpsyi_mugmurlzkpcnxzagudunc_argxsmzgbgvkbmlntexuzzkjtpjfilme_opcgepyndcozqwjknwycixpggqpgxuhfsrogapwks', 40], ['4.5.af_z_acx_hs', '4.9094947017729282379150390625.afknlsxfpsyi_mugmurlzkpcnxzagudunc_argxsmzgbgvkbmlntexuzzkjtpjfilme_opcgepyndcozqwjknwycixpggqpgxuhfsrogapwks', 40], ['4.5.a_af_a_z', '4.9094947017729282379150390625.afknlsxfpsyi_mugmurlzkpcnxzagudunc_argxsmzgbgvkbmlntexuzzkjtpjfilme_opcgepyndcozqwjknwycixpggqpgxuhfsrogapwks', 40], ['4.5.a_f_a_z', '4.9094947017729282379150390625.afknlsxfpsyi_mugmurlzkpcnxzagudunc_argxsmzgbgvkbmlntexuzzkjtpjfilme_opcgepyndcozqwjknwycixpggqpgxuhfsrogapwks', 40], ['4.5.f_f_az_adw', '4.9094947017729282379150390625.afknlsxfpsyi_mugmurlzkpcnxzagudunc_argxsmzgbgvkbmlntexuzzkjtpjfilme_opcgepyndcozqwjknwycixpggqpgxuhfsrogapwks', 40], ['4.5.f_p_z_by', '4.9094947017729282379150390625.afknlsxfpsyi_mugmurlzkpcnxzagudunc_argxsmzgbgvkbmlntexuzzkjtpjfilme_opcgepyndcozqwjknwycixpggqpgxuhfsrogapwks', 40], ['4.5.f_z_cx_hs', '4.9094947017729282379150390625.afknlsxfpsyi_mugmurlzkpcnxzagudunc_argxsmzgbgvkbmlntexuzzkjtpjfilme_opcgepyndcozqwjknwycixpggqpgxuhfsrogapwks', 40], ['4.5.k_cd_hs_uf', '4.9094947017729282379150390625.afknlsxfpsyi_mugmurlzkpcnxzagudunc_argxsmzgbgvkbmlntexuzzkjtpjfilme_opcgepyndcozqwjknwycixpggqpgxuhfsrogapwks', 40], ['4.5.af_k_az_cx', '4.752316384526264005099991383822237233803945956334136013765601092018187046051025390625.acmdkbwepaziwmxyglvzhlbmnymlxmui_crfhxahjdeekdvodzztqzbxrnodovisxmuklzhjtrcreaoirgorvboleuxrlc_abqrnlwxmsgohcbgmdkovzjthpuitbdxgpqfoijpqioaxuflewyvfifqxsazggvenizehgdcbrhouzwgvkeingwvqsge_qlptvaurceumrqpyusgqoshzpizdndgyhomthtmjnpmxezaialslexnnazdgjudtjxggxgtmpurretwbaeyejbdvzvddapebfkqgtyhhoumpmppryltjeras', 120], ['4.5.af_k_a_az', '4.752316384526264005099991383822237233803945956334136013765601092018187046051025390625.acmdkbwepaziwmxyglvzhlbmnymlxmui_crfhxahjdeekdvodzztqzbxrnodovisxmuklzhjtrcreaoirgorvboleuxrlc_abqrnlwxmsgohcbgmdkovzjthpuitbdxgpqfoijpqioaxuflewyvfifqxsazggvenizehgdcbrhouzwgvkeingwvqsge_qlptvaurceumrqpyusgqoshzpizdndgyhomthtmjnpmxezaialslexnnazdgjudtjxggxgtmpurretwbaeyejbdvzvddapebfkqgtyhhoumpmppryltjeras', 120], ['4.5.af_u_aby_ev', '4.752316384526264005099991383822237233803945956334136013765601092018187046051025390625.acmdkbwepaziwmxyglvzhlbmnymlxmui_crfhxahjdeekdvodzztqzbxrnodovisxmuklzhjtrcreaoirgorvboleuxrlc_abqrnlwxmsgohcbgmdkovzjthpuitbdxgpqfoijpqioaxuflewyvfifqxsazggvenizehgdcbrhouzwgvkeingwvqsge_qlptvaurceumrqpyusgqoshzpizdndgyhomthtmjnpmxezaialslexnnazdgjudtjxggxgtmpurretwbaeyejbdvzvddapebfkqgtyhhoumpmppryltjeras', 120], ['4.5.f_k_a_az', '4.752316384526264005099991383822237233803945956334136013765601092018187046051025390625.acmdkbwepaziwmxyglvzhlbmnymlxmui_crfhxahjdeekdvodzztqzbxrnodovisxmuklzhjtrcreaoirgorvboleuxrlc_abqrnlwxmsgohcbgmdkovzjthpuitbdxgpqfoijpqioaxuflewyvfifqxsazggvenizehgdcbrhouzwgvkeingwvqsge_qlptvaurceumrqpyusgqoshzpizdndgyhomthtmjnpmxezaialslexnnazdgjudtjxggxgtmpurretwbaeyejbdvzvddapebfkqgtyhhoumpmppryltjeras', 120], ['4.5.f_k_z_cx', '4.752316384526264005099991383822237233803945956334136013765601092018187046051025390625.acmdkbwepaziwmxyglvzhlbmnymlxmui_crfhxahjdeekdvodzztqzbxrnodovisxmuklzhjtrcreaoirgorvboleuxrlc_abqrnlwxmsgohcbgmdkovzjthpuitbdxgpqfoijpqioaxuflewyvfifqxsazggvenizehgdcbrhouzwgvkeingwvqsge_qlptvaurceumrqpyusgqoshzpizdndgyhomthtmjnpmxezaialslexnnazdgjudtjxggxgtmpurretwbaeyejbdvzvddapebfkqgtyhhoumpmppryltjeras', 120], ['4.5.f_u_by_ev', '4.752316384526264005099991383822237233803945956334136013765601092018187046051025390625.acmdkbwepaziwmxyglvzhlbmnymlxmui_crfhxahjdeekdvodzztqzbxrnodovisxmuklzhjtrcreaoirgorvboleuxrlc_abqrnlwxmsgohcbgmdkovzjthpuitbdxgpqfoijpqioaxuflewyvfifqxsazggvenizehgdcbrhouzwgvkeingwvqsge_qlptvaurceumrqpyusgqoshzpizdndgyhomthtmjnpmxezaialslexnnazdgjudtjxggxgtmpurretwbaeyejbdvzvddapebfkqgtyhhoumpmppryltjeras', 120]]}
• av_fq_endalg_factors •

  Column	Type
  base_label	text
  extension_degree	smallint
  extension_label	text
  multiplicity	smallint

  
  
  • id: 2844277
    {'base_label': '4.5.a_a_a_by', 'extension_degree': 1, 'extension_label': '2.5.a_a', 'multiplicity': 2}
  • id: 2844278
    {'base_label': '4.5.a_a_a_by', 'extension_degree': 2, 'extension_label': '2.25.a_by', 'multiplicity': 2}
  • id: 2844279
    {'base_label': '4.5.a_a_a_by', 'extension_degree': 4, 'extension_label': '1.625.by', 'multiplicity': 4}
• 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[]

  
  
  • id: 6463
    {'brauer_invariants': ['0', '0'], 'center': '4.0.6400.3', 'center_dim': 4, 'divalg_dim': 1, 'extension_label': '2.5.a_a', 'galois_group': '4T2', 'places': [['4', '1', '2/5', '0'], ['2', '3', '24/5', '2/5']]}
  • id: 1240399
    {'brauer_invariants': ['0', '0'], 'center': '4.0.6400.3', 'center_dim': 4, 'divalg_dim': 1, 'extension_label': '2.5.a_a', 'galois_group': '4T2', 'places': [['4', '4', '2/5', '24/5'], ['1', '4', '2/5', '1/5']]}
  • id: 2350275
    {'brauer_invariants': ['0', '0'], 'center': '4.0.6400.3', 'center_dim': 4, 'divalg_dim': 1, 'extension_label': '2.5.a_a', 'galois_group': '4T2', 'places': [['3', '0', '24/5', '24/5'], ['3', '0', '1/5', '24/5']]}
• 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': ['1/2', '1/2'], 'center': '2.0.4.1', 'center_dim': 2, 'divalg_dim': 4, 'extension_label': '2.25.a_by', 'galois_group': '2T1', 'places': [['2', '1'], ['3', '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': ['1/2'], 'center': '1.1.1.1', 'center_dim': 1, 'divalg_dim': 4, 'extension_label': '1.625.by', 'galois_group': '1T1', 'places': [['0']]}