Abelian variety isogeny class data - 4.5.a_ak_a_cx

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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': 441, 'abvar_counts': [441, 194481, 252047376, 179607287601, 95306425775001, 63527879748485376, 37251949328613125001, 23432673552555179690001, 14551945030712127693359376, 9083314794005774963476550001], 'abvar_counts_str': '441 194481 252047376 179607287601 95306425775001 63527879748485376 37251949328613125001 23432673552555179690001 14551945030712127693359376 9083314794005774963476550001 ', 'angle_corank': 4, 'angle_rank': 0, 'angles': [0.166666666666667, 0.166666666666667, 0.833333333333333, 0.833333333333333], 'center_dim': 4, 'curve_count': 6, 'curve_counts': [6, 6, 126, 726, 3126, 16626, 78126, 393126, 1953126, 9753126], 'curve_counts_str': '6 6 126 726 3126 16626 78126 393126 1953126 9753126 ', 'curves': [], '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': 6, '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': 0, 'has_principal_polarization': 1, 'hyp_count': 0, '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_ak_a_cx', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 4, 'max_twist_degree': 120, 'newton_coelevation': 0, 'newton_elevation': 6, 'noncyclic_primes': [3, 7], 'number_fields': ['4.0.3600.3'], 'p': 5, 'p_rank': 0, 'p_rank_deficit': 4, 'poly': [1, 0, -10, 0, 75, 0, -250, 0, 625], 'poly_str': '1 0 -10 0 75 0 -250 0 625 ', 'primitive_models': [], 'q': 5, 'real_poly': [1, 0, -30, 0, 225], 'simple_distinct': ['2.5.a_af'], 'simple_factors': ['2.5.a_afA', '2.5.a_afB'], 'simple_multiplicities': [2], 'slopes': ['1/2A', '1/2B', '1/2C', '1/2D', '1/2E', '1/2F', '1/2G', '1/2H'], 'splitting_field': '4.0.3600.3', 'splitting_polynomials': [[25, 0, -5, 0, 1]], 'twist_count': 33, 'twists': [['4.5.a_f_a_a', '4.125.a_tg_a_firu', 3], ['4.5.a_u_a_fu', '4.125.a_tg_a_firu', 3], ['4.5.a_a_a_z', '4.625.dw_jgk_ofvk_qghct', 4], ['4.5.a_k_a_cx', '4.625.dw_jgk_ofvk_qghct', 4], ['4.5.a_a_a_az', '4.390625.dse_iogmk_mqubciq_nwyzpwget', 8], ['4.5.a_au_a_fu', '4.244140625.ahcxs_wdjbxpc_abnizdflzfhw_brstyghqcemlus', 12], ['4.5.a_ap_a_dw', '4.244140625.ahcxs_wdjbxpc_abnizdflzfhw_brstyghqcemlus', 12], ['4.5.a_af_a_a', '4.244140625.ahcxs_wdjbxpc_abnizdflzfhw_brstyghqcemlus', 12], ['4.5.a_a_a_aby', '4.244140625.ahcxs_wdjbxpc_abnizdflzfhw_brstyghqcemlus', 12], ['4.5.a_p_a_dw', '4.244140625.ahcxs_wdjbxpc_abnizdflzfhw_brstyghqcemlus', 12], ['4.5.a_af_a_z', '4.30517578125.a_pfecibjg_a_diqdzialpfbabxlu', 15], ['4.5.af_k_az_cx', '4.95367431640625.dhmmtw_gtqvedaneek_iwztgvjwfwcrntfk_irlvrthfekgjlqbctghkt', 20], ['4.5.f_k_z_cx', '4.95367431640625.dhmmtw_gtqvedaneek_iwztgvjwfwcrntfk_irlvrthfekgjlqbctghkt', 20], ['4.5.a_ak_a_by', '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_by', '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_by', '4.59604644775390625.agikaoei_rmsjsdbgbupdc_abbqsulljfxtuxwtrcbie_bbiaogoorycxyqfdcriolzgpms', 24], ['4.5.a_a_a_a', '4.3552713678800500929355621337890625.aezxvixebtceii_kyafsfvmjqtzlrqvwnvjzsgfc_anquiklkseppdjnbabddlssmaetcbfdagvpyoe_kqzwgvtuparacmljwsdltylahvexkiykuhueczvfrwwwslyws', 48], ['4.5.ak_cd_ahs_uf', '4.867361737988403547205962240695953369140625.aelmwqkrycybitwps_iqlwgmqaqksatftwplxmzsewurprftc_ajpgxbrhuvpwkbrowfvuwwzbpemlvhodjxzvctzvrgbfkvw_gragsnsjuxkzjowjzzkdkrueuwiybivgszadyflkdtqxbjvrdksnqxbzaheos', 60], ['4.5.af_f_z_adw', '4.867361737988403547205962240695953369140625.aelmwqkrycybitwps_iqlwgmqaqksatftwplxmzsewurprftc_ajpgxbrhuvpwkbrowfvuwwzbpemlvhodjxzvctzvrgbfkvw_gragsnsjuxkzjowjzzkdkrueuwiybivgszadyflkdtqxbjvrdksnqxbzaheos', 60], ['4.5.af_k_a_az', '4.867361737988403547205962240695953369140625.aelmwqkrycybitwps_iqlwgmqaqksatftwplxmzsewurprftc_ajpgxbrhuvpwkbrowfvuwwzbpemlvhodjxzvctzvrgbfkvw_gragsnsjuxkzjowjzzkdkrueuwiybivgszadyflkdtqxbjvrdksnqxbzaheos', 60], ['4.5.af_u_aby_ev', '4.867361737988403547205962240695953369140625.aelmwqkrycybitwps_iqlwgmqaqksatftwplxmzsewurprftc_ajpgxbrhuvpwkbrowfvuwwzbpemlvhodjxzvctzvrgbfkvw_gragsnsjuxkzjowjzzkdkrueuwiybivgszadyflkdtqxbjvrdksnqxbzaheos', 60], ['4.5.af_z_acx_hs', '4.867361737988403547205962240695953369140625.aelmwqkrycybitwps_iqlwgmqaqksatftwplxmzsewurprftc_ajpgxbrhuvpwkbrowfvuwwzbpemlvhodjxzvctzvrgbfkvw_gragsnsjuxkzjowjzzkdkrueuwiybivgszadyflkdtqxbjvrdksnqxbzaheos', 60], ['4.5.a_f_a_z', '4.867361737988403547205962240695953369140625.aelmwqkrycybitwps_iqlwgmqaqksatftwplxmzsewurprftc_ajpgxbrhuvpwkbrowfvuwwzbpemlvhodjxzvctzvrgbfkvw_gragsnsjuxkzjowjzzkdkrueuwiybivgszadyflkdtqxbjvrdksnqxbzaheos', 60], ['4.5.f_f_az_adw', '4.867361737988403547205962240695953369140625.aelmwqkrycybitwps_iqlwgmqaqksatftwplxmzsewurprftc_ajpgxbrhuvpwkbrowfvuwwzbpemlvhodjxzvctzvrgbfkvw_gragsnsjuxkzjowjzzkdkrueuwiybivgszadyflkdtqxbjvrdksnqxbzaheos', 60], ['4.5.f_k_a_az', '4.867361737988403547205962240695953369140625.aelmwqkrycybitwps_iqlwgmqaqksatftwplxmzsewurprftc_ajpgxbrhuvpwkbrowfvuwwzbpemlvhodjxzvctzvrgbfkvw_gragsnsjuxkzjowjzzkdkrueuwiybivgszadyflkdtqxbjvrdksnqxbzaheos', 60], ['4.5.f_u_by_ev', '4.867361737988403547205962240695953369140625.aelmwqkrycybitwps_iqlwgmqaqksatftwplxmzsewurprftc_ajpgxbrhuvpwkbrowfvuwwzbpemlvhodjxzvctzvrgbfkvw_gragsnsjuxkzjowjzzkdkrueuwiybivgszadyflkdtqxbjvrdksnqxbzaheos', 60], ['4.5.f_z_cx_hs', '4.867361737988403547205962240695953369140625.aelmwqkrycybitwps_iqlwgmqaqksatftwplxmzsewurprftc_ajpgxbrhuvpwkbrowfvuwwzbpemlvhodjxzvctzvrgbfkvw_gragsnsjuxkzjowjzzkdkrueuwiybivgszadyflkdtqxbjvrdksnqxbzaheos', 60], ['4.5.k_cd_hs_uf', '4.867361737988403547205962240695953369140625.aelmwqkrycybitwps_iqlwgmqaqksatftwplxmzsewurprftc_ajpgxbrhuvpwkbrowfvuwwzbpemlvhodjxzvctzvrgbfkvw_gragsnsjuxkzjowjzzkdkrueuwiybivgszadyflkdtqxbjvrdksnqxbzaheos', 60], ['4.5.af_p_az_by', '4.752316384526264005099991383822237233803945956334136013765601092018187046051025390625.acmdkbwepaziwmxyglvzhlbmnymlxmui_crfhxahjdeekdvodzztqzbxrnodovisxmuklzhjtrcreaoirgorvboleuxrlc_abqrnlwxmsgohcbgmdkovzjthpuitbdxgpqfoijpqioaxuflewyvfifqxsazggvenizehgdcbrhouzwgvkeingwvqsge_qlptvaurceumrqpyusgqoshzpizdndgyhomthtmjnpmxezaialslexnnazdgjudtjxggxgtmpurretwbaeyejbdvzvddapebfkqgtyhhoumpmppryltjeras', 120], ['4.5.f_p_z_by', '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: 2845392
    {'base_label': '4.5.a_ak_a_cx', 'extension_degree': 1, 'extension_label': '2.5.a_af', 'multiplicity': 2}
  • id: 2845393
    {'base_label': '4.5.a_ak_a_cx', 'extension_degree': 2, 'extension_label': '1.25.af', 'multiplicity': 4}
  • id: 2845394
    {'base_label': '4.5.a_ak_a_cx', 'extension_degree': 3, 'extension_label': '1.125.a', 'multiplicity': 4}
  • id: 2845395
    {'base_label': '4.5.a_ak_a_cx', 'extension_degree': 6, 'extension_label': '1.15625.jq', '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[]

  
  {'brauer_invariants': ['0'], 'center': '4.0.3600.3', 'center_dim': 4, 'divalg_dim': 1, 'extension_label': '2.5.a_af', 'galois_group': '4T2', 'places': [['0', '1', '0', '0']]}
• 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'], 'center': '2.0.3.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.25.af', 'galois_group': '2T1', 'places': [['0', '0']]}
• 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'], 'center': '2.0.20.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.125.a', 'galois_group': '2T1', 'places': [['0', '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': '1.15625.jq', 'galois_group': '1T1', 'places': [['0']]}