Elliptic curve data - 128700.ba2

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• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  abc_quality	double precision
  absD	numeric
  adelic_genus	integer
  adelic_index	integer
  adelic_level	bigint
  ainvs	numeric[]
  analytic_rank	smallint
  bad_primes	integer[]
  class_deg	smallint
  class_size	smallint
  cm	smallint
  conductor	integer
  degree	bigint
  elladic_images	text[]
  faltings_height	numeric
  faltings_index	smallint
  faltings_ratio	smallint
  iso_nlabel	smallint
  isogeny_degrees	smallint[]
  jinv	numeric[]
  lmfdb_iso	text
  lmfdb_label	text
  lmfdb_number	smallint
  manin_constant	smallint
  min_quad_twist_ainvs	numeric[]
  min_quad_twist_disc	smallint
  modell_images	text[]
  modm_images	text[]
  nonmax_primes	smallint[]
  nonmax_rad	integer
  num_bad_primes	smallint
  num_int_pts	integer
  optimality	smallint
  potential_good_reduction	boolean
  rank	smallint
  regulator	numeric
  semistable	boolean
  serre_invariants	integer[]
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '128700bf', 'Clabel': '128700bf2', 'Cnumber': 2, 'abc_quality': 0.8723399489991361, 'absD': 417978346500000000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 8580, 'ainvs': [0, 0, 0, -33375, 31193750], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 11, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 128700, 'degree': 1013760, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0607233222737202876917598937', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 26, 'isogeny_degrees': [1, 2], 'jinv': [-11279504, 1146717], 'lmfdb_iso': '128700.ba', 'lmfdb_label': '128700.ba2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -148, -9292], 'min_quad_twist_disc': -15, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '260.6.0.?', '660.6.0.?', '1716.6.0.?', '8580.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 585], [3, 2, 14300], [5, 14, 5148], [11, 12, 11700], [13, 14, 9900]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.15775937675920671190125363899', 'prec': 107}, 'szpiro_ratio': 4.082756037093669, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
• ec_classdata •

  Column	Type
  anlist	smallint[]
  aplist	smallint[]
  class_deg	smallint
  class_size	smallint
  conductor	integer
  isogeny_matrix	smallint[]
  lmfdb_iso	text
  trace_hash	bigint

  
  {'anlist': [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 4, 0, -4, 0], 'aplist': [0, 0, 0, 0, -1, -1, 4, -4, 0, -6, 0, 2, 2, -4, -12, -10, -8, 6, 2, 0, 10, 10, -6, 0, -14], 'class_deg': 2, 'class_size': 2, 'conductor': 128700, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '128700.ba', 'trace_hash': 1002752057351064233}
• ec_mwbsd •

  Column	Type
  area	numeric
  conductor	integer
  gens	numeric[]
  heights	numeric[]
  lmfdb_label	text
  ngens	smallint
  rank_bounds	smallint[]
  real_period	numeric
  sha_an	numeric
  special_value	numeric
  tamagawa_product	integer
  torsion_generators	numeric[]
  xcoord_integral_points	numeric[]

  
  {'area': {'__RealLiteral__': 0, 'data': '0.016221031393613927752027496736', 'prec': 107}, 'conductor': 128700, 'gens': [], 'heights': [], 'lmfdb_label': '128700.ba2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.24538727875688238038118696353', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.98154911502752952152474785412705610617', 'prec': 133}, 'tamagawa_product': 16, 'torsion_generators': [[-350, 0, 1]], 'xcoord_integral_points': [-350]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': 'a', '11': [0, 0], '13': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '128700.ba2'}
• ec_torsion_growth •

  Column	Type
  degree	smallint
  field	numeric[]
  lmfdb_label	text
  torsion	smallint[]

  
  
  • id: 5853871
    {'degree': 2, 'field': [65, 0, 1], 'lmfdb_label': '128700.ba2', 'torsion': [2, 2]}
  • id: 5853872
    {'degree': 4, 'field': [-65, 0, -20, 0, 1], 'lmfdb_label': '128700.ba2', 'torsion': [4]}
  • id: 5853875
    {'degree': 8, 'field': [3756, -1914, -2041, 1822, -421, 14, 1, -2, 1], 'lmfdb_label': '128700.ba2', 'torsion': [6]}
  • id: 5853874
    {'degree': 8, 'field': [2327361, -1142436, 162292, 572, 3530, -292, -28, -4, 1], 'lmfdb_label': '128700.ba2', 'torsion': [2, 4]}
  • id: 5853873
    {'degree': 8, 'field': [44475561, 0, 3668652, 0, 86814, 0, 468, 0, 1], 'lmfdb_label': '128700.ba2', 'torsion': [2, 4]}
  • id: 5853877
    {'degree': 16, 'field': [223622116, 0, -2288720, 0, 15612328, 0, 2921520, 0, 554904, 0, 55980, 0, 4957, 0, 130, 0, 1], 'lmfdb_label': '128700.ba2', 'torsion': [2, 6]}
  • id: 5853876
    {'degree': 16, 'field': [17870075041, 0, 48283407484, 0, 480830350, 0, -364704704, 0, -13124501, 0, 205816, 0, 13090, 0, -116, 0, 1], 'lmfdb_label': '128700.ba2', 'torsion': [8]}
• ec_localdata •

  Column	Type
  conductor	integer
  conductor_valuation	smallint
  discriminant_valuation	smallint
  j_denominator_valuation	smallint
  kodaira_symbol	smallint
  lmfdb_label	text
  prime	integer
  reduction_type	smallint
  root_number	smallint
  tamagawa_number	smallint

  
  
  • id: 3173539
    {'conductor': 128700, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '128700.ba2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 3173540
    {'conductor': 128700, 'conductor_valuation': 2, 'discriminant_valuation': 12, 'j_denominator_valuation': 6, 'kodaira_symbol': -10, 'lmfdb_label': '128700.ba2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 3173541
    {'conductor': 128700, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '128700.ba2', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 3173542
    {'conductor': 128700, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '128700.ba2', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 3173543
    {'conductor': 128700, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '128700.ba2', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 2502703
    {'adelic_gens': [[7801, 4, 7022, 9], [1, 2, 2, 5], [2861, 4, 5722, 9], [6868, 1, 6863, 0], [1, 4, 0, 1], [1, 0, 4, 1], [5282, 1, 5939, 0], [3, 4, 8, 11], [6436, 2149, 2145, 6436], [8577, 4, 8576, 5]], 'adelic_image': '8580.12.0.?', 'conductor': 128700, 'lmfdb_label': '128700.ba2', 'prime': 0}
  • id: 501683
    {'conductor': 128700, 'elladic_image': '2.3.0.1', 'lmfdb_label': '128700.ba2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 128700.ba does not appear in ec_padic