Elliptic curve data - 440.b2

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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': '440b', 'Clabel': '440b1', 'Cnumber': 1, 'abc_quality': 0.968560330441743, 'absD': 4400, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 220, 'ainvs': [0, 0, 0, 2, -3], 'analytic_rank': 1, 'bad_primes': [2, 5, 11], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 440, 'degree': 16, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.61864261099717196433492286565', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [55296, 275], 'lmfdb_iso': '440.b', 'lmfdb_label': '440.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, 2, -3], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '20.6.0.c.1', '22.6.0.a.1', '220.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.78977794574878339939321611241', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 11], [5, 6, 88], [11, 12, 40]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.84969167118382040080733357280', 'prec': 107}, 'szpiro_ratio': 2.5827093691241214, '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, -1, 0, -2, 0, -3, 0, 1, 0, -4, 0, 0, 0, -4, 0, 0, 0], 'aplist': [0, 0, -1, -2, 1, -4, -4, 0, 0, -6, 0, -2, 6, 2, 0, -10, 12, -6, -12, 16, 4, -4, 2, 6, -2], 'class_deg': 2, 'class_size': 2, 'conductor': 440, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '440.b', 'trace_hash': 672833456072425217}
• 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': '3.4462449637865225556507516196', 'prec': 100}, 'conductor': 440, 'gens': [[2, 3, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.78977794574878339939321611241', 'prec': 103}], 'lmfdb_label': '440.b2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '2.1964080282505103442839440047', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.7346746205778238747577839777620275243', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[1, 0, 1]], 'xcoord_integral_points': [1, 2, 6]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 3, 0], '5': [3, 0], '7': [1, 0], '11': [2, 0], '13': [1, 0], '17': [1, 0], '19': [1, 1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '440.b2'}
• ec_torsion_growth •

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

  
  
  • id: 19267
    {'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '440.b2', 'torsion': [2, 2]}
  • id: 19268
    {'degree': 4, 'field': [-1, 2, 0, -1, 1], 'lmfdb_label': '440.b2', 'torsion': [4]}
  • id: 19271
    {'degree': 8, 'field': [-108, 0, -324, 0, 36, 0, 0, 0, 1], 'lmfdb_label': '440.b2', 'torsion': [6]}
  • id: 19270
    {'degree': 8, 'field': [1, -4, 11, -11, 18, -13, 9, -3, 1], 'lmfdb_label': '440.b2', 'torsion': [2, 4]}
  • id: 19269
    {'degree': 8, 'field': [25, 0, -102, 0, 107, 0, 6, 0, 1], 'lmfdb_label': '440.b2', 'torsion': [2, 4]}
  • id: 19272
    {'degree': 16, 'field': [-59, 132, 216, -422, -449, 656, 174, -566, 192, 344, -456, 206, -4, -42, 26, -8, 1], 'lmfdb_label': '440.b2', 'torsion': [8]}
  • id: 19273
    {'degree': 16, 'field': [5625, 0, -30600, 0, 42750, 0, 3600, 0, 1047, 0, -384, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '440.b2', 'torsion': [2, 6]}
• 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: 4640
    {'conductor': 440, 'conductor_valuation': 3, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '440.b2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4641
    {'conductor': 440, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '440.b2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4642
    {'conductor': 440, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '440.b2', 'prime': 11, '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: 1667711
    {'adelic_gens': [[57, 166, 164, 55], [1, 2, 2, 5], [202, 1, 119, 0], [217, 4, 216, 5], [3, 4, 8, 11], [177, 4, 134, 9], [1, 4, 0, 1], [1, 0, 4, 1]], 'adelic_image': '220.12.0.?', 'conductor': 440, 'lmfdb_label': '440.b2', 'prime': 0}
  • id: 1898
    {'conductor': 440, 'elladic_image': '2.3.0.1', 'lmfdb_label': '440.b2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 6259
    {'lmfdb_iso': '440.b', 'p': 7, 'prec': 20, 'unit': 11309404811348253, 'val': 1}
  • id: 6263
    {'lmfdb_iso': '440.b', 'p': 13, 'prec': 20, 'unit': 238837921695978879912, 'val': 1}
  • id: 6265
    {'lmfdb_iso': '440.b', 'p': 17, 'prec': 20, 'unit': 87761339723807074889669, 'val': 1}
  • id: 6262
    {'lmfdb_iso': '440.b', 'p': 29, 'prec': 20, 'unit': 3576114812225049701888773410, 'val': 1}
  • id: 6258
    {'lmfdb_iso': '440.b', 'p': 37, 'prec': 20, 'unit': 44678609881040365975951305710, 'val': 1}
  • id: 6260
    {'lmfdb_iso': '440.b', 'p': 41, 'prec': 20, 'unit': 4174147062068180887402964142850, 'val': 1}
  • id: 6261
    {'lmfdb_iso': '440.b', 'p': 43, 'prec': 20, 'unit': 5564904987344622534308778779670, 'val': 1}
  • id: 6267
    {'lmfdb_iso': '440.b', 'p': 53, 'prec': 20, 'unit': 444590284116083679529943553981417, 'val': 1}
  • id: 6271
    {'lmfdb_iso': '440.b', 'p': 59, 'prec': 20, 'unit': 4409689753763771509404666144190, 'val': 2}
  • id: 6272
    {'lmfdb_iso': '440.b', 'p': 61, 'prec': 20, 'unit': 1437057549499917286758495457590574, 'val': 1}
  • id: 6257
    {'lmfdb_iso': '440.b', 'p': 67, 'prec': 20, 'unit': 32468595305341632910074849622866781, 'val': 1}
  • id: 6270
    {'lmfdb_iso': '440.b', 'p': 71, 'prec': 20, 'unit': 54016314577082005742996139132106946, 'val': 1}
  • id: 6268
    {'lmfdb_iso': '440.b', 'p': 73, 'prec': 20, 'unit': 79448222917396680395560605375149729, 'val': 1}
  • id: 6264
    {'lmfdb_iso': '440.b', 'p': 79, 'prec': 20, 'unit': 1059637926292461656766274322819876059, 'val': 1}
  • id: 6266
    {'lmfdb_iso': '440.b', 'p': 83, 'prec': 20, 'unit': 2655458913475212672667398489374864543, 'val': 1}
  • id: 6269
    {'lmfdb_iso': '440.b', 'p': 89, 'prec': 20, 'unit': 5846459853652539767484454655570778655, 'val': 1}
  • id: 6256
    {'lmfdb_iso': '440.b', 'p': 97, 'prec': 20, 'unit': 16079911825457273257964182792309075662, 'val': 1}