Elliptic curve data - 51744.bk1

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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': '51744ct', 'Clabel': '51744ct2', 'Cnumber': 2, 'abc_quality': 0.9871420530707399, 'absD': 2629856097792, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 616, 'ainvs': [0, 1, 0, -4720, 95864], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 11], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 51744, 'degree': 122880, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0959316532419332804281131742', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 36, 'isogeny_degrees': [1, 2], 'jinv': [193100552, 43659], 'lmfdb_iso': '51744.bk', 'lmfdb_label': '51744.bk1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -96, -252], 'min_quad_twist_disc': -7, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '28.6.0.c.1', '88.6.0.?', '616.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 7, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.78552863256732164459985597328', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 4, 539], [3, 4, 17248], [7, 32, 1056], [11, 12, 4704]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.39688380670568235418748728862', 'prec': 107}, 'szpiro_ratio': 3.408171163837706, '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, 1, 0, -4, 0, 0, 0, 1, 0, 1, 0, -6, 0, -4, 0, 0, 0, 2, 0], 'aplist': [0, 1, -4, 0, 1, -6, 0, 2, 4, -2, 2, 2, 0, -4, -6, 2, 0, -14, -12, 8, 4, 8, -2, 14, -2], 'class_deg': 2, 'class_size': 2, 'conductor': 51744, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '51744.bk', 'trace_hash': 179920112222531648}
• 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': '0.11170840757586210962931650247', 'prec': 103}, 'conductor': 51744, 'gens': [[2, 294, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.78552863256732164459985597328', 'prec': 103}], 'lmfdb_label': '51744.bk1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.76341108982297159861346821804', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.7974501558029410961426192374800542987', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[23, 0, 1]], 'xcoord_integral_points': [2, 23, 59, 170]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [4, 0], '5': [1, 0], '7': 'a', '11': [2, 0], '13': [3, 0], '17': [3, 1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 1, 0], '43': [1, 0], '47': [3, 0]}, 'iwp0': 0, 'lmfdb_label': '51744.bk1'}
• ec_torsion_growth •

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

  
  
  • id: 2506574
    {'degree': 2, 'field': [-22, 0, 1], 'lmfdb_label': '51744.bk1', 'torsion': [2, 2]}
  • id: 2506575
    {'degree': 4, 'field': [7, -7, 2, -1, 1], 'lmfdb_label': '51744.bk1', 'torsion': [4]}
  • id: 2506578
    {'degree': 8, 'field': [-11907, 0, -2520, 0, 378, 0, 0, 0, 1], 'lmfdb_label': '51744.bk1', 'torsion': [6]}
  • id: 2506576
    {'degree': 8, 'field': [441, 0, 406, 0, -17, 0, 10, 0, 1], 'lmfdb_label': '51744.bk1', 'torsion': [2, 4]}
  • id: 2506577
    {'degree': 8, 'field': [5929, 0, -16940, 0, 1100, 0, -44, 0, 1], 'lmfdb_label': '51744.bk1', 'torsion': [2, 4]}
  • id: 2506579
    {'degree': 16, 'field': [538497, -860724, 2350368, -2064216, 2091067, -86804, 32974, 29268, 6420, 6476, 2664, -536, 363, -84, 34, -4, 1], 'lmfdb_label': '51744.bk1', 'torsion': [8]}
  • id: 2506580
    {'degree': 16, 'field': [122402719321, 0, -41182292768, 0, 562680244, 0, -58203824, 0, 8855182, 0, -568064, 0, 14308, 0, -176, 0, 1], 'lmfdb_label': '51744.bk1', '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: 1238702
    {'conductor': 51744, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '51744.bk1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1238703
    {'conductor': 51744, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '51744.bk1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1238704
    {'conductor': 51744, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '51744.bk1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1238705
    {'conductor': 51744, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '51744.bk1', '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: 2007853
    {'adelic_gens': [[1, 0, 4, 1], [353, 4, 90, 9], [3, 4, 8, 11], [613, 4, 612, 5], [1, 2, 2, 5], [1, 4, 0, 1], [2, 1, 307, 0], [540, 81, 385, 232], [114, 1, 559, 0]], 'adelic_image': '616.12.0.?', 'conductor': 51744, 'lmfdb_label': '51744.bk1', 'prime': 0}
  • id: 221377
    {'conductor': 51744, 'elladic_image': '2.3.0.1', 'lmfdb_label': '51744.bk1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 2604737
    {'lmfdb_iso': '51744.bk', 'p': 5, 'prec': 20, 'unit': 26746056240506, 'val': -1}
  • id: 2604743
    {'lmfdb_iso': '51744.bk', 'p': 13, 'prec': 20, 'unit': 26989178206686067254, 'val': 2}
  • id: 2604745
    {'lmfdb_iso': '51744.bk', 'p': 19, 'prec': 20, 'unit': 525041951399795093536218, 'val': 1}
  • id: 2604747
    {'lmfdb_iso': '51744.bk', 'p': 23, 'prec': 20, 'unit': 26480099258355360657175527, 'val': 1}
  • id: 2604742
    {'lmfdb_iso': '51744.bk', 'p': 29, 'prec': 20, 'unit': 1081789057472245326669401444, 'val': 1}
  • id: 2604739
    {'lmfdb_iso': '51744.bk', 'p': 31, 'prec': 20, 'unit': 11038579874851471627791606539, 'val': 1}
  • id: 2604751
    {'lmfdb_iso': '51744.bk', 'p': 37, 'prec': 20, 'unit': 209497773389327290567159932857, 'val': 1}
  • id: 2604741
    {'lmfdb_iso': '51744.bk', 'p': 43, 'prec': 20, 'unit': 201076899654712007574557606878, 'val': 1}
  • id: 2604744
    {'lmfdb_iso': '51744.bk', 'p': 47, 'prec': 20, 'unit': 1176666135980985232314868359122, 'val': 2}
  • id: 2604746
    {'lmfdb_iso': '51744.bk', 'p': 53, 'prec': 20, 'unit': 507903181803553108838974387248592, 'val': 1}
  • id: 2604750
    {'lmfdb_iso': '51744.bk', 'p': 61, 'prec': 20, 'unit': 4104733215517417617046733275931578, 'val': 1}
  • id: 2604736
    {'lmfdb_iso': '51744.bk', 'p': 67, 'prec': 20, 'unit': 24025105296995075039010137315461154, 'val': 1}
  • id: 2604738
    {'lmfdb_iso': '51744.bk', 'p': 71, 'prec': 20, 'unit': 5418714217590410319691730484576117, 'val': 1}
  • id: 2604740
    {'lmfdb_iso': '51744.bk', 'p': 73, 'prec': 20, 'unit': 137352497393427162468863153198269764, 'val': 1}
  • id: 2604749
    {'lmfdb_iso': '51744.bk', 'p': 79, 'prec': 20, 'unit': 359309227978546948254253619889413554, 'val': 1}
  • id: 2604735
    {'lmfdb_iso': '51744.bk', 'p': 83, 'prec': 20, 'unit': 1924376740067286667047129375711266835, 'val': 1}
  • id: 2604748
    {'lmfdb_iso': '51744.bk', 'p': 89, 'prec': 20, 'unit': 293143889281585969961010059678303299, 'val': 1}
  • id: 2604734
    {'lmfdb_iso': '51744.bk', 'p': 97, 'prec': 20, 'unit': 34152494439079888264654970566479278227, 'val': 1}