Elliptic curve data - 100048.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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '100048i', 'Clabel': '100048i2', 'Cnumber': 2, 'abc_quality': 0.9727427413985318, 'absD': 1001440691310592, 'adelic_genus': 43, 'adelic_index': 1296, 'adelic_level': 51948, 'ainvs': [0, -1, 0, -63093, 5927869], 'analytic_rank': 0, 'bad_primes': [2, 13, 37], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 100048, 'degree': 311040, 'elladic_images': ['9.36.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6483972744803621867531382293', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 1, 'isogeny_degrees': [1, 3], 'jinv': [1404928000, 50653], 'lmfdb_iso': '100048.b', 'lmfdb_label': '100048.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, -23, -50], 'min_quad_twist_disc': -52, 'modell_images': ['3Cs'], 'modm_images': ['3.12.0.a.1', '9.36.0.b.1', '74.2.0.?', '156.24.0.?', '222.24.1.?', '333.108.4.?', '468.72.0.?', '666.216.13.?', '999.324.16.?', '1998.648.43.?', '5772.48.1.?', '17316.432.13.?', '51948.1296.43.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.32722458481035149069083761294', 'prec': 107}, 'szpiro_ratio': 3.8885727414353712, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 0, 0, -1, 0, -2, 0, 3, 0, 0, 0, 0, 0, 6, 0, 2, 0], 'aplist': [0, -1, 0, -1, 3, 0, 6, 2, -6, -6, -4, -1, 9, -8, 3, -3, 12, 8, -4, -15, -11, 10, 9, -6, -8], 'class_deg': 9, 'class_size': 3, 'conductor': 100048, 'isogeny_matrix': [[1, 3, 9], [3, 1, 3], [9, 3, 1]], 'lmfdb_iso': '100048.b', 'trace_hash': 485444833447619431}
• 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': '0.037001584276873012844270757679', 'prec': 107}, 'conductor': 100048, 'gens': [], 'heights': [], 'lmfdb_label': '100048.b2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.49024699281424589371055810157', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.98049398562849178742111620314707764066', 'prec': 133}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '5': [0, 0, 0], '7': [0, 0], '11': [0, 0], '13': 'a', '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '100048.b2'}
• ec_torsion_growth •

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

  
  
  • id: 4642309
    {'degree': 2, 'field': [-39, 0, 1], 'lmfdb_label': '100048.b2', 'torsion': [3]}
  • id: 4642310
    {'degree': 2, 'field': [13, 0, 1], 'lmfdb_label': '100048.b2', 'torsion': [3]}
  • id: 4642311
    {'degree': 3, 'field': [1, -3, -1, 1], 'lmfdb_label': '100048.b2', 'torsion': [2]}
  • id: 4642312
    {'degree': 4, 'field': [169, 0, -13, 0, 1], 'lmfdb_label': '100048.b2', 'torsion': [3, 3]}
  • id: 4642314
    {'degree': 6, 'field': [-13718, -1444, 2964, 42, -118, -2, 1], 'lmfdb_label': '100048.b2', 'torsion': [6]}
  • id: 4642313
    {'degree': 6, 'field': [1, -5, 0, 9, -2, -3, 1], 'lmfdb_label': '100048.b2', 'torsion': [2, 2]}
  • id: 4642315
    {'degree': 6, 'field': [686, -196, 364, -10, 38, -2, 1], 'lmfdb_label': '100048.b2', 'torsion': [6]}
  • id: 4642317
    {'degree': 12, 'field': [470596, -134456, -211288, -57624, 104468, 9884, -12752, 880, 1060, -56, -34, -2, 1], 'lmfdb_label': '100048.b2', 'torsion': [3, 6]}
  • id: 4642316
    {'degree': 12, 'field': [805606, 1632080, 2126188, 990668, 96746, -63988, -34336, -7036, -858, -90, -2, -2, 1], 'lmfdb_label': '100048.b2', 'torsion': [4]}
  • id: 4642319
    {'degree': 12, 'field': [1075369, 678198, 913233, 318468, 199000, 19570, 22225, -890, 1776, -96, 69, -2, 1], 'lmfdb_label': '100048.b2', 'torsion': [2, 6]}
  • id: 4642318
    {'degree': 12, 'field': [114811225, -44338670, -68763751, 9339792, 12596684, -189626, -801975, -11498, 21172, 320, -243, -2, 1], 'lmfdb_label': '100048.b2', 'torsion': [2, 6]}
  • id: 4642320
    {'degree': 18, 'field': [-201746199934187, -2511674899344, 50324457196377, 361737822774, -5064546099015, -21167382834, 295564790526, 624626262, -11286238275, -8891876, 290559204, 27378, -4984779, 702, 54756, -6, -351, 0, 1], 'lmfdb_label': '100048.b2', 'torsion': [9]}
  • id: 4642321
    {'degree': 18, 'field': [9659288029, -4708181012, 8861275497, -3058078934, 3071723611, -865733986, 578723672, -137482582, 67424464, -13388924, 5092533, -821302, 249976, -31048, 7686, -660, 134, -6, 1], 'lmfdb_label': '100048.b2', 'torsion': [9]}
• 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: 2454497
    {'conductor': 100048, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '100048.b2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 2454498
    {'conductor': 100048, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '100048.b2', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2454499
    {'conductor': 100048, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '100048.b2', 'prime': 37, '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: 2321330
    {'adelic_gens': [[1, 0, 54, 1], [19, 54, 44532, 30871], [51895, 54, 51894, 55], [3977, 11934, 23400, 43055], [14039, 11934, 14040, 11933], [25973, 0, 0, 51947], [1, 27, 27, 730], [1, 54, 0, 1], [29771, 32812, 24960, 13027], [19979, 0, 0, 51947], [352, 20007, 40677, 25624], [43, 30, 47658, 48955]], 'adelic_image': '51948.1296.43.?', 'conductor': 100048, 'lmfdb_label': '100048.b2', 'prime': 0}
  • id: 401882
    {'conductor': 100048, 'elladic_image': '9.36.0.2', 'lmfdb_label': '100048.b2', 'modell_image': '3Cs', 'prime': 3}
• lmfdb_iso 100048.b does not appear in ec_padic