Elliptic curve data - 637.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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '637b', 'Clabel': '637b1', 'Cnumber': 1, 'abc_quality': 0.8714055948137694, 'absD': 10706059, 'adelic_genus': 3, 'adelic_index': 144, 'adelic_level': 1638, 'ainvs': [0, -1, 1, -359, -2507], 'analytic_rank': 0, 'bad_primes': [7, 13], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 637, 'degree': 192, 'elladic_images': ['9.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.23444662747598961495751185016', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 3, 9], 'jinv': [-43614208, 91], 'lmfdb_iso': '637.b', 'lmfdb_label': '637.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, -7, 5], 'min_quad_twist_disc': -7, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '9.12.0.a.1', '21.8.0-3.a.1.1', '63.24.0-9.a.1.1', '78.8.0.?', '117.36.0.?', '182.2.0.?', '234.72.0.?', '546.16.0.?', '819.72.0.?', '1638.144.3.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[7, 32, 13], [13, 14, 49]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.73850844705166703759516452156', 'prec': 107}, 'szpiro_ratio': 4.533219385095935, '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, 2, -2, 3, 0, 0, 0, 1, 0, 0, -4, -1, 0, 6, 4, 6, 0, 7, -6], 'aplist': [0, 2, 3, 0, 0, -1, 6, 7, 3, -9, -5, 2, 6, -1, -3, -9, 0, 10, 14, -6, -11, -1, -3, -15, 1], 'class_deg': 9, 'class_size': 3, 'conductor': 637, 'isogeny_matrix': [[1, 9, 3], [9, 1, 3], [3, 3, 1]], 'lmfdb_iso': '637.b', 'trace_hash': 1977031095258253576}
• 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': '0.62569436936720309684693018394', 'prec': 103}, 'conductor': 637, 'gens': [], 'heights': [], 'lmfdb_label': '637.b2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.54820234057076015866708372941', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.1928093622830406346683349176513443997', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [18, 3, 0], '3': [0, 0], '5': [0, 0], '7': 'a', '11': [0, 0, 0], '13': [0, 0], '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': '637.b2'}
• ec_torsion_growth •

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

  
  
  • id: 29462
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '637.b2', 'torsion': [3]}
  • id: 29463
    {'degree': 3, 'field': [-2, 4, 0, 1], 'lmfdb_label': '637.b2', 'torsion': [2]}
  • id: 29467
    {'degree': 6, 'field': [2, -4, 4, -1, 3, -3, 1], 'lmfdb_label': '637.b2', 'torsion': [6]}
  • id: 29464
    {'degree': 6, 'field': [9, -33, 44, -23, 14, -3, 1], 'lmfdb_label': '637.b2', 'torsion': [2, 2]}
  • id: 29465
    {'degree': 6, 'field': [64, -880, 697, -181, 2, -3, 1], 'lmfdb_label': '637.b2', 'torsion': [3]}
  • id: 29466
    {'degree': 6, 'field': [79, -55, 25, 7, -3, -1, 1], 'lmfdb_label': '637.b2', 'torsion': [9]}
  • id: 29468
    {'degree': 12, 'field': [-4363, 746, 316, 1616, 861, -844, -392, 116, 83, -2, -12, 0, 1], 'lmfdb_label': '637.b2', 'torsion': [4]}
  • id: 29471
    {'degree': 12, 'field': [1, -3, 11, -36, 75, -129, 166, -129, 75, -36, 11, -3, 1], 'lmfdb_label': '637.b2', 'torsion': [2, 6]}
  • id: 29470
    {'degree': 12, 'field': [43, -101, 173, -150, 80, 24, -63, 54, -15, -10, 13, -6, 1], 'lmfdb_label': '637.b2', 'torsion': [9]}
  • id: 29469
    {'degree': 12, 'field': [126736, -121752, 52160, -12654, 8607, -819, -335, 546, 30, 12, -1, -3, 1], 'lmfdb_label': '637.b2', 'torsion': [3, 3]}
  • id: 29472
    {'degree': 18, 'field': [-7426433, -10937409, -13064065, -15698662, -5973744, -4764830, 303038, -315906, 292979, -45661, 8483, -9258, -1240, 640, -36, 56, -13, -3, 1], 'lmfdb_label': '637.b2', 'torsion': [6]}
  • id: 29473
    {'degree': 18, 'field': [359, -1029, 3550, -6240, 8961, -9463, 7748, -4969, 2976, -1603, 764, -369, 192, -41, -13, -6, 16, -7, 1], 'lmfdb_label': '637.b2', 'torsion': [18]}
• 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: 7702
    {'conductor': 637, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '637.b2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 7703
    {'conductor': 637, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '637.b2', '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: 1668770
    {'adelic_gens': [[1015, 18, 1251, 1291], [1, 18, 0, 1], [1, 0, 18, 1], [10, 9, 81, 73], [1621, 18, 1620, 19], [11, 18, 1476, 1009], [935, 1620, 225, 1475], [1, 18, 10, 181]], 'adelic_image': '1638.144.3.?', 'conductor': 637, 'lmfdb_label': '637.b2', 'prime': 0}
  • id: 2880
    {'conductor': 637, 'elladic_image': '9.12.0.1', 'lmfdb_label': '637.b2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 637.b does not appear in ec_padic