Elliptic curve data - 38.b1

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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': '38b', 'Clabel': '38b2', 'Cnumber': 2, 'abc_quality': 0.9771431338914642, 'absD': 4952198, 'adelic_genus': 1, 'adelic_index': 48, 'adelic_level': 760, 'ainvs': [1, 1, 1, -70, -279], 'analytic_rank': 0, 'bad_primes': [2, 19], 'class_deg': 5, 'class_size': 2, 'cm': 0, 'conductor': 38, 'degree': 10, 'elladic_images': ['5.24.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.017784593456229730910376097421', 'prec': 107}, 'faltings_index': 1, 'faltings_ratio': 5, 'iso_nlabel': 1, 'isogeny_degrees': [1, 5], 'jinv': [-37966934881, 4952198], 'lmfdb_iso': '38.b', 'lmfdb_label': '38.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -70, -279], 'min_quad_twist_disc': 1, 'modell_images': ['5B.1.2'], 'modm_images': ['5.24.0-5.a.2.2', '152.2.0.?', '760.48.1.?'], 'nonmax_primes': [5], 'nonmax_rad': 5, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 19], [5, 2, 2], [19, 20, 2]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.017784593456229730910376097421', 'prec': 107}, 'szpiro_ratio': 6.752621168258083, '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, 1, -1, 1, -4, -1, 3, 1, -2, -4, 2, -1, -1, 3, 4, 1, 3, -2, -1, -4], 'aplist': [1, -1, -4, 3, 2, -1, 3, -1, -1, -5, -8, -2, -8, 4, 8, -1, 15, 2, 3, 2, 9, -10, -6, 0, -2], 'class_deg': 5, 'class_size': 2, 'conductor': 38, 'isogeny_matrix': [[1, 5], [5, 1]], 'lmfdb_iso': '38.b', 'trace_hash': 51301870551309226}
• 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': '0.96505596267776005973935411685', 'prec': 103}, 'conductor': 38, 'gens': [], 'heights': [], 'lmfdb_label': '38.b1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.81924563305510364627213156798', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.81924563305510364627213156797609703247', 'prec': 133}, 'tamagawa_product': 1, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 0], '3': [0, 0], '5': [2, 1], '19': [0, 0]}, 'iwp0': 7, 'lmfdb_label': '38.b1'}
• ec_torsion_growth •

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

  
  
  • id: 1147
    {'degree': 3, 'field': [-2, -2, -1, 1], 'lmfdb_label': '38.b1', 'torsion': [2]}
  • id: 1148
    {'degree': 4, 'field': [1, -1, 1, -1, 1], 'lmfdb_label': '38.b1', 'torsion': [5]}
  • id: 1149
    {'degree': 5, 'field': [-2, 0, 0, 0, 0, 1], 'lmfdb_label': '38.b1', 'torsion': [5]}
  • id: 1150
    {'degree': 6, 'field': [16, 16, 34, 4, 5, -2, 1], 'lmfdb_label': '38.b1', 'torsion': [2, 2]}
  • id: 1151
    {'degree': 8, 'field': [-4, 4, -10, 11, -2, -7, 7, -4, 1], 'lmfdb_label': '38.b1', 'torsion': [3]}
  • id: 1152
    {'degree': 12, 'field': [-4, 24, -42, 24, -20, 44, -25, -4, 1, 4, 5, -4, 1], 'lmfdb_label': '38.b1', 'torsion': [4]}
  • id: 1153
    {'degree': 12, 'field': [16, 16, 8, -8, -20, 4, 18, 26, 15, -7, 3, -1, 1], 'lmfdb_label': '38.b1', 'torsion': [10]}
  • id: 1154
    {'degree': 15, 'field': [-16, 0, 0, 0, 0, 122, 0, 0, 0, 0, -12, 0, 0, 0, 0, 1], 'lmfdb_label': '38.b1', 'torsion': [10]}
  • id: 1155
    {'degree': 20, 'field': [1, -5, 5, 15, -30, -21, 75, 15, -120, -5, 141, -5, -120, 15, 75, -21, -30, 15, 5, -5, 1], 'lmfdb_label': '38.b1', 'torsion': [5, 5]}
• 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: 154
    {'conductor': 38, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '38.b1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 155
    {'conductor': 38, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '38.b1', 'prime': 19, '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: 1665959
    {'adelic_gens': [[1, 0, 10, 1], [751, 10, 750, 11], [6, 5, 375, 756], [577, 390, 720, 361], [6, 13, 705, 641], [191, 10, 0, 1], [1, 10, 0, 1], [126, 5, 275, 756]], 'adelic_image': '760.48.1.?', 'conductor': 38, 'lmfdb_label': '38.b1', 'prime': 0}
  • id: 92
    {'conductor': 38, 'elladic_image': '5.24.0.3', 'lmfdb_label': '38.b1', 'modell_image': '5B.1.2', 'prime': 5}
• lmfdb_iso 38.b does not appear in ec_padic