Elliptic curve data - 491970.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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '491970b', 'Clabel': '491970b1', 'Cnumber': 1, 'abc_quality': 0.9361710166208397, 'absD': 11419180562810880, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 3720, 'ainvs': [1, 1, 0, 51567, -2452203], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 23, 31], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 491970, 'degree': 5101360, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7693438176821767617450352613', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1], 'jinv': [102437538839, 77137920], 'lmfdb_iso': '491970.b', 'lmfdb_label': '491970.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 98, 244], 'min_quad_twist_disc': -23, 'modell_images': [], 'modm_images': ['3720.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.20159670971760191634165884540', 'prec': 103}, 'szpiro_ratio': 3.3698230831759854, '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, -1, 1, -3, -1, 1, 1, -3, -1, -2, 3, 1, 1, -8, -1, 7, -1], 'aplist': [-1, -1, -1, -3, -3, -2, -8, 7, 0, -8, -1, 4, 0, -1, 6, -5, 6, -2, -10, 9, 1, -13, 16, 3, -6], 'class_deg': 1, 'class_size': 1, 'conductor': 491970, 'isogeny_matrix': [[1]], 'lmfdb_iso': '491970.b', 'trace_hash': 845535329460741224}
• 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': '0.029051428142395709545120810629', 'prec': 107}, 'conductor': 491970, 'gens': [], 'heights': [], 'lmfdb_label': '491970.b1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.22539804902063910592177114215', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.22539804902063910592177114214989493244', 'prec': 133}, 'tamagawa_product': 1, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 491970.b1 does not appear in ec_iwasawa
• lmfdb_label 491970.b1 does not appear in ec_torsion_growth
• 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: 12127068
    {'conductor': 491970, 'conductor_valuation': 1, 'discriminant_valuation': 11, 'j_denominator_valuation': 11, 'kodaira_symbol': 15, 'lmfdb_label': '491970.b1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 12127069
    {'conductor': 491970, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '491970.b1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 12127070
    {'conductor': 491970, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '491970.b1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 12127071
    {'conductor': 491970, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '491970.b1', 'prime': 23, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 12127072
    {'conductor': 491970, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '491970.b1', 'prime': 31, '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

  
  {'adelic_gens': [[3719, 2, 3718, 3], [1, 1, 3719, 0], [2791, 2, 2791, 3], [1, 2, 0, 1], [1, 0, 2, 1], [2977, 2, 2977, 3], [1241, 2, 1241, 3], [1861, 2, 1861, 3], [1801, 2, 1801, 3]], 'adelic_image': '3720.2.0.?', 'conductor': 491970, 'lmfdb_label': '491970.b1', 'prime': 0}
• lmfdb_iso 491970.b does not appear in ec_padic