Elliptic curve data - 58.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
  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': '58b', 'Clabel': '58b2', 'Cnumber': 2, 'abc_quality': 0.9948075287955614, 'absD': 82044596, 'adelic_genus': 1, 'adelic_index': 48, 'adelic_level': 580, 'ainvs': [1, 1, 1, -455, -3951], 'analytic_rank': 0, 'bad_primes': [2, 29], 'class_deg': 5, 'class_size': 2, 'cm': 0, 'conductor': 58, 'degree': 20, 'elladic_images': ['5.24.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.34716396974062546058994312884', 'prec': 97}, 'faltings_index': 1, 'faltings_ratio': 5, 'intrinsic_torsion': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 5], 'jinv': [-10418796526321, 82044596], 'lmfdb_iso': '58.b', 'lmfdb_label': '58.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -455, -3951], 'min_quad_twist_disc': 1, 'modell_images': ['5B.1.2'], 'modm_images': ['5.24.0-5.a.2.2', '116.2.0.?', '580.48.1.?'], '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, 29], [5, 2, 2], [29, 30, 2]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.34716396974062546058994312884', 'prec': 97}, 'szpiro_ratio': 7.385437562635282, '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, -2, 1, -2, 1, -3, -1, -1, -2, -1, 1, 8, -2, 0, 1], 'aplist': [1, -1, 1, -2, -3, -1, 8, 0, 4, -1, -3, 8, 2, -11, 13, -11, 0, -8, -12, 2, 4, 15, 4, -10, -2], 'class_deg': 5, 'class_size': 2, 'conductor': 58, 'isogeny_matrix': [[1, 5], [5, 1]], 'lmfdb_iso': '58.b', 'trace_hash': 708012337630994629}
• 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': '0.49940996895011155668522757073', 'prec': 97}, 'conductor': 58, 'gens': [], 'heights': [], 'lmfdb_label': '58.b1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.51660375468255350237902503720', 'prec': 97}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 97}, 'special_value': {'__RealLiteral__': 0, 'data': '1.0332075093651070047580500743988571235', 'prec': 127}, 'tamagawa_product': 2, '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], '29': [0, 0]}, 'iwp0': 7, 'lmfdb_label': '58.b1'}
• ec_torsion_growth •

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

  
  
  • id: 2078
    {'degree': 3, 'field': [-2, 0, -1, 1], 'lmfdb_label': '58.b1', 'torsion': [2]}
  • id: 2079
    {'degree': 4, 'field': [1, -1, 1, -1, 1], 'lmfdb_label': '58.b1', 'torsion': [5]}
  • id: 2080
    {'degree': 5, 'field': [-2, 0, 0, 0, 0, 1], 'lmfdb_label': '58.b1', 'torsion': [5]}
  • id: 2081
    {'degree': 6, 'field': [16, -8, 22, 10, -1, -2, 1], 'lmfdb_label': '58.b1', 'torsion': [2, 2]}
  • id: 2082
    {'degree': 8, 'field': [-3, 0, -20, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '58.b1', 'torsion': [3]}
  • id: 2083
    {'degree': 12, 'field': [-1, 3, 26, 13, -37, 20, 0, 12, -3, 1, -2, -1, 1], 'lmfdb_label': '58.b1', 'torsion': [4]}
  • id: 2084
    {'degree': 12, 'field': [16, 0, -8, -8, 4, -12, 2, 4, 5, -3, 1, -1, 1], 'lmfdb_label': '58.b1', 'torsion': [10]}
  • id: 2085
    {'degree': 15, 'field': [16, 0, 0, 0, 0, 22, 0, 0, 0, 0, -10, 0, 0, 0, 0, 1], 'lmfdb_label': '58.b1', 'torsion': [10]}
  • id: 2086
    {'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': '58.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: 306
    {'conductor': 58, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '58.b1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 307
    {'conductor': 58, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '58.b1', 'prime': 29, '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: 1666031
    {'adelic_gens': [[571, 10, 570, 11], [6, 5, 285, 576], [1, 0, 10, 1], [1, 10, 0, 1], [297, 10, 540, 1], [186, 5, 135, 576], [6, 13, 525, 461]], 'adelic_image': '580.48.1.?', 'conductor': 58, 'lmfdb_label': '58.b1', 'prime': 0}
  • id: 182
    {'conductor': 58, 'elladic_image': '5.24.0.3', 'lmfdb_label': '58.b1', 'modell_image': '5B.1.2', 'prime': 5}
• lmfdb_iso 58.b does not appear in ec_padic