Elliptic curve data - 57.b1

Formats: - HTML - YAML - JSON - 2024-04-20T02:28:14.241938

• 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': '57c', 'Clabel': '57c2', 'Cnumber': 2, 'abc_quality': 1.0683303788164564, 'absD': 22284891, 'adelic_genus': 1, 'adelic_index': 48, 'adelic_level': 190, 'ainvs': [0, 1, 1, -4390, -113432], 'analytic_rank': 0, 'bad_primes': [3, 19], 'class_deg': 5, 'class_size': 2, 'cm': 0, 'conductor': 57, 'degree': 60, 'elladic_images': ['5.24.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.65140725122842848756374343035', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 5, 'iso_nlabel': 1, 'isogeny_degrees': [1, 5], 'jinv': [-9358714467168256, 22284891], 'lmfdb_iso': '57.b', 'lmfdb_label': '57.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, -4390, -113432], 'min_quad_twist_disc': 1, 'modell_images': ['5B.1.2'], 'modm_images': ['5.24.0-5.a.2.2', '38.2.0.a.1', '190.48.1.?'], '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, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.65140725122842848756374343035', 'prec': 103}, 'szpiro_ratio': 9.095874875488168, '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, -2, 1, 2, 1, -2, 3, 0, 1, -2, -3, 2, -6, -6, 1, -4, 3, -2, -1, 2], 'aplist': [-2, 1, 1, 3, -3, -6, 3, -1, 4, -10, 2, 8, -8, -1, 3, -6, 0, 7, 8, 12, -11, 0, 4, 10, -2], 'class_deg': 5, 'class_size': 2, 'conductor': 57, 'isogeny_matrix': [[1, 5], [5, 1]], 'lmfdb_iso': '57.b', 'trace_hash': 27661726142936421}
• 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': '0.27176583004093608371960484374', 'prec': 103}, 'conductor': 57, 'gens': [], 'heights': [], 'lmfdb_label': '57.b1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.29325479582828399279210747717', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.58650959165656798558421495433617674241', 'prec': 133}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 4, 0], '3': [3, 0], '5': [2, 1], '19': [0, 0]}, 'iwp0': 7, 'lmfdb_label': '57.b1'}
• ec_torsion_growth •

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

  
  
  • id: 2060
    {'degree': 3, 'field': [-2, -2, 0, 1], 'lmfdb_label': '57.b1', 'torsion': [2]}
  • id: 2061
    {'degree': 4, 'field': [1, -1, 1, -1, 1], 'lmfdb_label': '57.b1', 'torsion': [5]}
  • id: 2062
    {'degree': 5, 'field': [-3, 0, 0, 0, 0, 1], 'lmfdb_label': '57.b1', 'torsion': [5]}
  • id: 2063
    {'degree': 6, 'field': [1, -3, 4, -3, 4, -3, 1], 'lmfdb_label': '57.b1', 'torsion': [2, 2]}
  • id: 2064
    {'degree': 8, 'field': [-3, 0, 11, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '57.b1', 'torsion': [3]}
  • id: 2065
    {'degree': 12, 'field': [-13, 18, -38, 20, -31, 12, -16, 4, -11, -6, 10, -4, 1], 'lmfdb_label': '57.b1', 'torsion': [4]}
  • id: 2066
    {'degree': 12, 'field': [16, 16, 16, 8, 0, 16, 12, 12, 4, -2, 2, 0, 1], 'lmfdb_label': '57.b1', 'torsion': [10]}
  • id: 2067
    {'degree': 15, 'field': [-864, 0, 0, 0, 0, 432, 0, 0, 0, 0, -60, 0, 0, 0, 0, 1], 'lmfdb_label': '57.b1', 'torsion': [10]}
  • id: 2068
    {'degree': 20, 'field': [41, -25, -30, -20, -20, -1, 60, -155, 420, -560, 711, -780, 770, -645, 460, -281, 140, -60, 20, -5, 1], 'lmfdb_label': '57.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: 300
    {'conductor': 57, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '57.b1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 301
    {'conductor': 57, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '57.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: 1666024
    {'adelic_gens': [[1, 0, 10, 1], [21, 10, 105, 51], [1, 10, 0, 1], [6, 13, 135, 71], [181, 10, 180, 11], [7, 10, 150, 171]], 'adelic_image': '190.48.1.?', 'conductor': 57, 'lmfdb_label': '57.b1', 'prime': 0}
  • id: 176
    {'conductor': 57, 'elladic_image': '5.24.0.3', 'lmfdb_label': '57.b1', 'modell_image': '5B.1.2', 'prime': 5}
• lmfdb_iso 57.b does not appear in ec_padic