Elliptic curve data - 270.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': '270d', 'Clabel': '270d1', 'Cnumber': 1, 'abc_quality': 1.055818861759989, 'absD': 108000, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 120, 'ainvs': [1, -1, 0, -159, 813], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 270, 'degree': 60, 'elladic_images': ['3.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.045372710035910972103610408367', 'prec': 110}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 3], 'jinv': [-16522921323, 4000], 'lmfdb_iso': '270.b', 'lmfdb_label': '270.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -159, 813], 'min_quad_twist_disc': 1, 'modell_images': ['3B.1.1'], 'modm_images': ['3.8.0-3.a.1.2', '120.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.32002578220293839495242171760', 'prec': 107}, 'szpiro_ratio': 4.791398313289864, 'torsion': 3, 'torsion_primes': [3], 'torsion_structure': [3]}
• 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, 0, 1, 1, 0, 2, -1, 0, -1, -3, 0, 5, -2, 0, 1, 3, 0, -4, 1], 'aplist': [-1, 0, 1, 2, -3, 5, 3, -4, 9, 3, 5, -10, 0, -1, -9, 12, -12, 2, -4, -12, -10, -13, -6, 12, 2], 'class_deg': 3, 'class_size': 2, 'conductor': 270, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '270.b', 'trace_hash': 870032548516211281}
• 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': '1.0949902072434661312296549748', 'prec': 100}, 'conductor': 270, 'gens': [], 'heights': [], 'lmfdb_label': '270.b1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '3.2587738278058442970289859595', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.0862579426019480990096619865128463384', 'prec': 130}, 'tamagawa_product': 3, 'torsion_generators': [[7, -1, 1]], 'xcoord_integral_points': [7]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': 'a', '5': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '270.b1'}
• ec_torsion_growth •

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

  
  
  • id: 11459
    {'degree': 3, 'field': [-6, 3, 0, 1], 'lmfdb_label': '270.b1', 'torsion': [6]}
  • id: 11461
    {'degree': 6, 'field': [1, -3, 0, 5, 0, -3, 1], 'lmfdb_label': '270.b1', 'torsion': [3, 3]}
  • id: 11460
    {'degree': 6, 'field': [30, 0, 21, 0, 12, 0, 1], 'lmfdb_label': '270.b1', 'torsion': [2, 6]}
  • id: 11462
    {'degree': 9, 'field': [36, -108, 0, 18, -36, -36, 3, 0, -3, 1], 'lmfdb_label': '270.b1', 'torsion': [9]}
  • id: 11463
    {'degree': 12, 'field': [-18500, 36660, -25965, 2230, 8745, -5412, 459, 702, -297, 28, 15, -6, 1], 'lmfdb_label': '270.b1', 'torsion': [12]}
  • id: 11464
    {'degree': 18, 'field': [64, -96, 96, 168, -144, -114, 93, 132, -81, -146, 42, 12, 75, -18, 6, -12, 3, 0, 1], 'lmfdb_label': '270.b1', 'torsion': [3, 6]}
• 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: 2468
    {'conductor': 270, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '270.b1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 2469
    {'conductor': 270, 'conductor_valuation': 3, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '270.b1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 2470
    {'conductor': 270, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '270.b1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1666892
    {'adelic_gens': [[97, 6, 51, 19], [61, 6, 63, 19], [1, 0, 6, 1], [4, 3, 9, 7], [115, 6, 114, 7], [31, 6, 0, 1], [3, 4, 8, 11], [6, 1, 43, 54], [1, 6, 0, 1]], 'adelic_image': '120.16.0.?', 'conductor': 270, 'lmfdb_label': '270.b1', 'prime': 0}
  • id: 1114
    {'conductor': 270, 'elladic_image': '3.8.0.1', 'lmfdb_label': '270.b1', 'modell_image': '3B.1.1', 'prime': 3}
• lmfdb_iso 270.b does not appear in ec_padic