Elliptic curve data - 193200.hb2

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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': '193200bn', 'Clabel': '193200bn2', 'Cnumber': 2, 'abc_quality': 0.9228103994399539, 'absD': 1360541448000000000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 3220, 'ainvs': [0, 1, 0, 157992, 50699988], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 23], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 193200, 'degree': 2359296, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1627897108665607600210413168', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 183, 'isogeny_degrees': [1, 2], 'jinv': [6814692748079, 21258460125], 'lmfdb_iso': '193200.hb', 'lmfdb_label': '193200.hb2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 395, -6298], 'min_quad_twist_disc': -20, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '20.6.0.a.1', '644.6.0.?', '3220.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 7, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.91498379166392168102729354873', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.66492357408956526330342952873', 'prec': 103}, 'szpiro_ratio': 4.026127850869949, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
• 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, 0, 1, 0, 0, 0, 1, 0, 1, 0, 2, 0, 4, 0, 0, 0, 2, 0, 0, 0], 'aplist': [0, 1, 0, 1, 2, 4, 2, 0, 1, -6, 2, -4, -2, -8, -8, 0, -2, -14, -12, 0, -8, -10, 12, 6, 14], 'class_deg': 2, 'class_size': 2, 'conductor': 193200, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '193200.hb', 'trace_hash': 28670921926986629}
• 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': '0.013225884511026528659411220775', 'prec': 107}, 'conductor': 193200, 'gens': [[-132, 5250, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.91498379166392168102729354873', 'prec': 103}], 'lmfdb_label': '193200.hb2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.19105262049463599830145670295', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '11.187843270880660342681900951405748987', 'prec': 130}, 'tamagawa_product': 256, 'torsion_generators': [[-237, 0, 1]], 'xcoord_integral_points': [-237, -132, 663, 2868]}
• lmfdb_label 193200.hb2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8499235
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '193200.hb2', 'torsion': [2, 2]}
  • id: 8499236
    {'degree': 4, 'field': [-20, 0, -9, 0, 1], 'lmfdb_label': '193200.hb2', 'torsion': [4]}
  • id: 8499239
    {'degree': 8, 'field': [-46875, 0, -8875, 0, 750, 0, 0, 0, 1], 'lmfdb_label': '193200.hb2', 'torsion': [6]}
  • id: 8499238
    {'degree': 8, 'field': [126, 140, 214, -100, 131, -40, 14, 0, 1], 'lmfdb_label': '193200.hb2', 'torsion': [2, 4]}
  • id: 8499237
    {'degree': 8, 'field': [2500, 0, 3320, 0, 101, 0, 2, 0, 1], 'lmfdb_label': '193200.hb2', 'torsion': [2, 4]}
  • id: 8499241
    {'degree': 16, 'field': [893025, 0, 2447010, 0, -57159, 0, -41440, 0, 9770, 0, 6542, 0, 760, 0, 40, 0, 1], 'lmfdb_label': '193200.hb2', 'torsion': [2, 6]}
  • id: 8499240
    {'degree': 16, 'field': [8294400, 0, 3540326400, 0, 161616640, 0, -39093120, 0, -5087664, 0, -186912, 0, -876, 0, 72, 0, 1], 'lmfdb_label': '193200.hb2', 'torsion': [8]}
• 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: 4783839
    {'conductor': 193200, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '193200.hb2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4783840
    {'conductor': 193200, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '193200.hb2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 4783841
    {'conductor': 193200, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '193200.hb2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 4783842
    {'conductor': 193200, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '193200.hb2', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4783843
    {'conductor': 193200, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '193200.hb2', 'prime': 23, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
• ec_galrep •

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

  
  
  • id: 2904178
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [281, 4, 562, 9], [1, 4, 0, 1], [1934, 1, 643, 0], [3217, 4, 3216, 5], [2761, 4, 2302, 9], [2416, 809, 805, 2416]], 'adelic_image': '3220.12.0.?', 'conductor': 193200, 'lmfdb_label': '193200.hb2', 'prime': 0}
  • id: 719613
    {'conductor': 193200, 'elladic_image': '2.3.0.1', 'lmfdb_label': '193200.hb2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 193200.hb does not appear in ec_padic