Elliptic curve data - 31200.b2

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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
  serre_invariants	integer[]
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '31200h', 'Clabel': '31200h2', 'Cnumber': 2, 'abc_quality': 0.8900787468395513, 'absD': 97344000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1560, 'ainvs': [0, -1, 0, 767, 12337], 'analytic_rank': 2, 'bad_primes': [2, 3, 5, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 31200, 'degree': 32768, 'elladic_images': ['4.6.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.79299423697072578033547882338', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [778688, 1521], 'lmfdb_iso': '31200.b', 'lmfdb_label': '31200.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 31, -111], 'min_quad_twist_disc': -20, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.a.1', '52.12.0.d.1', '104.24.0.?', '120.12.0.?', '1560.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 31, 'optimality': 0, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '0.58040412978974355949777665310', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 25], [3, 4, 10400], [5, 14, 1248], [13, 14, 2400]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.70487189980626971638213296469', 'prec': 107}, 'szpiro_ratio': 3.131458319091942, '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, -2, 0, 1, 0, -6, 0, 1, 0, 0, 0, 2, 0, -6, 0], 'aplist': [0, -1, 0, -2, -6, 1, 2, -6, 0, -6, 6, -2, -10, -8, -6, -6, -6, -10, -2, -14, 14, 4, -6, 6, 14], 'class_deg': 2, 'class_size': 2, 'conductor': 31200, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '31200.b', 'trace_hash': 179315313265360141}
• 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': '0.20474530765623104517462774170', 'prec': 103}, 'conductor': 31200, 'gens': [[37, 300, 1], [-3, 100, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.72585734982160570531951001056', 'prec': 103}, {'__RealLiteral__': 0, 'data': '0.80218785085248582175375464266', 'prec': 103}], 'lmfdb_label': '31200.b2', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.73563836505164036723179081957', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.8314807217239524525346396383824515372', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[-13, 0, 1]], 'xcoord_integral_points': [-13, -9, -8, -3, 13, 23, 37, 67, 117, 247, 312, 797, 1237, 1261, 20467, 13525187]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': 'a', '7': [2, 0], '11': [2, 0], '13': [3, 0], '17': [2, 0], '19': [2, 0], '23': [2, 2, 0], '29': [2, 0], '31': [2, 0], '37': [2, 0], '41': [2, 0], '43': [2, 0], '47': [2, 0]}, 'iwp0': 0, 'lmfdb_label': '31200.b2'}
• ec_torsion_growth •

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

  
  
  • id: 1555554
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '31200.b2', 'torsion': [2, 2]}
  • id: 1555555
    {'degree': 4, 'field': [-25, 0, -15, 0, 1], 'lmfdb_label': '31200.b2', 'torsion': [4]}
  • id: 1555558
    {'degree': 8, 'field': [-151875, 0, -18000, 0, 1350, 0, 0, 0, 1], 'lmfdb_label': '31200.b2', 'torsion': [6]}
  • id: 1555556
    {'degree': 8, 'field': [81, 198, 242, 202, 118, 42, 2, -2, 1], 'lmfdb_label': '31200.b2', 'torsion': [2, 4]}
  • id: 1555557
    {'degree': 8, 'field': [2041, 3880, 2782, 976, 168, -4, -14, -4, 1], 'lmfdb_label': '31200.b2', 'torsion': [2, 4]}
  • id: 1555560
    {'degree': 16, 'field': [16, 0, -1453696, 0, -2746032, 0, -286880, 0, 42460, 0, -35792, 0, 1980, 0, -88, 0, 1], 'lmfdb_label': '31200.b2', 'torsion': [8]}
  • id: 1555559
    {'degree': 16, 'field': [4410601, 1136720, -1035246, -96968, -174870, 161256, 96370, -76988, -36573, 23852, 8038, -6300, 504, 224, -12, -8, 1], 'lmfdb_label': '31200.b2', 'torsion': [4, 4]}
  • id: 1555561
    {'degree': 16, 'field': [503981396, -947927936, 1111492288, -503596912, 241266296, -6978936, -688880, -1627696, 660524, -157792, 20880, -688, 536, -84, 32, -8, 1], 'lmfdb_label': '31200.b2', 'torsion': [2, 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: 727770
    {'conductor': 31200, 'conductor_valuation': 5, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '31200.b2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 727771
    {'conductor': 31200, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '31200.b2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 727772
    {'conductor': 31200, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '31200.b2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 727773
    {'conductor': 31200, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '31200.b2', 'prime': 13, '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: 1872409
    {'adelic_gens': [[3, 8, 10, 27], [1, 0, 8, 1], [781, 940, 1250, 321], [1, 8, 0, 1], [623, 0, 0, 1559], [521, 320, 730, 641], [1553, 8, 1552, 9], [5, 8, 48, 77], [1171, 940, 585, 1], [1081, 1250, 0, 1]], 'adelic_image': '1560.48.0.?', 'conductor': 31200, 'lmfdb_label': '31200.b2', 'prime': 0}
  • id: 139710
    {'conductor': 31200, 'elladic_image': '4.6.0.5', 'lmfdb_label': '31200.b2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 1514198
    {'lmfdb_iso': '31200.b', 'p': 7, 'prec': 20, 'unit': 9624849455656746, 'val': 2}
  • id: 1514203
    {'lmfdb_iso': '31200.b', 'p': 11, 'prec': 20, 'unit': 3974195274400446680, 'val': 2}
  • id: 1514204
    {'lmfdb_iso': '31200.b', 'p': 17, 'prec': 20, 'unit': 169909520163121978321384, 'val': 2}
  • id: 1514205
    {'lmfdb_iso': '31200.b', 'p': 19, 'prec': 20, 'unit': 235125497995877879392789, 'val': 2}
  • id: 1514201
    {'lmfdb_iso': '31200.b', 'p': 29, 'prec': 20, 'unit': 2093488272578934449425130865, 'val': 2}
  • id: 1514213
    {'lmfdb_iso': '31200.b', 'p': 31, 'prec': 20, 'unit': 2163803233467941340885779485, 'val': 2}
  • id: 1514197
    {'lmfdb_iso': '31200.b', 'p': 37, 'prec': 20, 'unit': 486922697335861327232668917254, 'val': 2}
  • id: 1514199
    {'lmfdb_iso': '31200.b', 'p': 41, 'prec': 20, 'unit': 215968232181643673724142769491, 'val': 2}
  • id: 1514200
    {'lmfdb_iso': '31200.b', 'p': 43, 'prec': 20, 'unit': 5300347656030539749786922435996, 'val': 2}
  • id: 1514211
    {'lmfdb_iso': '31200.b', 'p': 47, 'prec': 20, 'unit': 22976811423770788810338461285758, 'val': 2}
  • id: 1514206
    {'lmfdb_iso': '31200.b', 'p': 53, 'prec': 20, 'unit': 112045125843727507983963523336590, 'val': 2}
  • id: 1514207
    {'lmfdb_iso': '31200.b', 'p': 59, 'prec': 20, 'unit': 3499240500838948798509731615969954, 'val': 2}
  • id: 1514212
    {'lmfdb_iso': '31200.b', 'p': 61, 'prec': 20, 'unit': 3356819055366441396327768724858742, 'val': 2}
  • id: 1514196
    {'lmfdb_iso': '31200.b', 'p': 67, 'prec': 20, 'unit': 36823120246176687489334103478195892, 'val': 2}
  • id: 1514210
    {'lmfdb_iso': '31200.b', 'p': 71, 'prec': 20, 'unit': 92459197259769541435095033076575942, 'val': 2}
  • id: 1514208
    {'lmfdb_iso': '31200.b', 'p': 73, 'prec': 20, 'unit': 80462404508579760432820384069769338, 'val': 2}
  • id: 1514202
    {'lmfdb_iso': '31200.b', 'p': 79, 'prec': 20, 'unit': 766418080712517183379085821049067742, 'val': 2}
  • id: 1514195
    {'lmfdb_iso': '31200.b', 'p': 83, 'prec': 20, 'unit': 407377252251725817102753045537039425, 'val': 2}
  • id: 1514209
    {'lmfdb_iso': '31200.b', 'p': 89, 'prec': 20, 'unit': 9450265453780793607435646661131070725, 'val': 2}
  • id: 1514194
    {'lmfdb_iso': '31200.b', 'p': 97, 'prec': 20, 'unit': 47044079952949682540040717095526919033, 'val': 2}