Elliptic curve data - 1872.e2

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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': '1872i', 'Clabel': '1872i2', 'Cnumber': 2, 'abc_quality': 0.9871496807008809, 'absD': 283855104, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 156, 'ainvs': [0, 0, 0, -471, -3850], 'analytic_rank': 1, 'bad_primes': [2, 3, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 1872, 'degree': 512, 'elladic_images': ['4.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.40585787855680116929900389829', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2], 'jinv': [61918288, 1521], 'lmfdb_iso': '1872.e', 'lmfdb_label': '1872.e2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -52, -160], 'min_quad_twist_disc': 12, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0-2.a.1.1', '12.24.0-12.b.1.1', '52.24.0-52.b.1.3', '156.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 7, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.6389807557398391454206555702', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 9], [3, 8, 208], [13, 14, 144]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.60554638615055054934344013448', 'prec': 107}, 'szpiro_ratio': 3.9919210045295364, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 4, 0], 'aplist': [0, 0, -2, 0, 0, 1, -2, 4, 0, -6, 0, -2, -6, 12, -4, -6, -8, -2, -4, -12, -14, 0, 8, 18, -6], 'class_deg': 4, 'class_size': 4, 'conductor': 1872, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '1872.e', 'trace_hash': 1311746732148815824}
• 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': '0.44409545224853484023110381478', 'prec': 103}, 'conductor': 1872, 'gens': [[38, 182, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.6389807557398391454206555702', 'prec': 100}], 'lmfdb_label': '1872.e2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.0263479457208250135732419848', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.7085124774503742006087399479640825557', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-11, 0, 1], [25, 0, 1]], 'xcoord_integral_points': [-14, -11, 25, 38, 133]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [3, 0], '7': [1, 1, 0], '11': [1, 1, 0], '13': [2, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '1872.e2'}
• ec_torsion_growth •

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

  
  
  • id: 94875
    {'degree': 2, 'field': [-39, 0, 1], 'lmfdb_label': '1872.e2', 'torsion': [2, 4]}
  • id: 94877
    {'degree': 4, 'field': [1, 0, -1, 0, 1], 'lmfdb_label': '1872.e2', 'torsion': [2, 4]}
  • id: 94876
    {'degree': 4, 'field': [9, 3, 4, -1, 1], 'lmfdb_label': '1872.e2', 'torsion': [2, 4]}
  • id: 94880
    {'degree': 8, 'field': [-117, 144, -288, 42, 12, 12, -10, -2, 1], 'lmfdb_label': '1872.e2', 'torsion': [2, 6]}
  • id: 94878
    {'degree': 8, 'field': [81, 0, -63, 0, 40, 0, -7, 0, 1], 'lmfdb_label': '1872.e2', 'torsion': [4, 4]}
  • id: 94879
    {'degree': 8, 'field': [1444, 0, -880, 0, 201, 0, -22, 0, 1], 'lmfdb_label': '1872.e2', 'torsion': [2, 8]}
  • id: 94883
    {'degree': 16, 'field': [-642758, 1594496, 2059004, -2199140, -4397546, -2095776, 281998, 551216, 111410, -45272, -20252, 1818, 1828, 26, -70, -2, 1], 'lmfdb_label': '1872.e2', 'torsion': [2, 12]}
  • id: 94882
    {'degree': 16, 'field': [81, 0, 0, 0, -135, 0, 0, 0, 54, 0, 0, 0, 12, 0, 0, 0, 1], 'lmfdb_label': '1872.e2', 'torsion': [2, 8]}
  • id: 94881
    {'degree': 16, 'field': [6561, 0, 10206, 0, 11502, 0, 4536, 0, 1071, 0, 504, 0, 142, 0, 14, 0, 1], 'lmfdb_label': '1872.e2', 'torsion': [2, 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: 30303
    {'conductor': 1872, 'conductor_valuation': 4, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '1872.e2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 30304
    {'conductor': 1872, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '1872.e2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 30305
    {'conductor': 1872, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '1872.e2', '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: 1676204
    {'adelic_gens': [[75, 152, 148, 145], [145, 2, 0, 1], [153, 4, 152, 5], [103, 152, 50, 147], [1, 4, 0, 1], [1, 0, 4, 1]], 'adelic_image': '156.48.0.?', 'conductor': 1872, 'lmfdb_label': '1872.e2', 'prime': 0}
  • id: 9142
    {'conductor': 1872, 'elladic_image': '4.12.0.1', 'lmfdb_label': '1872.e2', 'modell_image': '2Cs', 'prime': 2}
• ec_padic •

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

  
  
  • id: 53385
    {'lmfdb_iso': '1872.e', 'p': 5, 'prec': 20, 'unit': 1441094973634, 'val': 2}
  • id: 53378
    {'lmfdb_iso': '1872.e', 'p': 17, 'prec': 20, 'unit': 107662076420009938942970, 'val': 1}
  • id: 53369
    {'lmfdb_iso': '1872.e', 'p': 19, 'prec': 20, 'unit': 680640542565111368088191, 'val': 1}
  • id: 53376
    {'lmfdb_iso': '1872.e', 'p': 29, 'prec': 20, 'unit': 593488398077877079219709821, 'val': 1}
  • id: 53372
    {'lmfdb_iso': '1872.e', 'p': 37, 'prec': 20, 'unit': 208496650407368377913708955556, 'val': 1}
  • id: 53374
    {'lmfdb_iso': '1872.e', 'p': 41, 'prec': 20, 'unit': 1558176412375877769289824465873, 'val': 1}
  • id: 53375
    {'lmfdb_iso': '1872.e', 'p': 43, 'prec': 20, 'unit': 6789964918510116046300429477896, 'val': 1}
  • id: 53377
    {'lmfdb_iso': '1872.e', 'p': 47, 'prec': 20, 'unit': 17396929095682784619516971590434, 'val': 1}
  • id: 53380
    {'lmfdb_iso': '1872.e', 'p': 53, 'prec': 20, 'unit': 190870801973215195180771453981637, 'val': 1}
  • id: 53383
    {'lmfdb_iso': '1872.e', 'p': 59, 'prec': 20, 'unit': 2308422139180611419827007897929318, 'val': 1}
  • id: 53384
    {'lmfdb_iso': '1872.e', 'p': 61, 'prec': 20, 'unit': 8264965710248944194111220800218529, 'val': 1}
  • id: 53371
    {'lmfdb_iso': '1872.e', 'p': 67, 'prec': 20, 'unit': 48785493750139963863436293157429348, 'val': 1}
  • id: 53373
    {'lmfdb_iso': '1872.e', 'p': 71, 'prec': 20, 'unit': 58456679386803409066884305327740848, 'val': 1}
  • id: 53381
    {'lmfdb_iso': '1872.e', 'p': 73, 'prec': 20, 'unit': 92400720231886774220386917952281558, 'val': 1}
  • id: 53379
    {'lmfdb_iso': '1872.e', 'p': 83, 'prec': 20, 'unit': 1751194918910164542314323299936437570, 'val': 1}
  • id: 53382
    {'lmfdb_iso': '1872.e', 'p': 89, 'prec': 20, 'unit': 970282357669959500600329656968653826, 'val': 1}
  • id: 53370
    {'lmfdb_iso': '1872.e', 'p': 97, 'prec': 20, 'unit': 24508108208143714577864732243748790887, 'val': 1}