Elliptic curve data - 1872.d1

Formats: - HTML - YAML - JSON - 2026-03-10T10:26:38.658682

• 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': '1872b', 'Clabel': '1872b2', 'Cnumber': 2, 'abc_quality': 0.8549692080894192, 'absD': 4672512, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 156, 'ainvs': [0, 0, 0, -51, -94], 'analytic_rank': 1, 'bad_primes': [2, 3, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 1872, 'degree': 256, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.016441502017888575499045248284', 'prec': 110}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 3, 'isogeny_degrees': [1, 2], 'jinv': [530604, 169], 'lmfdb_iso': '1872.d', 'lmfdb_label': '1872.d1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -51, 94], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '12.6.0.a.1', '52.6.0.e.1', '156.12.0.?'], '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': '0.72020059558646639330007627756', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 3], [3, 6, 208], [13, 14, 144]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.86871722465153708952888332540', 'prec': 107}, 'szpiro_ratio': 3.1068105256152103, '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, 0, 0, -2, 0, -2, 0, 0, 0, 4, 0, -1, 0, 0, 0, 0, 0, 2, 0], 'aplist': [0, 0, -2, -2, 4, -1, 0, 2, 4, 0, -2, -10, -2, -8, 0, -12, 12, -6, 6, -8, -2, -12, -4, -14, -10], 'class_deg': 2, 'class_size': 2, 'conductor': 1872, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '1872.d', 'trace_hash': 2212481615064370741}
• 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': '1.0334296250727666810160718104', 'prec': 100}, 'conductor': 1872, 'gens': [[-5, 6, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.72020059558646639330007627756', 'prec': 103}], 'lmfdb_label': '1872.d1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.8314537416017549401157659659', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.6380281509812924624973502021204611672', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-2, 0, 1]], 'xcoord_integral_points': [-5, -2, 11, 14]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': [3, 0], '17': [1, 1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '1872.d1'}
• ec_torsion_growth •

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

  
  
  • id: 94744
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '1872.d1', 'torsion': [2, 2]}
  • id: 94745
    {'degree': 4, 'field': [4, 2, 6, -1, 1], 'lmfdb_label': '1872.d1', 'torsion': [4]}
  • id: 94748
    {'degree': 8, 'field': [-48, 0, 0, 0, 24, 0, 4, 0, 1], 'lmfdb_label': '1872.d1', 'torsion': [6]}
  • id: 94747
    {'degree': 8, 'field': [-11, 8, 8, 2, -5, -2, 2, -2, 1], 'lmfdb_label': '1872.d1', 'torsion': [2, 4]}
  • id: 94746
    {'degree': 8, 'field': [100, 0, -47, 0, 3, 0, 7, 0, 1], 'lmfdb_label': '1872.d1', 'torsion': [2, 4]}
  • id: 94750
    {'degree': 16, 'field': [9, 0, 0, 0, -252, 0, -312, 0, -546, 0, 48, 0, 88, 0, 8, 0, 1], 'lmfdb_label': '1872.d1', 'torsion': [2, 6]}
  • id: 94749
    {'degree': 16, 'field': [256, 0, -1504, 0, 1340, 0, 2678, 0, 1393, 0, 364, 0, 230, 0, 22, 0, 1], 'lmfdb_label': '1872.d1', '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: 30258
    {'conductor': 1872, 'conductor_valuation': 4, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -6, 'lmfdb_label': '1872.d1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 30259
    {'conductor': 1872, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '1872.d1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 30260
    {'conductor': 1872, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '1872.d1', '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: 1676201
    {'adelic_gens': [[145, 4, 134, 9], [1, 2, 2, 5], [40, 121, 117, 40], [3, 4, 8, 11], [153, 4, 152, 5], [56, 1, 103, 0], [1, 4, 0, 1], [1, 0, 4, 1]], 'adelic_image': '156.12.0.?', 'conductor': 1872, 'lmfdb_label': '1872.d1', 'prime': 0}
  • id: 9139
    {'conductor': 1872, 'elladic_image': '2.3.0.1', 'lmfdb_label': '1872.d1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 53276
    {'lmfdb_iso': '1872.d', 'p': 5, 'prec': 20, 'unit': 11920327246779, 'val': 1}
  • id: 53277
    {'lmfdb_iso': '1872.d', 'p': 7, 'prec': 20, 'unit': 4237056528471001, 'val': 1}
  • id: 53282
    {'lmfdb_iso': '1872.d', 'p': 11, 'prec': 20, 'unit': 44153233152561450505, 'val': 1}
  • id: 53283
    {'lmfdb_iso': '1872.d', 'p': 19, 'prec': 20, 'unit': 1374259649687768069112604, 'val': 1}
  • id: 53286
    {'lmfdb_iso': '1872.d', 'p': 23, 'prec': 20, 'unit': 44725577096254004973296450, 'val': 1}
  • id: 53278
    {'lmfdb_iso': '1872.d', 'p': 31, 'prec': 20, 'unit': 14099150153076363960345911069, 'val': 1}
  • id: 53291
    {'lmfdb_iso': '1872.d', 'p': 37, 'prec': 20, 'unit': 316837401488406645741937669178, 'val': 1}
  • id: 53279
    {'lmfdb_iso': '1872.d', 'p': 41, 'prec': 20, 'unit': 545400304975477766266322550420, 'val': 1}
  • id: 53280
    {'lmfdb_iso': '1872.d', 'p': 43, 'prec': 20, 'unit': 3405762846457821335438943607151, 'val': 1}
  • id: 53284
    {'lmfdb_iso': '1872.d', 'p': 53, 'prec': 20, 'unit': 530610059252818859757450062899944, 'val': 1}
  • id: 53289
    {'lmfdb_iso': '1872.d', 'p': 59, 'prec': 20, 'unit': 56567122138139178775793228968939, 'val': 2}
  • id: 53290
    {'lmfdb_iso': '1872.d', 'p': 61, 'prec': 20, 'unit': 5550557319260548582162974605752540, 'val': 1}
  • id: 53275
    {'lmfdb_iso': '1872.d', 'p': 67, 'prec': 20, 'unit': 3796951219777917772762471114003960, 'val': 1}
  • id: 53288
    {'lmfdb_iso': '1872.d', 'p': 71, 'prec': 20, 'unit': 54200299112557716708386463057535699, 'val': 1}
  • id: 53285
    {'lmfdb_iso': '1872.d', 'p': 73, 'prec': 20, 'unit': 125553180871782252065828988524430534, 'val': 1}
  • id: 53281
    {'lmfdb_iso': '1872.d', 'p': 79, 'prec': 20, 'unit': 896086946812941684679514496184992301, 'val': 1}
  • id: 53274
    {'lmfdb_iso': '1872.d', 'p': 83, 'prec': 20, 'unit': 1022441128658029720482201551620554082, 'val': 1}
  • id: 53287
    {'lmfdb_iso': '1872.d', 'p': 89, 'prec': 20, 'unit': 4191166326797246592543933815901265701, 'val': 1}
  • id: 53273
    {'lmfdb_iso': '1872.d', 'p': 97, 'prec': 20, 'unit': 14484009373506882230705611562212837398, 'val': 1}