Elliptic curve data - 1872.e1

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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': '1872i3', 'Cnumber': 3, 'abc_quality': 1.052193877800105, 'absD': 29113344, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 312, 'ainvs': [0, 0, 0, -7491, -249550], 'analytic_rank': 1, 'bad_primes': [2, 3, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 1872, 'degree': 1024, 'elladic_images': ['4.12.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.75243146883677382400761995902', 'prec': 103}, 'faltings_index': 2, 'faltings_ratio': 4, 'intrinsic_torsion': 2, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 4], 'jinv': [62275269892, 39], 'lmfdb_iso': '1872.e', 'lmfdb_label': '1872.e1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -832, -9520], 'min_quad_twist_disc': 12, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '24.24.0-24.z.1.16', '104.24.0.?', '156.24.0.?', '312.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '5.2779615114796782908413111404', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 117], [3, 8, 208], [13, 14, 144]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.37449732596390211287102942732', 'prec': 107}, 'szpiro_ratio': 5.093455164605873, '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, 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': '0.22204772612426742011555190739', 'prec': 103}, 'conductor': 1872, 'gens': [[146, 1330, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '5.2779615114796782908413111404', 'prec': 100}], 'lmfdb_label': '1872.e1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.51317397286041250678662099241', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.7085124774503742006087399479640825557', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[-50, 0, 1]], 'xcoord_integral_points': [-50, 146]}
• 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.e1'}
• ec_torsion_growth •

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

  
  
  • id: 94884
    {'degree': 2, 'field': [-39, 0, 1], 'lmfdb_label': '1872.e1', 'torsion': [2, 2]}
  • id: 94885
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '1872.e1', 'torsion': [4]}
  • id: 94886
    {'degree': 2, 'field': [10, -1, 1], 'lmfdb_label': '1872.e1', 'torsion': [4]}
  • id: 94887
    {'degree': 4, 'field': [-56, -20, 21, -2, 1], 'lmfdb_label': '1872.e1', 'torsion': [2, 4]}
  • id: 94888
    {'degree': 4, 'field': [100, 0, -19, 0, 1], 'lmfdb_label': '1872.e1', 'torsion': [2, 4]}
  • id: 94892
    {'degree': 8, 'field': [-117, 144, -288, 42, 12, 12, -10, -2, 1], 'lmfdb_label': '1872.e1', 'torsion': [6]}
  • id: 94889
    {'degree': 8, 'field': [256, 0, -191, 0, 291, 0, -29, 0, 1], 'lmfdb_label': '1872.e1', 'torsion': [4, 4]}
  • id: 94890
    {'degree': 8, 'field': [1521, 0, 0, 0, -69, 0, 0, 0, 1], 'lmfdb_label': '1872.e1', 'torsion': [8]}
  • id: 94891
    {'degree': 8, 'field': [24336, 0, -4056, 0, 520, 0, -26, 0, 1], 'lmfdb_label': '1872.e1', 'torsion': [8]}
  • id: 94896
    {'degree': 16, 'field': [-642758, 1594496, 2059004, -2199140, -4397546, -2095776, 281998, 551216, 111410, -45272, -20252, 1818, 1828, 26, -70, -2, 1], 'lmfdb_label': '1872.e1', 'torsion': [2, 6]}
  • id: 94897
    {'degree': 16, 'field': [729, 0, 0, 0, 5328, 0, 0, 0, 270, 0, 0, 0, -36, 0, 0, 0, 1], 'lmfdb_label': '1872.e1', 'torsion': [12]}
  • id: 94895
    {'degree': 16, 'field': [6561, 0, 0, 0, 1701, 0, 0, 0, 360, 0, 0, 0, 21, 0, 0, 0, 1], 'lmfdb_label': '1872.e1', 'torsion': [2, 8]}
  • id: 94898
    {'degree': 16, 'field': [81796, 0, 23660, 0, 55432, 0, -22204, 0, 8593, 0, -1456, 0, 274, 0, -28, 0, 1], 'lmfdb_label': '1872.e1', 'torsion': [12]}
  • id: 94893
    {'degree': 16, 'field': [950625, 0, 0, 0, -4788108, 0, 0, 0, 115050, 0, 0, 0, -780, 0, 0, 0, 1], 'lmfdb_label': '1872.e1', 'torsion': [2, 8]}
  • id: 94894
    {'degree': 16, 'field': [2313441, 0, 0, 0, -138411, 0, 0, 0, 6760, 0, 0, 0, -91, 0, 0, 0, 1], 'lmfdb_label': '1872.e1', '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: 30306
    {'conductor': 1872, 'conductor_valuation': 4, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -6, 'lmfdb_label': '1872.e1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 30307
    {'conductor': 1872, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '1872.e1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 30308
    {'conductor': 1872, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '1872.e1', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  
  • id: 1676203
    {'adelic_gens': [[268, 1, 215, 6], [7, 6, 306, 307], [1, 0, 8, 1], [43, 42, 130, 283], [200, 309, 203, 310], [192, 31, 167, 120], [1, 8, 0, 1], [1, 4, 4, 17], [305, 8, 304, 9]], 'adelic_image': '312.48.0.?', 'conductor': 1872, 'lmfdb_label': '1872.e1', 'prime': 0}
  • id: 9141
    {'conductor': 1872, 'elladic_image': '4.12.0.8', 'lmfdb_label': '1872.e1', 'modell_image': '2B', '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}