Elliptic curve data - 121680.p2

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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': '121680bc', 'Clabel': '121680bc2', 'Cnumber': 2, 'abc_quality': 1.044679748772945, 'absD': 1056687328366217437500000000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 156, 'ainvs': [0, 0, 0, 127647897, 1462157032102], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 121680, 'degree': 46964736, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.8678109206483118512762541221', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 15, 'isogeny_degrees': [1, 2], 'jinv': [116227003261808, 533935546875], 'lmfdb_iso': '121680.p', 'lmfdb_label': '121680.p2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 83924, 24621076], 'min_quad_twist_disc': 156, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '12.6.0.f.1', '52.6.0.c.1', '78.6.0.?', '156.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '33.767506577918752332233942404', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.93269463784480758059369450816', 'prec': 103}, 'szpiro_ratio': 5.939373373195547, '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, -1, 0, -2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 6, 0], 'aplist': [0, 0, -1, -2, -4, 0, 2, 6, 0, -10, 2, -8, 2, -4, 8, -2, 0, 10, -2, -12, 8, -8, -16, 6, -8], 'class_deg': 2, 'class_size': 2, 'conductor': 121680, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '121680.p', 'trace_hash': 1000364459658410410}
• 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': '0.00043698056335924914642873413175', 'prec': 113}, 'conductor': 121680, 'gens': [[27719049219234854, 9346117376578791575597922, 1706171]], 'heights': [{'__RealLiteral__': 0, 'data': '33.767506577918752332233942404', 'prec': 100}], 'lmfdb_label': '121680.p2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.035240238001460524530209504795', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.7598998740869625941281614025990178689', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-7774, 0, 1]], 'xcoord_integral_points': [-7774]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [3, 0], '11': [1, 0], '13': 'a', '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '121680.p2'}
• ec_torsion_growth •

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

  
  
  • id: 5556206
    {'degree': 2, 'field': [10, -1, 1], 'lmfdb_label': '121680.p2', 'torsion': [2, 2]}
  • id: 5556207
    {'degree': 4, 'field': [3, -9, 2, -1, 1], 'lmfdb_label': '121680.p2', 'torsion': [4]}
  • id: 5556209
    {'degree': 8, 'field': [1, 0, -9, 0, 32, 0, -9, 0, 1], 'lmfdb_label': '121680.p2', 'torsion': [2, 4]}
  • id: 5556208
    {'degree': 8, 'field': [16, 0, 20, 0, 24, 0, 5, 0, 1], 'lmfdb_label': '121680.p2', 'torsion': [2, 4]}
  • id: 5556210
    {'degree': 8, 'field': [1587, -4508, 4354, -1350, -220, 140, -12, -2, 1], 'lmfdb_label': '121680.p2', 'torsion': [6]}
  • id: 5556211
    {'degree': 16, 'field': [81, 0, -4320, 0, -423, 0, 15948, 0, -2496, 0, -222, 0, 109, 0, 22, 0, 1], 'lmfdb_label': '121680.p2', 'torsion': [8]}
  • id: 5556212
    {'degree': 16, 'field': [95850, -105840, -270666, -67680, 371412, 482010, 203982, -14418, -36059, -10756, -38, 1450, 548, -62, -20, -4, 1], 'lmfdb_label': '121680.p2', '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: 2994583
    {'conductor': 121680, 'conductor_valuation': 4, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '121680.p2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2994584
    {'conductor': 121680, 'conductor_valuation': 2, 'discriminant_valuation': 13, 'j_denominator_valuation': 7, 'kodaira_symbol': -11, 'lmfdb_label': '121680.p2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2994585
    {'conductor': 121680, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '121680.p2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2994586
    {'conductor': 121680, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '121680.p2', 'prime': 13, 'reduction_type': 0, '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: 2458014
    {'adelic_gens': [[1, 2, 2, 5], [106, 1, 103, 0], [112, 1, 11, 0], [3, 4, 8, 11], [153, 4, 152, 5], [1, 4, 0, 1], [41, 118, 116, 39], [1, 0, 4, 1]], 'adelic_image': '156.12.0.?', 'conductor': 121680, 'lmfdb_label': '121680.p2', 'prime': 0}
  • id: 477531
    {'conductor': 121680, 'elladic_image': '2.3.0.1', 'lmfdb_label': '121680.p2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 6360594
    {'lmfdb_iso': '121680.p', 'p': 7, 'prec': 20, 'unit': 1334391851712040, 'val': 2}
  • id: 6360599
    {'lmfdb_iso': '121680.p', 'p': 11, 'prec': 20, 'unit': 45212928723246516641, 'val': 1}
  • id: 6360600
    {'lmfdb_iso': '121680.p', 'p': 17, 'prec': 20, 'unit': 200315225864959452738772, 'val': 1}
  • id: 6360601
    {'lmfdb_iso': '121680.p', 'p': 19, 'prec': 20, 'unit': 762876074298318512371863, 'val': 1}
  • id: 6360597
    {'lmfdb_iso': '121680.p', 'p': 29, 'prec': 20, 'unit': 4256736061936521181685616541, 'val': 1}
  • id: 6360608
    {'lmfdb_iso': '121680.p', 'p': 31, 'prec': 20, 'unit': 15050976288310978860904855461, 'val': 1}
  • id: 6360593
    {'lmfdb_iso': '121680.p', 'p': 37, 'prec': 20, 'unit': 623022674385654837059732969098, 'val': 1}
  • id: 6360595
    {'lmfdb_iso': '121680.p', 'p': 41, 'prec': 20, 'unit': 2346104204880214358668324371179, 'val': 1}
  • id: 6360596
    {'lmfdb_iso': '121680.p', 'p': 43, 'prec': 20, 'unit': 381791709692933131904173789142, 'val': 1}
  • id: 6360598
    {'lmfdb_iso': '121680.p', 'p': 47, 'prec': 20, 'unit': 35370331302276390244251363732281, 'val': 1}
  • id: 6360602
    {'lmfdb_iso': '121680.p', 'p': 53, 'prec': 20, 'unit': 568021132905022676140531727695243, 'val': 1}
  • id: 6360607
    {'lmfdb_iso': '121680.p', 'p': 61, 'prec': 20, 'unit': 2788940794770929104917123669981398, 'val': 1}
  • id: 6360592
    {'lmfdb_iso': '121680.p', 'p': 67, 'prec': 20, 'unit': 10219837368743383406451073679287535, 'val': 1}
  • id: 6360605
    {'lmfdb_iso': '121680.p', 'p': 71, 'prec': 20, 'unit': 10604540670477135760056671281006005, 'val': 1}
  • id: 6360603
    {'lmfdb_iso': '121680.p', 'p': 73, 'prec': 20, 'unit': 158547793411744774738488588101856693, 'val': 1}
  • id: 6360606
    {'lmfdb_iso': '121680.p', 'p': 79, 'prec': 20, 'unit': 139367025475488341680895552458331746, 'val': 1}
  • id: 6360591
    {'lmfdb_iso': '121680.p', 'p': 83, 'prec': 20, 'unit': 2601272420533168336583231002907126441, 'val': 1}
  • id: 6360604
    {'lmfdb_iso': '121680.p', 'p': 89, 'prec': 20, 'unit': 412753705106815834947100565094094112, 'val': 1}
  • id: 6360590
    {'lmfdb_iso': '121680.p', 'p': 97, 'prec': 20, 'unit': 53067853949929975209304868750026726701, 'val': 1}