Elliptic curve data - 68354.f1

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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': '68354i', 'Clabel': '68354i2', 'Cnumber': 2, 'abc_quality': 1.0426823729346897, 'absD': 12739469393917574594, 'adelic_genus': 2, 'adelic_index': 96, 'adelic_level': 1913912, 'ainvs': [1, -1, 1, -550339173, -4969145682177], 'analytic_rank': 1, 'bad_primes': [2, 11, 13, 239], 'class_deg': 7, 'class_size': 2, 'cm': 0, 'conductor': 68354, 'degree': 21282464, 'elladic_images': ['7.48.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.4142618253103543139004593712', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 7, 'intrinsic_torsion': 1, 'iso_nlabel': 5, 'isogeny_degrees': [1, 7], 'jinv': [-18433805126765920887235189777569, 12739469393917574594], 'lmfdb_iso': '68354.f', 'lmfdb_label': '68354.f1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -550339173, -4969145682177], 'min_quad_twist_disc': 1, 'modell_images': ['7B.1.3'], 'modm_images': ['7.48.0-7.a.2.2', '273416.2.0.?', '1913912.96.2.?'], 'nonmax_primes': [7], 'nonmax_rad': 7, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '56.350133333631132339694356873', 'prec': 100}, 'semistable': True, 'serre_invariants': [[2, 4, 34177], [7, 2, 286], [11, 12, 6214], [13, 14, 5258], [239, 240, 286]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '3.4142618253103543139004593712', 'prec': 100}, 'szpiro_ratio': 6.466833834879716, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 1, -3, 1, -1, -3, 1, 1, 6, -1, 1, -3, 1, 1, 3, 1, 4, 6, 6, -1], 'aplist': [1, -3, -1, 1, 1, 1, 4, 6, -4, 9, -3, -4, 0, -12, 6, 5, 4, 6, 12, -5, 4, 10, 0, -15, 7], 'class_deg': 7, 'class_size': 2, 'conductor': 68354, 'isogeny_matrix': [[1, 7], [7, 1]], 'lmfdb_iso': '68354.f', 'trace_hash': 1278107940876629968}
• 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': '0.0010824550203174578562093587140', 'prec': 110}, 'conductor': 68354, 'gens': [[2064288047994980639759629, 1492429052374114276463145804348419023, 8171208780]], 'heights': [{'__RealLiteral__': 0, 'data': '56.350133333631132339694356873', 'prec': 100}], 'lmfdb_label': '68354.f1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.015585184659491322550445169854', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.1475906351411898061296580776465605499', 'prec': 130}, 'tamagawa_product': 7, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': [3, 1, 0], '5': [1, 0], '7': [3, 1], '11': [2, 0], '13': [2, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 1, 0], '43': [1, 0], '47': [1, 0], '239': [2, 0]}, 'iwp0': 0, 'lmfdb_label': '68354.f1'}
• ec_torsion_growth •

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

  
  
  • id: 3250099
    {'degree': 3, 'field': [-166, -49, 0, 1], 'lmfdb_label': '68354.f1', 'torsion': [2]}
  • id: 3250101
    {'degree': 6, 'field': [1, -1, 1, -1, 1, -1, 1], 'lmfdb_label': '68354.f1', 'torsion': [7]}
  • id: 3250100
    {'degree': 6, 'field': [273416, 0, 21609, 0, -294, 0, 1], 'lmfdb_label': '68354.f1', 'torsion': [2, 2]}
  • id: 3250102
    {'degree': 7, 'field': [-25168, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '68354.f1', 'torsion': [7]}
  • id: 3250103
    {'degree': 8, 'field': [-70382, -29524, 28558, 1931, -962, -7, 7, -4, 1], 'lmfdb_label': '68354.f1', 'torsion': [3]}
  • id: 3250104
    {'degree': 12, 'field': [-21358628539348, 6827981922028, 270265891682, -170991544104, 7949848516, -2172532838, 105136843, -5737508, 569373, -2990, 809, 0, 1], 'lmfdb_label': '68354.f1', 'torsion': [4]}
  • id: 3250105
    {'degree': 18, 'field': [20924183895616, 6176415728224, 1823158859536, 412112049528, 84440209028, 13942237246, 1632876961, 1017351916, 216313293, 54014906, 9815533, 1594264, 145205, -16268, 2401, -166, 49, 0, 1], 'lmfdb_label': '68354.f1', 'torsion': [14]}
  • id: 3250106
    {'degree': 21, 'field': [-862855657735952, -4353580806135904, -7993067522148464, -3007387918123568, -474189524383064, 69534025707132, 58121867075622, 14413854343811, 343600855164, -500020233713, -63601829382, 8927122659, 2617225520, 59992415, -41773926, -3539039, 341628, 50421, -1162, -343, 0, 1], 'lmfdb_label': '68354.f1', 'torsion': [14]}
• 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: 1652733
    {'conductor': 68354, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '68354.f1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1652734
    {'conductor': 68354, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '68354.f1', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1652735
    {'conductor': 68354, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '68354.f1', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1652736
    {'conductor': 68354, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '68354.f1', 'prime': 239, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 7}
• ec_galrep •

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

  
  
  • id: 2115994
    {'adelic_gens': [[1565929, 14, 1391943, 99], [1913899, 14, 1913898, 15], [1766689, 14, 883351, 99], [8, 5, 91, 57], [1, 14, 0, 1], [1, 0, 14, 1], [956957, 14, 956963, 99], [478481, 820256, 956942, 751857], [478479, 14, 1435441, 99], [32033, 14, 224231, 99]], 'adelic_image': '1913912.96.2.?', 'conductor': 68354, 'lmfdb_label': '68354.f1', 'prime': 0}
  • id: 285176
    {'conductor': 68354, 'elladic_image': '7.48.0.5', 'lmfdb_label': '68354.f1', 'modell_image': '7B.1.3', 'prime': 7}
• ec_padic •

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

  
  
  • id: 3493868
    {'lmfdb_iso': '68354.f', 'p': 5, 'prec': 20, 'unit': 10888975140077, 'val': 1}
  • id: 3493869
    {'lmfdb_iso': '68354.f', 'p': 7, 'prec': 20, 'unit': 62589713352461535, 'val': 0}
  • id: 3493875
    {'lmfdb_iso': '68354.f', 'p': 17, 'prec': 20, 'unit': 199908667534627457676392, 'val': 1}
  • id: 3493876
    {'lmfdb_iso': '68354.f', 'p': 19, 'prec': 20, 'unit': 1473952913438967273451747, 'val': 1}
  • id: 3493879
    {'lmfdb_iso': '68354.f', 'p': 23, 'prec': 20, 'unit': 11892226238661691424248059, 'val': 1}
  • id: 3493873
    {'lmfdb_iso': '68354.f', 'p': 29, 'prec': 20, 'unit': 692207597506086721592544844, 'val': 1}
  • id: 3493870
    {'lmfdb_iso': '68354.f', 'p': 31, 'prec': 20, 'unit': 120031373623119743399804531, 'val': 1}
  • id: 3493884
    {'lmfdb_iso': '68354.f', 'p': 37, 'prec': 20, 'unit': 258640667182670865709943086607, 'val': 1}
  • id: 3493872
    {'lmfdb_iso': '68354.f', 'p': 43, 'prec': 20, 'unit': 5990579538559077691920989860557, 'val': 1}
  • id: 3493882
    {'lmfdb_iso': '68354.f', 'p': 47, 'prec': 20, 'unit': 43650733769125353963734781012864, 'val': 1}
  • id: 3493877
    {'lmfdb_iso': '68354.f', 'p': 53, 'prec': 20, 'unit': 523437000175717363151756484975165, 'val': 1}
  • id: 3493878
    {'lmfdb_iso': '68354.f', 'p': 59, 'prec': 20, 'unit': 804149389196689034342538253687937, 'val': 1}
  • id: 3493883
    {'lmfdb_iso': '68354.f', 'p': 61, 'prec': 20, 'unit': 4990019203220534541356574250301230, 'val': 1}
  • id: 3493867
    {'lmfdb_iso': '68354.f', 'p': 67, 'prec': 20, 'unit': 35244681320210532825567022631960977, 'val': 1}
  • id: 3493881
    {'lmfdb_iso': '68354.f', 'p': 71, 'prec': 20, 'unit': 119885836227965908351232933723788589, 'val': 1}
  • id: 3493871
    {'lmfdb_iso': '68354.f', 'p': 73, 'prec': 20, 'unit': 204445845842167512865874521651767208, 'val': 1}
  • id: 3493874
    {'lmfdb_iso': '68354.f', 'p': 79, 'prec': 20, 'unit': 231283846026962598819509451583048370, 'val': 1}
  • id: 3493880
    {'lmfdb_iso': '68354.f', 'p': 89, 'prec': 20, 'unit': 2499701747529049512511752893380897188, 'val': 1}
  • id: 3493866
    {'lmfdb_iso': '68354.f', 'p': 97, 'prec': 20, 'unit': 33168475777748801495195563772686145729, 'val': 1}