Elliptic curve data - 69366.u2

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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': '69366w', 'Clabel': '69366w1', 'Cnumber': 1, 'abc_quality': 0.9773037383757964, 'absD': 93935597925332680704, 'adelic_genus': 2, 'adelic_index': 96, 'adelic_level': 1942248, 'ainvs': [1, 0, 0, 430484, 453494672], 'analytic_rank': 1, 'bad_primes': [2, 3, 11, 1051], 'class_deg': 7, 'class_size': 2, 'cm': 0, 'conductor': 69366, 'degree': 1893360, 'elladic_images': ['7.48.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.5134696460212187668208989430', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 20, 'isogeny_degrees': [1, 7], 'jinv': [8822561460536124355391, 93935597925332680704], 'lmfdb_iso': '69366.u', 'lmfdb_label': '69366.u2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 430484, 453494672], 'min_quad_twist_disc': 1, 'modell_images': ['7B.1.1'], 'modm_images': ['7.48.0-7.a.1.2', '277464.2.0.?', '1942248.96.2.?'], 'nonmax_primes': [7], 'nonmax_rad': 7, 'num_bad_primes': 4, 'num_int_pts': 10, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.4199104274240500580387096773', 'prec': 100}, 'semistable': True, 'serre_invariants': [[2, 4, 34683], [3, 4, 11561], [7, 2, 1051], [11, 12, 6306], [1051, 1052, 66]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.5134696460212187668208989430', 'prec': 100}, 'szpiro_ratio': 4.789382520163407, 'torsion': 7, 'torsion_primes': [7], 'torsion_structure': [7]}
• 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, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 0, 1, -1, 1, 4, 1, 6, -1], 'aplist': [1, 1, -1, 1, 1, 0, 4, 6, 3, 2, -10, 3, 0, -5, -8, -9, 4, -1, -2, -12, -3, -4, -14, -8, 14], 'class_deg': 7, 'class_size': 2, 'conductor': 69366, 'isogeny_matrix': [[1, 7], [7, 1]], 'lmfdb_iso': '69366.u', 'trace_hash': 670495197072936290}
• 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': '0.0065588546189369335848971584112', 'prec': 110}, 'conductor': 69366, 'gens': [[176, 23036, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '4.4199104274240500580387096773', 'prec': 100}], 'lmfdb_label': '69366.u2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.13998118069041130253231448728', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '12.992789883710259058323810845917152118', 'prec': 130}, 'tamagawa_product': 1029, 'torsion_generators': [[344, 25172, 1]], 'xcoord_integral_points': [-448, 176, 344, 2456, 82712]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 0], '3': [4, 0], '5': [1, 0], '7': [3, 0], '11': [4, 0], '13': [1, 1, 0], '17': [5, 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], '1051': 'o?'}, 'iwp0': 0, 'lmfdb_label': '69366.u2'}
• ec_torsion_growth •

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

  
  
  • id: 3297466
    {'degree': 3, 'field': [-204, -32, -1, 1], 'lmfdb_label': '69366.u2', 'torsion': [14]}
  • id: 3297467
    {'degree': 6, 'field': [1109856, 0, 9409, 0, -194, 0, 1], 'lmfdb_label': '69366.u2', 'torsion': [2, 14]}
  • id: 3297468
    {'degree': 8, 'field': [-20172, 0, -9025, 0, -492, 0, 0, 0, 1], 'lmfdb_label': '69366.u2', 'torsion': [21]}
  • id: 3297469
    {'degree': 12, 'field': [791408974956, -326807343732, 56989633842, -3509024880, -297591808, 65697446, -1936799, -448016, 35587, 2402, -307, -4, 1], 'lmfdb_label': '69366.u2', 'torsion': [28]}
• 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: 1679170
    {'conductor': 69366, 'conductor_valuation': 1, 'discriminant_valuation': 21, 'j_denominator_valuation': 21, 'kodaira_symbol': 25, 'lmfdb_label': '69366.u2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 21}
  • id: 1679171
    {'conductor': 69366, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '69366.u2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 7}
  • id: 1679172
    {'conductor': 69366, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '69366.u2', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 7}
  • id: 1679173
    {'conductor': 69366, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '69366.u2', 'prime': 1051, '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: 2122870
    {'adelic_gens': [[1009016, 7, 1544921, 1942242], [1589120, 7, 1765673, 1942242], [1, 14, 0, 1], [485563, 971138, 0, 208099], [8, 7, 971117, 1942242], [1456687, 14, 0, 1], [1, 0, 14, 1], [8, 5, 91, 57], [1942235, 14, 1942234, 15], [1294840, 7, 1294825, 1942242]], 'adelic_image': '1942248.96.2.?', 'conductor': 69366, 'lmfdb_label': '69366.u2', 'prime': 0}
  • id: 289262
    {'conductor': 69366, 'elladic_image': '7.48.0.1', 'lmfdb_label': '69366.u2', 'modell_image': '7B.1.1', 'prime': 7}
• ec_padic •

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

  
  
  • id: 3550498
    {'lmfdb_iso': '69366.u', 'p': 5, 'prec': 20, 'unit': 18366609512007, 'val': 1}
  • id: 3550499
    {'lmfdb_iso': '69366.u', 'p': 7, 'prec': 20, 'unit': 67791401385579026, 'val': 0}
  • id: 3550505
    {'lmfdb_iso': '69366.u', 'p': 17, 'prec': 20, 'unit': 11743508640591458418168, 'val': 2}
  • id: 3550495
    {'lmfdb_iso': '69366.u', 'p': 19, 'prec': 20, 'unit': 975830543099919929851853, 'val': 1}
  • id: 3550509
    {'lmfdb_iso': '69366.u', 'p': 23, 'prec': 20, 'unit': 12727224291332368496778146, 'val': 1}
  • id: 3550503
    {'lmfdb_iso': '69366.u', 'p': 29, 'prec': 20, 'unit': 2008583325977699072939609518, 'val': 1}
  • id: 3550500
    {'lmfdb_iso': '69366.u', 'p': 31, 'prec': 20, 'unit': 13093209629193177101035227025, 'val': 1}
  • id: 3550514
    {'lmfdb_iso': '69366.u', 'p': 37, 'prec': 20, 'unit': 390580276232783491502835910635, 'val': 1}
  • id: 3550502
    {'lmfdb_iso': '69366.u', 'p': 43, 'prec': 20, 'unit': 779417445456544320631081006194, 'val': 1}
  • id: 3550512
    {'lmfdb_iso': '69366.u', 'p': 47, 'prec': 20, 'unit': 10752721850038253873898801463563, 'val': 1}
  • id: 3550507
    {'lmfdb_iso': '69366.u', 'p': 53, 'prec': 20, 'unit': 48685821913122753457525042425052, 'val': 1}
  • id: 3550508
    {'lmfdb_iso': '69366.u', 'p': 59, 'prec': 20, 'unit': 2869458185999174065191059427214225, 'val': 1}
  • id: 3550513
    {'lmfdb_iso': '69366.u', 'p': 61, 'prec': 20, 'unit': 3049824806676815604394226532646966, 'val': 1}
  • id: 3550497
    {'lmfdb_iso': '69366.u', 'p': 67, 'prec': 20, 'unit': 18606710358324240637071379717965521, 'val': 1}
  • id: 3550511
    {'lmfdb_iso': '69366.u', 'p': 71, 'prec': 20, 'unit': 140477518530935518413185090108196419, 'val': 1}
  • id: 3550501
    {'lmfdb_iso': '69366.u', 'p': 73, 'prec': 20, 'unit': 226693118761894172039225750984019568, 'val': 1}
  • id: 3550504
    {'lmfdb_iso': '69366.u', 'p': 79, 'prec': 20, 'unit': 364187159379486791030749108617192131, 'val': 1}
  • id: 3550506
    {'lmfdb_iso': '69366.u', 'p': 83, 'prec': 20, 'unit': 1659393479703797747431930172792563075, 'val': 1}
  • id: 3550510
    {'lmfdb_iso': '69366.u', 'p': 89, 'prec': 20, 'unit': 9764954181499360803748474074045298499, 'val': 1}
  • id: 3550496
    {'lmfdb_iso': '69366.u', 'p': 97, 'prec': 20, 'unit': 28637044235400288255098733537639157772, 'val': 1}