Elliptic curve data - 121680.o1

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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
  serre_invariants	integer[]
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '121680dx', 'Clabel': '121680dx1', 'Cnumber': 1, 'abc_quality': 0.662277327620974, 'absD': 237867078243600, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 780, 'ainvs': [0, 0, 0, -19773, 771147], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 121680, 'degree': 419328, 'elladic_images': ['2.2.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4658287358448960610719129832', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 14, 'isogeny_degrees': [1], 'jinv': [89856, 25], 'lmfdb_iso': '121680.o', 'lmfdb_label': '121680.o1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -13, 13], 'min_quad_twist_disc': 156, 'modell_images': ['2Cn'], 'modm_images': ['2.2.0.a.1', '26.6.0.a.1', '60.4.0-2.a.1.1', '780.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.9473598298604465007432830345', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 1521], [3, 6, 13520], [5, 6, 24336], [13, 74, 720]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0244927069834983784671119701', 'prec': 103}, 'szpiro_ratio': 3.5262868132649037, '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, 0, 0, 0, -1, 0, -3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 7, 0, -1, 0], 'aplist': [0, 0, -1, -3, 3, 0, 7, -1, -7, 5, 4, -3, -7, 9, 8, 6, 5, -5, -13, -3, -14, 8, 12, -7, -11], 'class_deg': 1, 'class_size': 1, 'conductor': 121680, 'isogeny_matrix': [[1]], 'lmfdb_iso': '121680.o', 'trace_hash': 857820073042671275}
• 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': '0.053308607372148934327087458277', 'prec': 107}, 'conductor': 121680, 'gens': [[169, 845, 2]], 'heights': [{'__RealLiteral__': 0, 'data': '1.9473598298604465007432830345', 'prec': 100}], 'lmfdb_label': '121680.o1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.51873610209951236673477120947', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.0609950851618656439724709752346413556', 'prec': 130}, 'tamagawa_product': 6, 'torsion_generators': [], 'xcoord_integral_points': []}
• 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': 'a', '17': [1, 0], '19': [1, 0], '23': [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.o1'}
• ec_torsion_growth •

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

  
  
  • id: 5557516
    {'degree': 3, 'field': [-1, -4, -1, 1], 'lmfdb_label': '121680.o1', 'torsion': [2, 2]}
  • id: 5557517
    {'degree': 8, 'field': [-507, 0, 0, 0, 78, 0, -12, 0, 1], 'lmfdb_label': '121680.o1', 'torsion': [3]}
  • id: 5557518
    {'degree': 12, 'field': [-6869, 3128, 3136, -9652, 3355, 1030, -2180, 294, 120, -24, 20, -2, 1], 'lmfdb_label': '121680.o1', 'torsion': [2, 4]}
• 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: 2995155
    {'conductor': 121680, 'conductor_valuation': 4, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '121680.o1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 2995156
    {'conductor': 121680, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '121680.o1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 2995157
    {'conductor': 121680, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '121680.o1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2995158
    {'conductor': 121680, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '121680.o1', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 3}
• ec_galrep •

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

  
  
  • id: 2458012
    {'adelic_gens': [[1, 0, 4, 1], [1, 2, 2, 5], [1, 4, 0, 1], [356, 519, 657, 779], [211, 264, 216, 271], [647, 516, 642, 509], [3, 2, 772, 775], [777, 4, 776, 5], [259, 0, 0, 779]], 'adelic_image': '780.12.0.?', 'conductor': 121680, 'lmfdb_label': '121680.o1', 'prime': 0}
  • id: 477529
    {'conductor': 121680, 'elladic_image': '2.2.0.1', 'lmfdb_label': '121680.o1', 'modell_image': '2Cn', 'prime': 2}
• ec_padic •

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

  
  
  • id: 6361733
    {'lmfdb_iso': '121680.o', 'p': 7, 'prec': 20, 'unit': 5676327797488598, 'val': 1}
  • id: 6361738
    {'lmfdb_iso': '121680.o', 'p': 11, 'prec': 20, 'unit': 42899717907067582063, 'val': 1}
  • id: 6361739
    {'lmfdb_iso': '121680.o', 'p': 17, 'prec': 20, 'unit': 73166386899862062000074, 'val': 1}
  • id: 6361740
    {'lmfdb_iso': '121680.o', 'p': 19, 'prec': 20, 'unit': 1195822701113544486385303, 'val': 1}
  • id: 6361744
    {'lmfdb_iso': '121680.o', 'p': 23, 'prec': 20, 'unit': 35153769068719252323837932, 'val': 1}
  • id: 6361736
    {'lmfdb_iso': '121680.o', 'p': 29, 'prec': 20, 'unit': 3205802190481597287441622582, 'val': 1}
  • id: 6361749
    {'lmfdb_iso': '121680.o', 'p': 31, 'prec': 20, 'unit': 15696922447265613532252820099, 'val': 1}
  • id: 6361732
    {'lmfdb_iso': '121680.o', 'p': 37, 'prec': 20, 'unit': 55050824218505512447175554235, 'val': 1}
  • id: 6361734
    {'lmfdb_iso': '121680.o', 'p': 41, 'prec': 20, 'unit': 3138375448488515175592436280375, 'val': 1}
  • id: 6361735
    {'lmfdb_iso': '121680.o', 'p': 43, 'prec': 20, 'unit': 6431289512212566165640022800345, 'val': 1}
  • id: 6361747
    {'lmfdb_iso': '121680.o', 'p': 47, 'prec': 20, 'unit': 17392953414452503312151748024302, 'val': 1}
  • id: 6361741
    {'lmfdb_iso': '121680.o', 'p': 53, 'prec': 20, 'unit': 257316782178558829028839680059740, 'val': 1}
  • id: 6361742
    {'lmfdb_iso': '121680.o', 'p': 59, 'prec': 20, 'unit': 39234834640685298433226941457925, 'val': 1}
  • id: 6361748
    {'lmfdb_iso': '121680.o', 'p': 61, 'prec': 20, 'unit': 6114043296608498110459360875710455, 'val': 1}
  • id: 6361731
    {'lmfdb_iso': '121680.o', 'p': 67, 'prec': 20, 'unit': 17757166196396065768706773059323869, 'val': 1}
  • id: 6361746
    {'lmfdb_iso': '121680.o', 'p': 71, 'prec': 20, 'unit': 35230753172270646961780328477530421, 'val': 1}
  • id: 6361743
    {'lmfdb_iso': '121680.o', 'p': 73, 'prec': 20, 'unit': 76021430928011157815728420771409656, 'val': 1}
  • id: 6361737
    {'lmfdb_iso': '121680.o', 'p': 79, 'prec': 20, 'unit': 485775776156080131668422404505786177, 'val': 1}
  • id: 6361730
    {'lmfdb_iso': '121680.o', 'p': 83, 'prec': 20, 'unit': 1642203640866357982425032572032624426, 'val': 1}
  • id: 6361745
    {'lmfdb_iso': '121680.o', 'p': 89, 'prec': 20, 'unit': 9081736326450867157007992547670082123, 'val': 1}
  • id: 6361729
    {'lmfdb_iso': '121680.o', 'p': 97, 'prec': 20, 'unit': 37909252319222998940345882081356827411, 'val': 1}