Elliptic curve data - 121968.bi2

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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': '121968ek', 'Clabel': '121968ek1', 'Cnumber': 1, 'abc_quality': 0.8744790360864115, 'absD': 71688085159477248, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 308, 'ainvs': [0, 0, 0, -253011, 50649874], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 11], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 121968, 'degree': 1105920, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0025128730868342241398790559', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 34, 'isogeny_degrees': [1, 2], 'jinv': [-338608873, 13552], 'lmfdb_iso': '121968.bi', 'lmfdb_label': '121968.bi2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -14, -28], 'min_quad_twist_disc': -132, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '14.6.0.b.1', '44.6.0.b.1', '308.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.43888808820635120300594747300', 'prec': 107}, 'szpiro_ratio': 4.184261758449877, '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, -1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0], 'aplist': [0, 0, -2, -1, 0, 4, 0, 4, 4, 2, 10, -6, 0, -4, 10, 14, 10, 8, -8, -4, -4, 16, -4, -10, 6], 'class_deg': 2, 'class_size': 2, 'conductor': 121968, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '121968.bi', 'trace_hash': 2102774989106655041}
• 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': '0.018223820059001137727203072863', 'prec': 107}, 'conductor': 121968, 'gens': [], 'heights': [], 'lmfdb_label': '121968.bi2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.34324335867396929690533938773', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.7459468693917543752427151018376976268', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-583, 0, 1]], 'xcoord_integral_points': [-583]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '7': [0, 0], '11': 'a'}, 'iwp0': 3, 'lmfdb_label': '121968.bi2'}
• ec_torsion_growth •

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

  
  
  • id: 5570830
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '121968.bi2', 'torsion': [2, 2]}
  • id: 5570831
    {'degree': 4, 'field': [-8, 32, 2, -2, 1], 'lmfdb_label': '121968.bi2', 'torsion': [4]}
  • id: 5570834
    {'degree': 8, 'field': [-59142, -10838, 19531, 5232, -23, 196, 27, -2, 1], 'lmfdb_label': '121968.bi2', 'torsion': [6]}
  • id: 5570833
    {'degree': 8, 'field': [1908, -1008, 48, -276, 133, -46, 26, -2, 1], 'lmfdb_label': '121968.bi2', 'torsion': [2, 4]}
  • id: 5570832
    {'degree': 8, 'field': [2143, 390, 198, 32, 139, -24, 16, -2, 1], 'lmfdb_label': '121968.bi2', 'torsion': [2, 4]}
  • id: 5570835
    {'degree': 16, 'field': [16, 0, -2016, 0, 1240, 0, -19992, 0, 1209, 0, 1020, 0, -86, 0, -12, 0, 1], 'lmfdb_label': '121968.bi2', 'torsion': [8]}
  • id: 5570836
    {'degree': 16, 'field': [2327136592, -2627993984, 1113192212, -136227432, 72727116, -116586404, 59614162, -9667898, -1976051, 1000710, -63462, -30712, 5216, 386, -118, -2, 1], 'lmfdb_label': '121968.bi2', '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: 3002887
    {'conductor': 121968, 'conductor_valuation': 4, 'discriminant_valuation': 16, 'j_denominator_valuation': 4, 'kodaira_symbol': -12, 'lmfdb_label': '121968.bi2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 3002888
    {'conductor': 121968, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '121968.bi2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 3002889
    {'conductor': 121968, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '121968.bi2', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 3002890
    {'conductor': 121968, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '121968.bi2', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 2459743
    {'adelic_gens': [[1, 0, 4, 1], [90, 1, 263, 0], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [81, 232, 76, 231], [57, 4, 114, 9], [305, 4, 304, 5]], 'adelic_image': '308.12.0.?', 'conductor': 121968, 'lmfdb_label': '121968.bi2', 'prime': 0}
  • id: 478362
    {'conductor': 121968, 'elladic_image': '2.3.0.1', 'lmfdb_label': '121968.bi2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 121968.bi does not appear in ec_padic