Elliptic curve data - 121968.w1

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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': '121968el', 'Clabel': '121968el1', 'Cnumber': 1, 'abc_quality': 1.0588704220842826, 'absD': 216724085652154113589248, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 168, 'ainvs': [0, 0, 0, 7817469, 20758099714], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 11], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 121968, 'degree': 12579840, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.1603755120022580062365940455', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 22, 'isogeny_degrees': [1], 'jinv': [146234339790153527, 599838494072832], 'lmfdb_iso': '121968.w', 'lmfdb_label': '121968.w1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, 54288, 12035409], 'min_quad_twist_disc': 12, 'modell_images': [], 'modm_images': ['168.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.5182729749751960937780820426', 'prec': 100}, 'szpiro_ratio': 5.211584964841349, '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, -2, 0, -1, 0, 0, 0, 0, 0, -5, 0, 0, 0, -6, 0, 4, 0], 'aplist': [0, 0, -2, -1, 0, -5, -6, 4, 1, -1, 1, 12, -9, 5, 10, 2, 13, 11, 7, -1, -4, 4, 11, -13, -12], 'class_deg': 1, 'class_size': 1, 'conductor': 121968, 'isogeny_matrix': [[1]], 'lmfdb_iso': '121968.w', 'trace_hash': 1521560979193659407}
• 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': '0.0017985922129410034562196042106', 'prec': 110}, 'conductor': 121968, 'gens': [], 'heights': [], 'lmfdb_label': '121968.w1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.071206225952955571947076688187', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.1392996152472891511532270109919574601', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [0, 0], '7': [0, 0], '11': 'a', '13': [0, 0], '17': [0, 0], '19': [0, 0], '23': [2, 0], '29': [0, 0], '31': [4, 0], '37': [0, 0], '41': [0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '121968.w1'}
• ec_torsion_growth •

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

  
  
  • id: 5570844
    {'degree': 3, 'field': [-53, -7, -1, 1], 'lmfdb_label': '121968.w1', 'torsion': [2]}
  • id: 5570845
    {'degree': 6, 'field': [2058, 0, 1213, 0, -8, 0, 1], 'lmfdb_label': '121968.w1', 'torsion': [2, 2]}
  • id: 5570846
    {'degree': 8, 'field': [-59142, -10838, 19531, 5232, -23, 196, 27, -2, 1], 'lmfdb_label': '121968.w1', 'torsion': [3]}
  • id: 5570847
    {'degree': 12, 'field': [-803853, 497416, -354640, 102300, -4521, 24464, -9680, 88, -187, 264, 0, -4, 1], 'lmfdb_label': '121968.w1', 'torsion': [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: 3002895
    {'conductor': 121968, 'conductor_valuation': 4, 'discriminant_valuation': 25, 'j_denominator_valuation': 13, 'kodaira_symbol': -21, 'lmfdb_label': '121968.w1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 3002896
    {'conductor': 121968, 'conductor_valuation': 2, 'discriminant_valuation': 27, 'j_denominator_valuation': 21, 'kodaira_symbol': -25, 'lmfdb_label': '121968.w1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 3002897
    {'conductor': 121968, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '121968.w1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 3002898
    {'conductor': 121968, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '121968.w1', 'prime': 11, 'reduction_type': 0, '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

  
  {'adelic_gens': [[1, 1, 167, 0], [1, 2, 0, 1], [113, 2, 113, 3], [1, 0, 2, 1], [127, 2, 127, 3], [85, 2, 85, 3], [167, 2, 166, 3], [73, 2, 73, 3]], 'adelic_image': '168.2.0.?', 'conductor': 121968, 'lmfdb_label': '121968.w1', 'prime': 0}
• lmfdb_iso 121968.w does not appear in ec_padic