Elliptic curve data - 221067.g2

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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': '221067f', 'Clabel': '221067f2', 'Cnumber': 2, 'abc_quality': 0.8231384216112029, 'absD': 119955154473, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 26796, 'ainvs': [1, -1, 1, 1165, 6284], 'analytic_rank': 1, 'bad_primes': [3, 7, 11, 29], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 221067, 'degree': 159744, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.81448342754681150740015030572', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 6, 'isogeny_degrees': [1, 2], 'jinv': [180362125, 123627], 'lmfdb_iso': '221067.g', 'lmfdb_label': '221067.g2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 129, -233], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '132.6.0.?', '2436.6.0.?', '8932.6.0.?', '26796.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.0792606546998140156145585241', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.33429653498683597431295820723', 'prec': 107}, 'szpiro_ratio': 2.6649802950948467, '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, -1, 0, -1, 0, 0, 1, 3, 0, 0, 0, 0, 2, -1, 0, -1, 6, 0, 4, 0], 'aplist': [-1, 0, 0, 1, 0, 2, 6, 4, 8, -1, -4, 2, 2, -12, 0, -2, 4, 12, -8, 8, 4, 0, -4, -10, -14], 'class_deg': 2, 'class_size': 2, 'conductor': 221067, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '221067.g', 'trace_hash': 1611479191033921869}
• 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': '0.19613210237092433800875244504', 'prec': 103}, 'conductor': 221067, 'gens': [[3, 97, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.0792606546998140156145585241', 'prec': 100}], 'lmfdb_label': '221067.g2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.66104652611425082250416343165', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.7075320524888323629115946979626662451', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-21, 17, 2]], 'xcoord_integral_points': [3, 147]}
• lmfdb_label 221067.g2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9617816
    {'degree': 2, 'field': [33, 0, 1], 'lmfdb_label': '221067.g2', 'torsion': [2, 2]}
  • id: 9617817
    {'degree': 4, 'field': [-4752, 0, 33, 0, 1], 'lmfdb_label': '221067.g2', 'torsion': [4]}
  • id: 9617820
    {'degree': 8, 'field': [-29403, 0, 0, 0, -594, 0, 11, 0, 1], 'lmfdb_label': '221067.g2', 'torsion': [6]}
  • id: 9617818
    {'degree': 8, 'field': [207936, 0, 19440, 0, 3297, 0, -72, 0, 1], 'lmfdb_label': '221067.g2', 'torsion': [2, 4]}
  • id: 9617819
    {'degree': 8, 'field': [1679616, 0, 229392, 0, 5400, 0, 177, 0, 1], 'lmfdb_label': '221067.g2', 'torsion': [2, 4]}
  • id: 9617822
    {'degree': 16, 'field': [3958520097609, 0, 0, 0, 18909186912, 0, 209368962, 0, 20327274, 0, 209088, 0, 9625, 0, 22, 0, 1], 'lmfdb_label': '221067.g2', 'torsion': [2, 6]}
  • id: 9617821
    {'degree': 16, 'field': [899055607873536, 0, -165824510349312, 0, 3950085636864, 0, -138815296128, 0, 1322344476, 0, 3990996, 0, -81309, 0, 60, 0, 1], 'lmfdb_label': '221067.g2', 'torsion': [8]}
• 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: 5480414
    {'conductor': 221067, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '221067.g2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5480415
    {'conductor': 221067, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '221067.g2', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5480416
    {'conductor': 221067, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '221067.g2', 'prime': 11, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5480417
    {'conductor': 221067, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '221067.g2', 'prime': 29, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
• ec_galrep •

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

  
  
  • id: 3075487
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [6469, 4, 12938, 9], [1, 4, 0, 1], [19141, 4, 11486, 9], [7312, 1, 4871, 0], [6700, 20101, 20097, 6700], [17866, 1, 17863, 0], [26793, 4, 26792, 5]], 'adelic_image': '26796.12.0.?', 'conductor': 221067, 'lmfdb_label': '221067.g2', 'prime': 0}
  • id: 810403
    {'conductor': 221067, 'elladic_image': '2.3.0.1', 'lmfdb_label': '221067.g2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 221067.g does not appear in ec_padic