Elliptic curve data - 156816.d1

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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': '156816cq', 'Clabel': '156816cq1', 'Cnumber': 1, 'abc_quality': 0.8345574460809416, 'absD': 25255373616, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 22, 'ainvs': [0, 0, 0, 726, 1331], 'analytic_rank': 0, 'bad_primes': [2, 3, 11], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 156816, 'degree': 149760, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.68533378356230366740009783499', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 3, 'isogeny_degrees': [1], 'jinv': [18432, 11], 'lmfdb_iso': '156816.d', 'lmfdb_label': '156816.d1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, 6, 1], 'min_quad_twist_disc': 44, 'modell_images': [], 'modm_images': ['22.2.0.a.1'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 9801], [3, 8, 1936], [11, 72, 1296]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1108670092462332715683664068', 'prec': 103}, 'szpiro_ratio': 2.6228122622039183, '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, -3, 0, -4, 0, 0, 0, 0, 0, -6, 0, 0, 0, 4, 0, 2, 0], 'aplist': [0, 0, -3, -4, 0, -6, 4, 2, 4, -6, 3, 7, 2, 10, -3, 11, 1, -8, 3, 5, 12, -16, 4, -10, 13], 'class_deg': 1, 'class_size': 1, 'conductor': 156816, 'isogeny_matrix': [[1]], 'lmfdb_iso': '156816.d', 'trace_hash': 1878579481565261754}
• 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': '0.25393738270872962760426622838', 'prec': 103}, 'conductor': 156816, 'gens': [], 'heights': [], 'lmfdb_label': '156816.d1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.72931962826690546893728473620', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4586392565338109378745694723898917477', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 156816.d1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7027229
    {'degree': 3, 'field': [-1, 6, 0, 1], 'lmfdb_label': '156816.d1', 'torsion': [2]}
  • id: 7027230
    {'degree': 6, 'field': [44, 0, 9, 0, -6, 0, 1], 'lmfdb_label': '156816.d1', 'torsion': [2, 2]}
  • id: 7027231
    {'degree': 8, 'field': [-3267, 0, -264, 0, -198, 0, 0, 0, 1], 'lmfdb_label': '156816.d1', 'torsion': [3]}
  • id: 7027232
    {'degree': 12, 'field': [-8, 48, -192, 480, -804, 822, -475, 66, 60, -60, 24, -6, 1], 'lmfdb_label': '156816.d1', '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: 3879128
    {'conductor': 156816, 'conductor_valuation': 4, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '156816.d1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 3879129
    {'conductor': 156816, 'conductor_valuation': 4, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '156816.d1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 3879130
    {'conductor': 156816, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '156816.d1', 'prime': 11, 'reduction_type': 0, '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

  
  {'adelic_gens': [[1, 1, 21, 0], [1, 2, 0, 1], [1, 0, 2, 1], [21, 2, 20, 3], [13, 2, 13, 3]], 'adelic_image': '22.2.0.?', 'conductor': 156816, 'lmfdb_label': '156816.d1', 'prime': 0}
• lmfdb_iso 156816.d does not appear in ec_padic