Elliptic curve data - 81144.bc1

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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': '81144bj', 'Clabel': '81144bj2', 'Cnumber': 2, 'abc_quality': 1.0288641261342233, 'absD': 101606193157819392, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 276, 'ainvs': [0, 0, 0, -20571915, 35913700438], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 23], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 81144, 'degree': 2580480, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.6915822672985978467563894425', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 28, 'isogeny_degrees': [1, 2], 'jinv': [10963069081334500, 1156923], 'lmfdb_iso': '81144.bc', 'lmfdb_label': '81144.bc1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -46648, 3893500], 'min_quad_twist_disc': 21, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '12.6.0.a.1', '92.6.0.?', '276.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 441], [3, 8, 9016], [7, 26, 1656], [23, 24, 3528]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.59169839797026525732506368443', 'prec': 103}, 'szpiro_ratio': 5.496463335504107, '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, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 8, 0, -6, 0], 'aplist': [0, 0, 0, 0, 0, -2, 8, -6, -1, -2, 4, 6, 10, 6, 0, -12, 4, 10, -6, 0, -2, -6, 0, -12, -6], 'class_deg': 2, 'class_size': 2, 'conductor': 81144, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '81144.bc', 'trace_hash': 1770231168822724272}
• 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': '0.0045932633657671199841995153757', 'prec': 110}, 'conductor': 81144, 'gens': [], 'heights': [], 'lmfdb_label': '81144.bc1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.25917938896655242830000117881', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.0734351117324194264000094304432353098', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[2618, 0, 1]], 'xcoord_integral_points': [2618]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '7': 'a', '23': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '81144.bc1'}
• ec_torsion_growth •

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

  
  
  • id: 3815634
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '81144.bc1', 'torsion': [2, 2]}
  • id: 3815635
    {'degree': 4, 'field': [32, -26, 12, -1, 1], 'lmfdb_label': '81144.bc1', 'torsion': [4]}
  • id: 3815638
    {'degree': 8, 'field': [-151668, -97208, 50092, 13728, 2660, 32, -60, -2, 1], 'lmfdb_label': '81144.bc1', 'torsion': [6]}
  • id: 3815636
    {'degree': 8, 'field': [1521, 0, -846, 0, 231, 0, -30, 0, 1], 'lmfdb_label': '81144.bc1', 'torsion': [2, 4]}
  • id: 3815637
    {'degree': 8, 'field': [3406, 874, 1435, -910, 233, -58, 13, -2, 1], 'lmfdb_label': '81144.bc1', 'torsion': [2, 4]}
  • id: 3815640
    {'degree': 16, 'field': [-126048359, 57095390, -126929646, -110213706, -7671894, -7264572, 6081382, -368596, 289764, -294474, 136140, -15054, -2830, 568, -48, -4, 1], 'lmfdb_label': '81144.bc1', 'torsion': [2, 6]}
  • id: 3815639
    {'degree': 16, 'field': [5386432, -19850112, 21010176, -6628160, 3563008, -533696, 312144, -161616, 152320, -63336, 26380, -7000, 1997, -276, 74, -4, 1], 'lmfdb_label': '81144.bc1', '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: 1974578
    {'conductor': 81144, 'conductor_valuation': 3, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '81144.bc1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1974579
    {'conductor': 81144, 'conductor_valuation': 2, 'discriminant_valuation': 13, 'j_denominator_valuation': 7, 'kodaira_symbol': -11, 'lmfdb_label': '81144.bc1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1974580
    {'conductor': 81144, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '81144.bc1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1974581
    {'conductor': 81144, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '81144.bc1', 'prime': 23, '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: 2198824
    {'adelic_gens': [[1, 2, 2, 5], [1, 4, 0, 1], [97, 4, 194, 9], [273, 4, 272, 5], [208, 73, 69, 208], [1, 0, 4, 1], [3, 4, 8, 11], [94, 1, 91, 0]], 'adelic_image': '276.12.0.?', 'conductor': 81144, 'lmfdb_label': '81144.bc1', 'prime': 0}
  • id: 332766
    {'conductor': 81144, 'elladic_image': '2.3.0.1', 'lmfdb_label': '81144.bc1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 81144.bc does not appear in ec_padic