Elliptic curve data - 162576.e2

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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': '162576u', 'Clabel': '162576u1', 'Cnumber': 1, 'abc_quality': 0.9460280203305138, 'absD': 401420140848, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 13548, 'ainvs': [0, 0, 0, -3306, -79261], 'analytic_rank': 0, 'bad_primes': [2, 3, 1129], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 162576, 'degree': 221184, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.96668723037557641163927163122', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2], 'jinv': [-342597941248, 34415307], 'lmfdb_iso': '162576.e', 'lmfdb_label': '162576.e2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -367, -3058], 'min_quad_twist_disc': 12, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '6.6.0.a.1', '4516.6.0.?', '13548.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 9], [3, 6, 18064], [1129, 1130, 144]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.18633202585487312946923830561', 'prec': 103}, 'szpiro_ratio': 3.0072878269570666, '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, 0, 0, 0, 0, -6, 0, -6, 0, 0, 0, 0, 0, 8, 0], 'aplist': [0, 0, -2, 0, -6, -6, 0, 8, 4, 0, 8, -2, 0, -12, -4, -6, 6, 14, 0, 0, -2, -16, -2, 12, 2], 'class_deg': 2, 'class_size': 2, 'conductor': 162576, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '162576.e', 'trace_hash': 505923030079695523}
• 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': '0.14465922705617783011170952747', 'prec': 103}, 'conductor': 162576, 'gens': [], 'heights': [], 'lmfdb_label': '162576.e2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.31302454511440085611340866874', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.62604909022880171222681733748295098774', 'prec': 133}, 'tamagawa_product': 8, 'torsion_generators': [[67, 0, 1]], 'xcoord_integral_points': [67]}
• lmfdb_label 162576.e2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7264998
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '162576.e2', 'torsion': [2, 2]}
  • id: 7264999
    {'degree': 4, 'field': [-192, 0, -19, 0, 1], 'lmfdb_label': '162576.e2', 'torsion': [4]}
  • id: 7265002
    {'degree': 8, 'field': [-2187, 0, 14472, 0, 162, 0, 0, 0, 1], 'lmfdb_label': '162576.e2', 'torsion': [6]}
  • id: 7265000
    {'degree': 8, 'field': [2404, 1220, -1612, -490, 457, 52, -37, -2, 1], 'lmfdb_label': '162576.e2', 'torsion': [2, 4]}
  • id: 7265001
    {'degree': 8, 'field': [36864, 0, -3648, 0, 553, 0, 19, 0, 1], 'lmfdb_label': '162576.e2', 'torsion': [2, 4]}
  • id: 7265004
    {'degree': 16, 'field': [729, 0, -14472, 0, 287782, 0, 9648, 0, 351, 0, -1072, 0, -18, 0, 0, 0, 1], 'lmfdb_label': '162576.e2', 'torsion': [2, 6]}
  • id: 7265003
    {'degree': 16, 'field': [497871360000, 0, 35559115776, 0, -3136920012, 0, 976835232, 0, 4391985, 0, -978072, 0, -3782, 0, 152, 0, 1], 'lmfdb_label': '162576.e2', '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: 4023693
    {'conductor': 162576, 'conductor_valuation': 4, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '162576.e2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 4023694
    {'conductor': 162576, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '162576.e2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4023695
    {'conductor': 162576, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '162576.e2', 'prime': 1129, '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: 2715370
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [3389, 10162, 10160, 3387], [1, 2, 2, 5], [2269, 4, 4538, 9], [1, 4, 0, 1], [13545, 4, 13544, 5], [9034, 1, 9031, 0]], 'adelic_image': '13548.12.0.?', 'conductor': 162576, 'lmfdb_label': '162576.e2', 'prime': 0}
  • id: 618356
    {'conductor': 162576, 'elladic_image': '2.3.0.1', 'lmfdb_label': '162576.e2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 162576.e does not appear in ec_padic