Elliptic curve data - 162.b4

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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': '162c', 'Clabel': '162c1', 'Cnumber': 1, 'abc_quality': 1.4265653296335434, 'absD': 1458, 'adelic_genus': 21, 'adelic_index': 768, 'adelic_level': 504, 'ainvs': [1, -1, 0, 3, -1], 'analytic_rank': 0, 'bad_primes': [2, 3], 'class_deg': 21, 'class_size': 4, 'cm': 0, 'conductor': 162, 'degree': 6, 'elladic_images': ['8.2.0.1', '3.8.0.1', '7.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.70358699565001647072183612100', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 3, 7, 21], 'jinv': [3375, 2], 'lmfdb_iso': '162.b', 'lmfdb_label': '162.b4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, 3, -1], 'min_quad_twist_disc': 1, 'modell_images': ['3B.1.1', '7B'], 'modm_images': ['3.8.0-3.a.1.2', '7.8.0.a.1', '8.2.0.a.1', '21.128.1-21.a.2.2', '24.16.0-24.a.1.8', '56.16.0.a.1', '63.384.5-63.e.2.1', '168.256.5.?', '504.768.21.?'], 'nonmax_primes': [2, 3, 7], 'nonmax_rad': 42, 'num_bad_primes': 2, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 81], [3, 6, 2]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.2528931399840713164194587395', 'prec': 103}, 'szpiro_ratio': 2.8924905526419127, 'torsion': 3, 'torsion_primes': [3], 'torsion_structure': [3]}
• 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, 2, -1, 0, 0, 3, 0, 2, -2, 0, 1, 3, 0, -1, 0], 'aplist': [-1, 0, 0, 2, 3, 2, 3, -1, 6, -6, -4, -4, -9, -1, 6, -12, -3, 8, 5, 12, 11, -4, -12, -6, 5], 'class_deg': 21, 'class_size': 4, 'conductor': 162, 'isogeny_matrix': [[1, 3, 21, 7], [3, 1, 7, 21], [21, 7, 1, 3], [7, 21, 3, 1]], 'lmfdb_iso': '162.b', 'trace_hash': 253532594654622027}
• 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': '4.0843965388841212595817515612', 'prec': 100}, 'conductor': 162, 'gens': [], 'heights': [], 'lmfdb_label': '162.b4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '2.8006777425532496677500992009', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.93355924751774988925003306697011232344', 'prec': 133}, 'tamagawa_product': 3, 'torsion_generators': [[1, 1, 1]], 'xcoord_integral_points': [1]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 0], '3': 'a', '5': [0, 0, 0], '7': [0, 0]}, 'iwp0': 11, 'lmfdb_label': '162.b4'}
• ec_torsion_growth •

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

  
  
  • id: 6488
    {'degree': 3, 'field': [-10, -3, 0, 1], 'lmfdb_label': '162.b4', 'torsion': [6]}
  • id: 6490
    {'degree': 6, 'field': [1, -3, 0, 5, 0, -3, 1], 'lmfdb_label': '162.b4', 'torsion': [3, 3]}
  • id: 6491
    {'degree': 6, 'field': [1, 0, 0, -1, 0, 0, 1], 'lmfdb_label': '162.b4', 'torsion': [21]}
  • id: 6489
    {'degree': 6, 'field': [8, 0, 9, 0, -6, 0, 1], 'lmfdb_label': '162.b4', 'torsion': [2, 6]}
  • id: 6492
    {'degree': 9, 'field': [-1, -9, -27, -33, -9, 0, -12, -9, 0, 1], 'lmfdb_label': '162.b4', 'torsion': [9]}
  • id: 6493
    {'degree': 12, 'field': [-8, 48, -114, 130, -81, 72, -120, 126, -63, 4, 12, -6, 1], 'lmfdb_label': '162.b4', 'torsion': [12]}
  • id: 6494
    {'degree': 18, 'field': [1, -9, 33, -60, 60, -84, 222, -318, 153, 5, 153, -318, 222, -84, 60, -60, 33, -9, 1], 'lmfdb_label': '162.b4', 'torsion': [3, 6]}
  • id: 6495
    {'degree': 18, 'field': [1, 0, -3, 14, -12, -12, 114, -270, 480, -636, 702, -630, 479, -300, 159, -68, 24, -6, 1], 'lmfdb_label': '162.b4', 'torsion': [42]}
  • id: 6496
    {'degree': 18, 'field': [3, 0, -9, 0, 18, -9, -6, 0, 0, 27, -63, 72, -21, -63, 105, -81, 36, -9, 1], 'lmfdb_label': '162.b4', 'torsion': [3, 21]}
• 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: 1247
    {'conductor': 162, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '162.b4', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1248
    {'conductor': 162, 'conductor_valuation': 4, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '162.b4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
• ec_galrep •

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

  
  
  • id: 1666431
    {'adelic_gens': [[281, 392, 112, 393], [1, 426, 42, 253], [1, 216, 0, 1], [1, 0, 462, 1], [33, 154, 448, 129], [85, 42, 189, 43], [1, 0, 168, 1], [337, 168, 336, 169], [295, 42, 231, 211], [22, 321, 189, 169], [1, 42, 0, 73], [1, 0, 420, 1], [1, 168, 0, 1], [463, 282, 420, 295]], 'adelic_image': '504.768.21.?', 'conductor': 162, 'lmfdb_label': '162.b4', 'prime': 0}
  • id: 643
    {'conductor': 162, 'elladic_image': '8.2.0.1', 'lmfdb_label': '162.b4', 'modell_image': '2G', 'prime': 2}
  • id: 644
    {'conductor': 162, 'elladic_image': '3.8.0.1', 'lmfdb_label': '162.b4', 'modell_image': '3B.1.1', 'prime': 3}
  • id: 645
    {'conductor': 162, 'elladic_image': '7.8.0.1', 'lmfdb_label': '162.b4', 'modell_image': '7B', 'prime': 7}
• lmfdb_iso 162.b does not appear in ec_padic