Elliptic curve data - 396.b2

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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': '396a', 'Clabel': '396a1', 'Cnumber': 1, 'abc_quality': 1.0879123577519636, 'absD': 7576222896, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 132, 'ainvs': [0, 0, 0, -696, -8215], 'analytic_rank': 0, 'bad_primes': [2, 3, 11], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 396, 'degree': 240, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.61809544713524779430248083045', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [-3196715008, 649539], 'lmfdb_iso': '396.b', 'lmfdb_label': '396.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -77, 330], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '12.6.0.b.1', '22.6.0.a.1', '132.12.0.?'], '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, 99], [3, 8, 44], [11, 12, 36]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.16225975738545548786755249516', 'prec': 107}, 'szpiro_ratio': 5.274769224172113, '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, 2, 0, 0, 0, 1, 0, 6, 0, 0, 0, 4, 0, -2, 0], 'aplist': [0, 0, -2, 2, 1, 6, 4, -2, 8, 0, 0, -6, 0, 10, 0, -14, 12, -14, 4, 0, 6, 2, -16, 14, -2], 'class_deg': 2, 'class_size': 2, 'conductor': 396, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '396.b', 'trace_hash': 2105894361210024978}
• 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': '0.29048861506901392148171624317', 'prec': 103}, 'conductor': 396, 'gens': [], 'heights': [], 'lmfdb_label': '396.b2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.45972287336910045552348577054', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.3791686201073013665704573116067283059', 'prec': 130}, 'tamagawa_product': 12, 'torsion_generators': [[31, 0, 1]], 'xcoord_integral_points': [31]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '11': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '396.b2'}
• ec_torsion_growth •

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

  
  
  • id: 17221
    {'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '396.b2', 'torsion': [2, 2]}
  • id: 17222
    {'degree': 4, 'field': [-11, 0, -2, 0, 1], 'lmfdb_label': '396.b2', 'torsion': [4]}
  • id: 17225
    {'degree': 8, 'field': [8, -4, -20, -16, -4, -8, 8, -1, 1], 'lmfdb_label': '396.b2', 'torsion': [6]}
  • id: 17224
    {'degree': 8, 'field': [81, 54, 78, -18, 31, 2, 0, -4, 1], 'lmfdb_label': '396.b2', 'torsion': [2, 4]}
  • id: 17223
    {'degree': 8, 'field': [625, 0, 600, 0, 238, 0, 24, 0, 1], 'lmfdb_label': '396.b2', 'torsion': [2, 4]}
  • id: 17227
    {'degree': 16, 'field': [36, -246, 925, -2258, 4165, -5904, 6756, -6102, 4330, -2252, 808, -198, 84, -42, 7, -2, 1], 'lmfdb_label': '396.b2', 'torsion': [2, 6]}
  • id: 17226
    {'degree': 16, 'field': [676, 0, -9344, 0, -11288, 0, 4384, 0, 3280, 0, 784, 0, 124, 0, 16, 0, 1], 'lmfdb_label': '396.b2', '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: 4045
    {'conductor': 396, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '396.b2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
  • id: 4046
    {'conductor': 396, 'conductor_valuation': 2, 'discriminant_valuation': 16, 'j_denominator_valuation': 10, 'kodaira_symbol': -14, 'lmfdb_label': '396.b2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4047
    {'conductor': 396, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '396.b2', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  
  • id: 1667494
    {'adelic_gens': [[89, 4, 46, 9], [1, 2, 2, 5], [37, 100, 32, 99], [3, 4, 8, 11], [26, 1, 119, 0], [1, 4, 0, 1], [129, 4, 128, 5], [1, 0, 4, 1]], 'adelic_image': '132.12.0.?', 'conductor': 396, 'lmfdb_label': '396.b2', 'prime': 0}
  • id: 1679
    {'conductor': 396, 'elladic_image': '2.3.0.1', 'lmfdb_label': '396.b2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 396.b does not appear in ec_padic