Elliptic curve data - 81312.be1

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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': '81312bn', 'Clabel': '81312bn4', 'Cnumber': 4, 'abc_quality': 0.9742513195817183, 'absD': 5657203689984, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1848, 'ainvs': [0, 1, 0, -99744, 12091176], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 81312, 'degree': 307200, 'elladic_images': ['4.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5163349890786751422362210193', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 2, 'iso_nlabel': 30, 'isogeny_degrees': [1, 2, 4], 'jinv': [120993582536, 6237], 'lmfdb_iso': '81312.be', 'lmfdb_label': '81312.be1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -824, 9384], 'min_quad_twist_disc': 44, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '168.24.0.?', '264.24.0.?', '616.24.0.?', '1848.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 847], [3, 4, 27104], [7, 8, 11616], [11, 72, 672]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.20247303274046911185767486078', 'prec': 107}, 'szpiro_ratio': 4.081416953956773, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
• 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, 1, 0, -2, 0, -1, 0, 1, 0, 0, 0, 2, 0, -2, 0, 2, 0, 4, 0], 'aplist': [0, 1, -2, -1, 0, 2, 2, 4, -8, -2, 4, -2, -6, -12, 0, 2, -4, -14, 8, 8, -14, 16, 0, 6, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 81312, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '81312.be', 'trace_hash': 1190802000439374439}
• 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': '0.048186808490302697360444502521', 'prec': 107}, 'conductor': 81312, 'gens': [], 'heights': [], 'lmfdb_label': '81312.be1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.71747919867704178592739880984', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4349583973540835718547976196814631022', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[150, 726, 1]], 'xcoord_integral_points': [150, 183]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '7': [0, 0], '11': 'a'}, 'iwp0': 3, 'lmfdb_label': '81312.be1'}
• ec_torsion_growth •

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

  
  
  • id: 3823209
    {'degree': 2, 'field': [-154, 0, 1], 'lmfdb_label': '81312.be1', 'torsion': [2, 4]}
  • id: 3823210
    {'degree': 4, 'field': [1386, 0, 66, 0, 1], 'lmfdb_label': '81312.be1', 'torsion': [8]}
  • id: 3823214
    {'degree': 8, 'field': [-264627, 0, -28512, 0, 1782, 0, 0, 0, 1], 'lmfdb_label': '81312.be1', 'torsion': [12]}
  • id: 3823213
    {'degree': 8, 'field': [379456, 0, -120736, 0, 9450, 0, -196, 0, 1], 'lmfdb_label': '81312.be1', 'torsion': [2, 8]}
  • id: 3823212
    {'degree': 8, 'field': [11932650, -234720, -535116, 20232, 9094, -232, -72, -4, 1], 'lmfdb_label': '81312.be1', 'torsion': [2, 8]}
  • id: 3823211
    {'degree': 8, 'field': [56957209, 0, -90548, 0, 15098, 0, 4, 0, 1], 'lmfdb_label': '81312.be1', 'torsion': [4, 4]}
  • id: 3823216
    {'degree': 16, 'field': [387420489, 0, 63084172464, 0, -18570438108, 0, 1557633888, 0, 196830, 0, -3205008, 0, -972, 0, 0, 0, 1], 'lmfdb_label': '81312.be1', 'torsion': [2, 12]}
  • id: 3823215
    {'degree': 16, 'field': [3690225632016, 0, 702900120384, 0, 69985726272, 0, 4103247456, 0, 142852248, 0, 2960496, 0, 36432, 0, 264, 0, 1], 'lmfdb_label': '81312.be1', 'torsion': [16]}
• 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: 1979045
    {'conductor': 81312, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '81312.be1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1979046
    {'conductor': 81312, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '81312.be1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1979047
    {'conductor': 81312, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '81312.be1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1979048
    {'conductor': 81312, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '81312.be1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 2199962
    {'adelic_gens': [[617, 8, 620, 33], [1, 0, 8, 1], [1004, 1847, 1153, 1842], [1, 8, 0, 1], [1841, 8, 1840, 9], [1, 4, 4, 17], [7, 6, 1842, 1843], [232, 1163, 697, 726], [1625, 1620, 1622, 695], [1592, 3, 533, 2]], 'adelic_image': '1848.48.0.?', 'conductor': 81312, 'lmfdb_label': '81312.be1', 'prime': 0}
  • id: 333295
    {'conductor': 81312, 'elladic_image': '4.12.0.7', 'lmfdb_label': '81312.be1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 81312.be does not appear in ec_padic