Elliptic curve data - 768.b1

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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': '768a', 'Clabel': '768a1', 'Cnumber': 1, 'abc_quality': 1.106715441314673, 'absD': 4608, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 48, 'ainvs': [0, -1, 0, -23, 51], 'analytic_rank': 1, 'bad_primes': [2, 3], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 768, 'degree': 64, 'elladic_images': ['16.48.0.247'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.43171442438310503261991559624', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [2744000, 9], 'lmfdb_iso': '768.b', 'lmfdb_label': '768.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -23, 51], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.e.1', '8.24.0.s.1', '12.12.0.n.1', '16.48.0-8.s.1.3', '24.48.1.dl.1', '48.96.1-24.dl.1.3'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 7, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.43929586130482440834533239014', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 4, 1], [3, 4, 256]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.95157480980306401468283968733', 'prec': 107}, 'szpiro_ratio': 3.1703670252803358, '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, -1, 0, 0, 0, -4, 0, 1, 0, 4, 0, 4, 0, 0, 0, -2, 0, -4, 0], 'aplist': [0, -1, 0, -4, 4, 4, -2, -4, -8, -8, -4, -4, 6, 4, -8, -8, -12, 12, 12, 8, -6, -4, -4, -6, -2], 'class_deg': 2, 'class_size': 2, 'conductor': 768, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '768.b', 'trace_hash': 2254865981465863613}
• 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': '2.3712775220707629205649158807', 'prec': 100}, 'conductor': 768, 'gens': [[2, 3, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.43929586130482440834533239014', 'prec': 103}], 'lmfdb_label': '768.b1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '4.3656747145718101333424083404', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.9178228339145167907527079608572176348', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[3, 0, 1]], 'xcoord_integral_points': [-5, 2, 3, 5]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 0], '5': [1, 1, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '768.b1'}
• ec_torsion_growth •

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

  
  
  • id: 35445
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '768.b1', 'torsion': [2, 2]}
  • id: 35446
    {'degree': 4, 'field': [2, 0, 0, 0, 1], 'lmfdb_label': '768.b1', 'torsion': [4]}
  • id: 35451
    {'degree': 8, 'field': [-27, 0, 36, 0, 0, 0, -12, 0, 1], 'lmfdb_label': '768.b1', 'torsion': [6]}
  • id: 35447
    {'degree': 8, 'field': [1, 0, -4, 0, -12, 0, -4, 0, 1], 'lmfdb_label': '768.b1', 'torsion': [2, 4]}
  • id: 35448
    {'degree': 8, 'field': [1, 0, -4, 0, 8, 0, -4, 0, 1], 'lmfdb_label': '768.b1', 'torsion': [2, 4]}
  • id: 35449
    {'degree': 8, 'field': [1, 0, -4, 0, 14, 0, -4, 0, 1], 'lmfdb_label': '768.b1', 'torsion': [8]}
  • id: 35450
    {'degree': 8, 'field': [9, 0, -4, 0, 2, 0, 4, 0, 1], 'lmfdb_label': '768.b1', 'torsion': [8]}
  • id: 35452
    {'degree': 16, 'field': [1, 0, -4, 0, 8, 0, -24, 0, 47, 0, -24, 0, 8, 0, -4, 0, 1], 'lmfdb_label': '768.b1', 'torsion': [4, 4]}
  • id: 35453
    {'degree': 16, 'field': [1, 0, 0, 0, -12, 0, 0, 0, 166, 0, 0, 0, -12, 0, 0, 0, 1], 'lmfdb_label': '768.b1', 'torsion': [2, 8]}
  • id: 35454
    {'degree': 16, 'field': [36, 0, -480, 0, -488, 0, -240, 0, -276, 0, -80, 0, -48, 0, 0, 0, 1], 'lmfdb_label': '768.b1', 'torsion': [2, 6]}
• 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: 9663
    {'conductor': 768, 'conductor_valuation': 8, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '768.b1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 9664
    {'conductor': 768, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '768.b1', 'prime': 3, '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: 1669461
    {'adelic_gens': [[1, 0, 16, 1], [1, 16, 0, 1], [11, 8, 16, 3], [17, 10, 46, 45], [34, 13, 27, 10], [13, 8, 8, 5], [11, 12, 44, 35], [33, 16, 32, 17], [41, 38, 10, 3]], 'adelic_image': '48.96.1.?', 'conductor': 768, 'lmfdb_label': '768.b1', 'prime': 0}
  • id: 3458
    {'conductor': 768, 'elladic_image': '16.48.0.247', 'lmfdb_label': '768.b1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 14987
    {'lmfdb_iso': '768.b', 'p': 7, 'prec': 20, 'unit': 3225028833345279, 'val': 1}
  • id: 14988
    {'lmfdb_iso': '768.b', 'p': 11, 'prec': 20, 'unit': 25773762357781032145, 'val': 1}
  • id: 14989
    {'lmfdb_iso': '768.b', 'p': 13, 'prec': 20, 'unit': 556205901664914996256, 'val': 1}
  • id: 14990
    {'lmfdb_iso': '768.b', 'p': 17, 'prec': 20, 'unit': 193580000682316262336894, 'val': 1}
  • id: 14991
    {'lmfdb_iso': '768.b', 'p': 19, 'prec': 20, 'unit': 1423612239895052753871630, 'val': 1}
  • id: 14992
    {'lmfdb_iso': '768.b', 'p': 23, 'prec': 20, 'unit': 46840051487025454034604703, 'val': 1}
  • id: 14993
    {'lmfdb_iso': '768.b', 'p': 29, 'prec': 20, 'unit': 2233664955223392266632643664, 'val': 1}
  • id: 14994
    {'lmfdb_iso': '768.b', 'p': 31, 'prec': 20, 'unit': 15839491987184165807664060811, 'val': 1}
  • id: 14995
    {'lmfdb_iso': '768.b', 'p': 37, 'prec': 20, 'unit': 506031872366591687071715764316, 'val': 1}
  • id: 14996
    {'lmfdb_iso': '768.b', 'p': 41, 'prec': 20, 'unit': 217756515314275146287983085947, 'val': 1}
  • id: 14997
    {'lmfdb_iso': '768.b', 'p': 43, 'prec': 20, 'unit': 8260739580410946581060875448938, 'val': 1}
  • id: 14998
    {'lmfdb_iso': '768.b', 'p': 47, 'prec': 20, 'unit': 14151431688334920221546831711584, 'val': 1}
  • id: 14999
    {'lmfdb_iso': '768.b', 'p': 53, 'prec': 20, 'unit': 411496697580868336271152910115705, 'val': 1}
  • id: 15000
    {'lmfdb_iso': '768.b', 'p': 59, 'prec': 20, 'unit': 149670446390491296704886221484287, 'val': 1}
  • id: 15001
    {'lmfdb_iso': '768.b', 'p': 61, 'prec': 20, 'unit': 130001831349308701284387387359142, 'val': 2}
  • id: 15002
    {'lmfdb_iso': '768.b', 'p': 67, 'prec': 20, 'unit': 11587371223423945610331653776068715, 'val': 1}
  • id: 15003
    {'lmfdb_iso': '768.b', 'p': 71, 'prec': 20, 'unit': 29040129581764423767651586294654121, 'val': 1}
  • id: 15004
    {'lmfdb_iso': '768.b', 'p': 73, 'prec': 20, 'unit': 93520756005348861259145986755142207, 'val': 1}
  • id: 15005
    {'lmfdb_iso': '768.b', 'p': 79, 'prec': 20, 'unit': 579095889536716231432910692793122970, 'val': 1}
  • id: 15006
    {'lmfdb_iso': '768.b', 'p': 83, 'prec': 20, 'unit': 1090379612389424949376385900065485303, 'val': 1}
  • id: 15007
    {'lmfdb_iso': '768.b', 'p': 89, 'prec': 20, 'unit': 1299995211659101986740292451926774230, 'val': 1}
  • id: 15008
    {'lmfdb_iso': '768.b', 'p': 97, 'prec': 20, 'unit': 2651571189567575694809203718480066496, 'val': 1}