Elliptic curve data - 27690.bg1

Formats: - HTML - YAML - JSON - 2024-04-27T10:23:45.937724

• 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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '27690bc', 'Clabel': '27690bc2', 'Cnumber': 2, 'abc_quality': 1.0366235007006561, 'absD': 68484636225100842737640, 'adelic_genus': 2, 'adelic_index': 96, 'adelic_level': 775320, 'ainvs': [1, 0, 0, -8462840, -15758963160], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 13, 71], 'class_deg': 7, 'class_size': 2, 'cm': 0, 'conductor': 27690, 'degree': 3687936, 'elladic_images': ['7.48.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.0772210886679891993291478289', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 7, 'iso_nlabel': 32, 'isogeny_degrees': [1, 7], 'jinv': [-67030445471226692469644161, 68484636225100842737640], 'lmfdb_iso': '27690.bg', 'lmfdb_label': '27690.bg1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -8462840, -15758963160], 'min_quad_twist_disc': 1, 'modell_images': ['7B.1.3'], 'modm_images': ['7.48.0-7.a.2.2', '110760.2.0.?', '775320.96.2.?'], 'nonmax_primes': [7], 'nonmax_rad': 7, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '12.263533475735357376126728701', 'prec': 100}, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '3.0772210886679891993291478289', 'prec': 100}, 'szpiro_ratio': 5.913132420959779, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 1, 1, 1, 1, 1, 1, 1, 1, -2, 1, -1, 1, 1, 1, 4, 1, -8, 1], 'aplist': [1, 1, 1, 1, -2, -1, 4, -8, 3, -5, -10, -4, 0, -12, 6, -2, 4, 13, 12, 1, -10, -4, 0, -15, 14], 'class_deg': 7, 'class_size': 2, 'conductor': 27690, 'isogeny_matrix': [[1, 7], [7, 1]], 'lmfdb_iso': '27690.bg', 'trace_hash': 1007995997044588785}
• 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': '0.0021240254844708587521472545032', 'prec': 110}, 'conductor': 27690, 'gens': [[243618, 86641458, 7]], 'heights': [{'__RealLiteral__': 0, 'data': '12.263533475735357376126728701', 'prec': 100}], 'lmfdb_label': '27690.bg1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.042515992916836070217919259801', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '10.949322350184676231192661398464374617', 'prec': 130}, 'tamagawa_product': 21, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [9, 0], '3': [2, 0], '5': [2, 0], '7': [3, 1], '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, 1, 0], '43': [1, 0], '47': [1, 0], '71': [2, 0]}, 'iwp0': 0, 'lmfdb_label': '27690.bg1'}
• ec_torsion_growth •

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

  
  
  • id: 1385381
    {'degree': 3, 'field': [136, -16, -1, 1], 'lmfdb_label': '27690.bg1', 'torsion': [2]}
  • id: 1385383
    {'degree': 6, 'field': [1, -1, 1, -1, 1, -1, 1], 'lmfdb_label': '27690.bg1', 'torsion': [7]}
  • id: 1385382
    {'degree': 6, 'field': [443040, 0, 2401, 0, -98, 0, 1], 'lmfdb_label': '27690.bg1', 'torsion': [2, 2]}
  • id: 1385384
    {'degree': 7, 'field': [-2400, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '27690.bg1', 'torsion': [7]}
  • id: 1385385
    {'degree': 8, 'field': [-588, 0, 1247, 0, 84, 0, 0, 0, 1], 'lmfdb_label': '27690.bg1', 'torsion': [3]}
  • id: 1385386
    {'degree': 12, 'field': [13855670960, -19933958832, 2943725672, -406551136, 97551558, -6017966, 867993, -146016, 943, -1586, 93, -4, 1], 'lmfdb_label': '27690.bg1', 'torsion': [4]}
  • id: 1385387
    {'degree': 18, 'field': [6327518887936, -744413986816, 134103990272, 25275301888, -7461138432, 2049687552, -110153216, 94651392, 3125824, -481728, 775624, -71808, 10609, 3927, 33, 103, 17, -1, 1], 'lmfdb_label': '27690.bg1', 'torsion': [14]}
  • id: 1385388
    {'degree': 21, 'field': [900920827165696, -632942656095232, 173123472026624, 17265195121664, -42702941725696, 11837589381632, 574658074368, -544613923904, 59488601536, 15950698176, -7552096384, 739819136, 144182136, -39409664, 1327111, 735063, -101773, -1981, 1589, -91, -7, 1], 'lmfdb_label': '27690.bg1', 'torsion': [14]}
• 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: 639396
    {'conductor': 27690, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '27690.bg1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 639397
    {'conductor': 27690, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '27690.bg1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 639398
    {'conductor': 27690, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '27690.bg1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 639399
    {'conductor': 27690, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '27690.bg1', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 639400
    {'conductor': 27690, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '27690.bg1', 'prime': 71, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 7}
• ec_galrep •

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

  
  
  • id: 1848613
    {'adelic_gens': [[387661, 14, 387667, 99], [1, 14, 0, 1], [178921, 14, 477127, 99], [516881, 14, 516887, 99], [620257, 14, 465199, 99], [193831, 14, 581497, 99], [193833, 553808, 387646, 636833], [775307, 14, 775306, 15], [1, 0, 14, 1], [8, 5, 91, 57], [327601, 14, 742567, 99]], 'adelic_image': '775320.96.2.?', 'conductor': 27690, 'lmfdb_label': '27690.bg1', 'prime': 0}
  • id: 125135
    {'conductor': 27690, 'elladic_image': '7.48.0.5', 'lmfdb_label': '27690.bg1', 'modell_image': '7B.1.3', 'prime': 7}
• ec_padic •

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

  
  
  • id: 1327076
    {'lmfdb_iso': '27690.bg', 'p': 7, 'prec': 20, 'unit': 44174021298613708, 'val': 0}
  • id: 1327081
    {'lmfdb_iso': '27690.bg', 'p': 11, 'prec': 20, 'unit': 25477372827546998813, 'val': 1}
  • id: 1327082
    {'lmfdb_iso': '27690.bg', 'p': 17, 'prec': 20, 'unit': 6729674965003403520474, 'val': 1}
  • id: 1327083
    {'lmfdb_iso': '27690.bg', 'p': 19, 'prec': 20, 'unit': 1430880971743765581942797, 'val': 1}
  • id: 1327086
    {'lmfdb_iso': '27690.bg', 'p': 23, 'prec': 20, 'unit': 57408138486991382983238303, 'val': 1}
  • id: 1327079
    {'lmfdb_iso': '27690.bg', 'p': 29, 'prec': 20, 'unit': 4990086921196260338504373611, 'val': 1}
  • id: 1327090
    {'lmfdb_iso': '27690.bg', 'p': 31, 'prec': 20, 'unit': 12359709619549666072989016713, 'val': 1}
  • id: 1327075
    {'lmfdb_iso': '27690.bg', 'p': 37, 'prec': 20, 'unit': 148078623820677335224332107230, 'val': 1}
  • id: 1327078
    {'lmfdb_iso': '27690.bg', 'p': 43, 'prec': 20, 'unit': 7131961634068759526107531913109, 'val': 1}
  • id: 1327088
    {'lmfdb_iso': '27690.bg', 'p': 47, 'prec': 20, 'unit': 24253619572259256183360526030355, 'val': 1}
  • id: 1327084
    {'lmfdb_iso': '27690.bg', 'p': 53, 'prec': 20, 'unit': 173028205333710392056714081657087, 'val': 1}
  • id: 1327085
    {'lmfdb_iso': '27690.bg', 'p': 59, 'prec': 20, 'unit': 2531023645280372379570995330856849, 'val': 1}
  • id: 1327089
    {'lmfdb_iso': '27690.bg', 'p': 61, 'prec': 20, 'unit': 2768245616188448194110109920547267, 'val': 1}
  • id: 1327074
    {'lmfdb_iso': '27690.bg', 'p': 67, 'prec': 20, 'unit': 12549572482303746948194546558999107, 'val': 1}
  • id: 1327077
    {'lmfdb_iso': '27690.bg', 'p': 73, 'prec': 20, 'unit': 102582206502263129702608144314808682, 'val': 1}
  • id: 1327080
    {'lmfdb_iso': '27690.bg', 'p': 79, 'prec': 20, 'unit': 940974196341565246955318132054715780, 'val': 1}
  • id: 1327087
    {'lmfdb_iso': '27690.bg', 'p': 89, 'prec': 20, 'unit': 114755859992455462435323252413788233, 'val': 2}
  • id: 1327073
    {'lmfdb_iso': '27690.bg', 'p': 97, 'prec': 20, 'unit': 12083978189297555211511931656622042480, 'val': 1}