Elliptic curve data - 800.b1

Formats: - HTML - YAML - JSON - 2025-12-08T08:41:58.101446

• 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': '800i', 'Clabel': '800i1', 'Cnumber': 1, 'abc_quality': 0.9949912704917342, 'absD': 200000000, 'adelic_genus': 3, 'adelic_index': 60, 'adelic_level': 40, 'ainvs': [0, -1, 0, -208, 1412], 'analytic_rank': 1, 'bad_primes': [2, 5], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 800, 'degree': 240, 'elladic_images': ['8.2.0.1', '5.15.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.31558410008219759058368225303', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1], 'jinv': [-5000, 1], 'lmfdb_iso': '800.b', 'lmfdb_label': '800.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -8, -8], 'min_quad_twist_disc': -20, 'modell_images': ['5Ns'], 'modm_images': ['5.15.0.a.1', '8.2.0.a.1', '20.30.0.b.1', '40.60.3.u.1'], 'nonmax_primes': [2, 5], 'nonmax_rad': 10, 'num_bad_primes': 2, 'num_int_pts': 6, 'optimality': 1, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.19637779133168667685371410477', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 4, 25], [5, 10, 32]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.2772348936271616412130813935', 'prec': 103}, 'szpiro_ratio': 4.177933179061148, '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, 0, -1, 0, 0, 0, 2, 0, -2, 0, -5, 0, 0, 0, 0, 0, 5, 0, -5, 0], 'aplist': [0, -1, 0, 2, -5, 0, 5, -5, -6, 4, -10, -10, 5, -4, 8, -10, 0, -10, -3, 0, -5, -10, 1, -9, 10], 'class_deg': 1, 'class_size': 1, 'conductor': 800, 'isogeny_matrix': [[1]], 'lmfdb_iso': '800.b', 'trace_hash': 584720505788691135}
• 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': '0.53196999044771910407456934002', 'prec': 103}, 'conductor': 800, 'gens': [[-8, 50, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.19637779133168667685371410477', 'prec': 103}], 'lmfdb_label': '800.b1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.7115587321269884745620801932', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.0166727412973597372967082909344774460', 'prec': 130}, 'tamagawa_product': 6, 'torsion_generators': [], 'xcoord_integral_points': [-8, 8, 17]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': 'a', '7': [1, 0], '11': [3, 0], '13': [1, 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': '800.b1'}
• ec_torsion_growth •

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

  
  
  • id: 37819
    {'degree': 3, 'field': [2, 2, -1, 1], 'lmfdb_label': '800.b1', 'torsion': [2]}
  • id: 37820
    {'degree': 6, 'field': [2, 0, -3, 0, 4, 0, 1], 'lmfdb_label': '800.b1', 'torsion': [2, 2]}
  • id: 37821
    {'degree': 8, 'field': [-3, 0, 16, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '800.b1', 'torsion': [3]}
  • id: 37822
    {'degree': 8, 'field': [45, 0, 40, 0, 10, 0, 0, 0, 1], 'lmfdb_label': '800.b1', 'torsion': [5]}
  • id: 37823
    {'degree': 12, 'field': [1, -1, 0, -1, -3, -4, 0, -4, -3, -1, 0, -1, 1], 'lmfdb_label': '800.b1', 'torsion': [4]}
  • id: 37824
    {'degree': 16, 'field': [-4, 8, 0, 40, -240, 704, -1488, 2240, -2350, 1740, -888, 256, 20, -60, 30, -8, 1], 'lmfdb_label': '800.b1', 'torsion': [5]}
• 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: 10362
    {'conductor': 800, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '800.b1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 10363
    {'conductor': 800, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '800.b1', 'prime': 5, '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: 1669685
    {'adelic_gens': [[21, 0, 0, 21], [31, 32, 8, 39], [1, 16, 0, 9], [31, 10, 20, 31], [31, 30, 30, 11], [21, 20, 20, 21], [31, 0, 0, 31], [9, 0, 0, 9], [1, 20, 0, 1], [31, 25, 25, 6], [9, 8, 15, 23], [33, 0, 0, 33], [31, 22, 3, 9]], 'adelic_image': '40.60.3.?', 'conductor': 800, 'lmfdb_label': '800.b1', 'prime': 0}
  • id: 3695
    {'conductor': 800, 'elladic_image': '8.2.0.1', 'lmfdb_label': '800.b1', 'modell_image': '2G', 'prime': 2}
  • id: 3696
    {'conductor': 800, 'elladic_image': '5.15.0.1', 'lmfdb_label': '800.b1', 'modell_image': '5Ns', 'prime': 5}
• ec_padic •

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

  
  
  • id: 16059
    {'lmfdb_iso': '800.b', 'p': 7, 'prec': 20, 'unit': 1107788330306513, 'val': 1}
  • id: 16064
    {'lmfdb_iso': '800.b', 'p': 11, 'prec': 20, 'unit': 792215766665271089, 'val': 2}
  • id: 16065
    {'lmfdb_iso': '800.b', 'p': 17, 'prec': 20, 'unit': 100219055035163990300291, 'val': 1}
  • id: 16066
    {'lmfdb_iso': '800.b', 'p': 19, 'prec': 20, 'unit': 1525480882377546442100803, 'val': 1}
  • id: 16069
    {'lmfdb_iso': '800.b', 'p': 23, 'prec': 20, 'unit': 21470884513692961231318297, 'val': 1}
  • id: 16062
    {'lmfdb_iso': '800.b', 'p': 29, 'prec': 20, 'unit': 4900626369337410160950111623, 'val': 1}
  • id: 16073
    {'lmfdb_iso': '800.b', 'p': 31, 'prec': 20, 'unit': 6962776620787686526174507570, 'val': 1}
  • id: 16058
    {'lmfdb_iso': '800.b', 'p': 37, 'prec': 20, 'unit': 618416071064487712529699510583, 'val': 1}
  • id: 16060
    {'lmfdb_iso': '800.b', 'p': 41, 'prec': 20, 'unit': 3166441722693993744720642276273, 'val': 1}
  • id: 16061
    {'lmfdb_iso': '800.b', 'p': 43, 'prec': 20, 'unit': 10666408217849414027280846661214, 'val': 1}
  • id: 16063
    {'lmfdb_iso': '800.b', 'p': 47, 'prec': 20, 'unit': 15430150324071953206336636107898, 'val': 1}
  • id: 16067
    {'lmfdb_iso': '800.b', 'p': 53, 'prec': 20, 'unit': 438176343122214022938741045535982, 'val': 1}
  • id: 16072
    {'lmfdb_iso': '800.b', 'p': 61, 'prec': 20, 'unit': 1182092151189312962216895429547076, 'val': 1}
  • id: 16057
    {'lmfdb_iso': '800.b', 'p': 67, 'prec': 20, 'unit': 25950069572273359165836528277105825, 'val': 1}
  • id: 16068
    {'lmfdb_iso': '800.b', 'p': 73, 'prec': 20, 'unit': 88385223046069637372757556319521947, 'val': 1}
  • id: 16071
    {'lmfdb_iso': '800.b', 'p': 79, 'prec': 20, 'unit': 1023997553933470094741840047870225986, 'val': 1}
  • id: 16056
    {'lmfdb_iso': '800.b', 'p': 83, 'prec': 20, 'unit': 232854974048109806498705281203942656515, 'val': -1}
  • id: 16070
    {'lmfdb_iso': '800.b', 'p': 89, 'prec': 20, 'unit': 585742078672356756773405127358831931, 'val': 1}
  • id: 16055
    {'lmfdb_iso': '800.b', 'p': 97, 'prec': 20, 'unit': 26582289416445576227339793616030629373, 'val': 1}