Elliptic curve data - 400.d2

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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': '400c', 'Clabel': '400c3', 'Cnumber': 3, 'abc_quality': 0.9433414068835279, 'absD': 51200000000, 'adelic_genus': 9, 'adelic_index': 384, 'adelic_level': 120, 'ainvs': [0, -1, 0, -1208, -19088], 'analytic_rank': 1, 'bad_primes': [2, 5], 'class_deg': 15, 'class_size': 4, 'cm': 0, 'conductor': 400, 'degree': 240, 'elladic_images': ['8.2.0.1', '3.4.0.1', '5.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.77176654063311396396378640808', 'prec': 103}, 'faltings_index': 2, 'faltings_ratio': 5, 'iso_nlabel': 3, 'isogeny_degrees': [1, 3, 5, 15], 'jinv': [-121945, 32], 'lmfdb_iso': '400.d', 'lmfdb_label': '400.d2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -3, 1], 'min_quad_twist_disc': -20, 'modell_images': ['3B', '5B.4.1'], 'modm_images': ['3.4.0.a.1', '5.12.0.a.1', '8.2.0.a.1', '12.8.0-3.a.1.1', '15.96.1.a.4', '20.24.0-5.a.1.1', '24.16.0-24.a.1.5', '40.48.1-40.bx.1.1', '60.192.1-15.a.4.4', '120.384.9.?'], 'nonmax_primes': [2, 3, 5], 'nonmax_rad': 30, 'num_bad_primes': 2, 'num_int_pts': 8, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.32449604926990433759677170018', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 4, 25], [5, 14, 16]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.99433924821623159518728526886', 'prec': 107}, 'szpiro_ratio': 5.554323967354545, '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, 3, 0, -4, 0, 0, 0, -3, 0, -5, 0], 'aplist': [0, -1, 0, -2, 3, -4, -3, -5, -6, 0, -2, 2, -3, 4, -12, 6, 0, 2, 13, -12, 11, 10, 9, 15, 2], 'class_deg': 15, 'class_size': 4, 'conductor': 400, 'isogeny_matrix': [[1, 15, 3, 5], [15, 1, 5, 3], [3, 5, 1, 15], [5, 3, 15, 1]], 'lmfdb_iso': '400.d', 'trace_hash': 2204203944625626078}
• 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': '0.21362501202284827131821663468', 'prec': 103}, 'conductor': 400, 'gens': [[92, 800, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.32449604926990433759677170018', 'prec': 103}], 'lmfdb_label': '400.d2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.39939334765616992615588584260', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.5552187610293025813988289082243501080', 'prec': 130}, 'tamagawa_product': 12, 'torsion_generators': [], 'xcoord_integral_points': [42, 92, 156, 1517]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': 'a', '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 1, 0], '31': [3, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '400.d2'}
• ec_torsion_growth •

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

  
  
  • id: 17461
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '400.d2', 'torsion': [3]}
  • id: 17462
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '400.d2', 'torsion': [5]}
  • id: 17463
    {'degree': 3, 'field': [2, 2, -1, 1], 'lmfdb_label': '400.d2', 'torsion': [2]}
  • id: 17464
    {'degree': 4, 'field': [1, 0, 3, 0, 1], 'lmfdb_label': '400.d2', 'torsion': [15]}
  • id: 17466
    {'degree': 6, 'field': [-3, 0, 7, 0, -1, 0, 1], 'lmfdb_label': '400.d2', 'torsion': [3]}
  • id: 17465
    {'degree': 6, 'field': [2, 0, -3, 0, 4, 0, 1], 'lmfdb_label': '400.d2', 'torsion': [2, 2]}
  • id: 17467
    {'degree': 6, 'field': [2, 2, 1, 4, 2, -2, 1], 'lmfdb_label': '400.d2', 'torsion': [6]}
  • id: 17468
    {'degree': 6, 'field': [4, -12, 10, 0, 0, -2, 1], 'lmfdb_label': '400.d2', 'torsion': [10]}
  • id: 17469
    {'degree': 12, 'field': [1, -1, 0, -1, -3, -4, 0, -4, -3, -1, 0, -1, 1], 'lmfdb_label': '400.d2', 'torsion': [4]}
  • id: 17474
    {'degree': 12, 'field': [1, 0, 4, 0, 0, 0, 10, 0, 0, 0, 4, 0, 1], 'lmfdb_label': '400.d2', 'torsion': [30]}
  • id: 17473
    {'degree': 12, 'field': [4, 0, -8, 0, 0, 0, 5, 0, 15, 0, 7, 0, 1], 'lmfdb_label': '400.d2', 'torsion': [15]}
  • id: 17472
    {'degree': 12, 'field': [4, 0, 8, 0, 20, 0, 20, 0, 25, 0, 8, 0, 1], 'lmfdb_label': '400.d2', 'torsion': [2, 10]}
  • id: 17470
    {'degree': 12, 'field': [9, 0, 21, 0, 46, 0, 1, 0, -6, 0, 1, 0, 1], 'lmfdb_label': '400.d2', 'torsion': [3, 3]}
  • id: 17471
    {'degree': 12, 'field': [16, 0, 0, 0, 88, 0, 0, 0, -7, 0, 0, 0, 1], 'lmfdb_label': '400.d2', 'torsion': [2, 6]}
  • id: 17476
    {'degree': 18, 'field': [-2, 0, 6, 2, -18, -2, 19, 26, -64, -10, 105, -122, 108, -82, 35, -2, 0, -2, 1], 'lmfdb_label': '400.d2', 'torsion': [6]}
  • id: 17475
    {'degree': 18, 'field': [1, 0, -6, 0, -15, 0, 78, 0, 108, 0, 27, 0, -13, 0, -3, 0, 3, 0, 1], 'lmfdb_label': '400.d2', 'torsion': [9]}
  • id: 17477
    {'degree': 20, 'field': [80, 0, -100, 0, -175, 0, 300, 0, 50, 0, -270, 0, 135, 0, -30, 0, 15, 0, -5, 0, 1], 'lmfdb_label': '400.d2', '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: 4105
    {'conductor': 400, 'conductor_valuation': 4, 'discriminant_valuation': 17, 'j_denominator_valuation': 5, 'kodaira_symbol': -13, 'lmfdb_label': '400.d2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4106
    {'conductor': 400, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '400.d2', '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: 1667513
    {'adelic_gens': [[46, 105, 45, 1], [1, 42, 90, 61], [1, 0, 60, 1], [81, 10, 40, 81], [1, 72, 0, 1], [41, 80, 40, 81], [39, 70, 80, 23], [61, 90, 45, 91], [1, 0, 30, 1], [89, 30, 105, 29], [1, 36, 60, 1]], 'adelic_image': '120.384.9.?', 'conductor': 400, 'lmfdb_label': '400.d2', 'prime': 0}
  • id: 1704
    {'conductor': 400, 'elladic_image': '8.2.0.1', 'lmfdb_label': '400.d2', 'modell_image': '2G', 'prime': 2}
  • id: 1705
    {'conductor': 400, 'elladic_image': '3.4.0.1', 'lmfdb_label': '400.d2', 'modell_image': '3B', 'prime': 3}
  • id: 1706
    {'conductor': 400, 'elladic_image': '5.12.0.1', 'lmfdb_label': '400.d2', 'modell_image': '5B.4.1', 'prime': 5}
• ec_padic •

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

  
  
  • id: 5225
    {'lmfdb_iso': '400.d', 'p': 7, 'prec': 20, 'unit': 5258619631401372, 'val': 1}
  • id: 5230
    {'lmfdb_iso': '400.d', 'p': 11, 'prec': 20, 'unit': 35075820801103337465, 'val': 1}
  • id: 5228
    {'lmfdb_iso': '400.d', 'p': 13, 'prec': 20, 'unit': 1093649978282668721527, 'val': 1}
  • id: 5231
    {'lmfdb_iso': '400.d', 'p': 17, 'prec': 20, 'unit': 201677776449359128181482, 'val': 1}
  • id: 5232
    {'lmfdb_iso': '400.d', 'p': 19, 'prec': 20, 'unit': 480371524057024206232463, 'val': 1}
  • id: 5235
    {'lmfdb_iso': '400.d', 'p': 23, 'prec': 20, 'unit': 37356696658464141341701730, 'val': 1}
  • id: 5240
    {'lmfdb_iso': '400.d', 'p': 31, 'prec': 20, 'unit': 344209282900336102905494329, 'val': 2}
  • id: 5224
    {'lmfdb_iso': '400.d', 'p': 37, 'prec': 20, 'unit': 544323371352079504951857259728, 'val': 1}
  • id: 5226
    {'lmfdb_iso': '400.d', 'p': 41, 'prec': 20, 'unit': 1083330455425726933286706026786, 'val': 1}
  • id: 5227
    {'lmfdb_iso': '400.d', 'p': 43, 'prec': 20, 'unit': 6234415608986565377185378573212, 'val': 1}
  • id: 5229
    {'lmfdb_iso': '400.d', 'p': 47, 'prec': 20, 'unit': 49827627725588255702134573520325, 'val': 1}
  • id: 5233
    {'lmfdb_iso': '400.d', 'p': 53, 'prec': 20, 'unit': 20112526490429012818096646261444, 'val': 1}
  • id: 5239
    {'lmfdb_iso': '400.d', 'p': 61, 'prec': 20, 'unit': 2155205710889467899147229997156772, 'val': 1}
  • id: 5223
    {'lmfdb_iso': '400.d', 'p': 67, 'prec': 20, 'unit': 20148173186589713799768677145605138, 'val': 1}
  • id: 5237
    {'lmfdb_iso': '400.d', 'p': 71, 'prec': 20, 'unit': 7914763844523298971567119960128496, 'val': 1}
  • id: 5234
    {'lmfdb_iso': '400.d', 'p': 73, 'prec': 20, 'unit': 85229481280823924074498613041959661, 'val': 1}
  • id: 5238
    {'lmfdb_iso': '400.d', 'p': 79, 'prec': 20, 'unit': 1048801850221654331071794517872660151, 'val': 1}
  • id: 5222
    {'lmfdb_iso': '400.d', 'p': 83, 'prec': 20, 'unit': 1711265874083799718750350358926581478, 'val': 1}
  • id: 5236
    {'lmfdb_iso': '400.d', 'p': 89, 'prec': 20, 'unit': 10843421264522328324407414107079782496, 'val': 1}
  • id: 5221
    {'lmfdb_iso': '400.d', 'p': 97, 'prec': 20, 'unit': 38215609705601950169320303246284125456, 'val': 1}