Elliptic curve data - 400.a1

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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': '400h', 'Clabel': '400h1', 'Cnumber': 1, 'abc_quality': 1.018975235452531, 'absD': 51200, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 8, 'ainvs': [0, 0, 0, 5, 10], 'analytic_rank': 1, 'bad_primes': [2, 5], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 400, 'degree': 48, 'elladic_images': ['8.2.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.41352042872867736321470958332', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1], 'jinv': [270, 1], 'lmfdb_iso': '400.a', 'lmfdb_label': '400.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, 5, -10], 'min_quad_twist_disc': -4, 'modell_images': [], 'modm_images': ['8.2.0.a.1'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 8, 'optimality': 1, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.12837506294605086906217592378', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 4, 25], [5, 10, 16]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.3171449963143106259472989169', 'prec': 103}, 'szpiro_ratio': 3.0256902266652905, '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, -3, 0, 0, 0, 2, 0, 6, 0, -1, 0, -4, 0, 0, 0, -5, 0, -1, 0], 'aplist': [0, -3, 0, 2, -1, -4, -5, -1, -2, -8, -10, 6, -3, 4, 4, -6, -8, 10, -1, 12, -3, -6, -13, -9, 14], 'class_deg': 1, 'class_size': 1, 'conductor': 400, 'isogeny_matrix': [[1]], 'lmfdb_iso': '400.a', 'trace_hash': 1624048841899094709}
• 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': '2.2865425140703078042026374234', 'prec': 100}, 'conductor': 400, 'gens': [[1, 4, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.12837506294605086906217592378', 'prec': 103}], 'lmfdb_label': '400.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '2.5292107620580267572591609418', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2987503631321138881888327746917277891', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': [-1, 1, 6, 9]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 3, 0], '5': 'a', '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': '400.a1'}
• ec_torsion_growth •

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

  
  
  • id: 17583
    {'degree': 3, 'field': [2, 2, -1, 1], 'lmfdb_label': '400.a1', 'torsion': [2]}
  • id: 17584
    {'degree': 6, 'field': [2, 0, -3, 0, 4, 0, 1], 'lmfdb_label': '400.a1', 'torsion': [2, 2]}
  • id: 17585
    {'degree': 8, 'field': [-5, -10, 10, -40, 40, -10, 4, -4, 1], 'lmfdb_label': '400.a1', 'torsion': [3]}
  • id: 17586
    {'degree': 12, 'field': [-16, 6, 18, 5, -15, -4, 4, -8, 0, 10, -2, -3, 1], 'lmfdb_label': '400.a1', 'torsion': [4]}
• 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: 4127
    {'conductor': 400, 'conductor_valuation': 4, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -7, 'lmfdb_label': '400.a1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 4128
    {'conductor': 400, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '400.a1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  
  • id: 1667505
    {'adelic_gens': [[5, 2, 5, 3], [1, 2, 0, 1], [7, 2, 6, 3], [1, 0, 2, 1], [1, 1, 7, 0], [7, 2, 7, 3]], 'adelic_image': '8.2.0.?', 'conductor': 400, 'lmfdb_label': '400.a1', 'prime': 0}
  • id: 1690
    {'conductor': 400, 'elladic_image': '8.2.0.1', 'lmfdb_label': '400.a1', 'modell_image': '2G', 'prime': 2}
• ec_padic •

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

  
  
  • id: 5318
    {'lmfdb_iso': '400.a', 'p': 7, 'prec': 20, 'unit': 3273849426356217, 'val': 1}
  • id: 5319
    {'lmfdb_iso': '400.a', 'p': 11, 'prec': 20, 'unit': 40882355373932253428, 'val': 1}
  • id: 5320
    {'lmfdb_iso': '400.a', 'p': 13, 'prec': 20, 'unit': 336342249231144897840, 'val': 1}
  • id: 5321
    {'lmfdb_iso': '400.a', 'p': 17, 'prec': 20, 'unit': 111560179233031429825155, 'val': 1}
  • id: 5322
    {'lmfdb_iso': '400.a', 'p': 19, 'prec': 20, 'unit': 25589646570112815490248, 'val': 1}
  • id: 5323
    {'lmfdb_iso': '400.a', 'p': 23, 'prec': 20, 'unit': 66147439760842247285265722, 'val': 1}
  • id: 5324
    {'lmfdb_iso': '400.a', 'p': 29, 'prec': 20, 'unit': 3144032113576284840001240703, 'val': 1}
  • id: 5325
    {'lmfdb_iso': '400.a', 'p': 31, 'prec': 20, 'unit': 6654418665379907909942646053, 'val': 1}
  • id: 5326
    {'lmfdb_iso': '400.a', 'p': 37, 'prec': 20, 'unit': 112940578930341848382773658088, 'val': 1}
  • id: 5327
    {'lmfdb_iso': '400.a', 'p': 41, 'prec': 20, 'unit': 919785522037980195417971952656, 'val': 1}
  • id: 5328
    {'lmfdb_iso': '400.a', 'p': 43, 'prec': 20, 'unit': 7882904450643548906143087490889, 'val': 1}
  • id: 5329
    {'lmfdb_iso': '400.a', 'p': 47, 'prec': 20, 'unit': 45225376521249182661497071006265, 'val': 1}
  • id: 5330
    {'lmfdb_iso': '400.a', 'p': 53, 'prec': 20, 'unit': 246654389244004471763446440698925, 'val': 1}
  • id: 5331
    {'lmfdb_iso': '400.a', 'p': 59, 'prec': 20, 'unit': 316549718299073781707593292115031, 'val': 1}
  • id: 5332
    {'lmfdb_iso': '400.a', 'p': 61, 'prec': 20, 'unit': 3581899516351311405250130622678308, 'val': 1}
  • id: 5333
    {'lmfdb_iso': '400.a', 'p': 67, 'prec': 20, 'unit': 34959916509053322703778827654557203, 'val': 1}
  • id: 5334
    {'lmfdb_iso': '400.a', 'p': 71, 'prec': 20, 'unit': 105362111617876813164444516643984868, 'val': 1}
  • id: 5335
    {'lmfdb_iso': '400.a', 'p': 73, 'prec': 20, 'unit': 80863432883687175364995647599127982, 'val': 1}
  • id: 5336
    {'lmfdb_iso': '400.a', 'p': 79, 'prec': 20, 'unit': 964922156794937202670466407242306481, 'val': 1}
  • id: 5337
    {'lmfdb_iso': '400.a', 'p': 83, 'prec': 20, 'unit': 104545821221539975956622437686486456, 'val': 1}
  • id: 5338
    {'lmfdb_iso': '400.a', 'p': 89, 'prec': 20, 'unit': 3511850616155451667499532789400044898, 'val': 1}
  • id: 5339
    {'lmfdb_iso': '400.a', 'p': 97, 'prec': 20, 'unit': 28058078767152715092148583085254618276, 'val': 1}