Elliptic curve data - 5077.a1

Formats: - HTML - YAML - JSON - 2023-06-06T15:53:11.031158

• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  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
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '5077a', 'Clabel': '5077a1', 'Cnumber': 1, 'absD': 5077, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 10154, 'ainvs': [0, 0, 1, -7, 6], 'analytic_rank': 3, 'bad_primes': [5077], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 5077, 'degree': 1984, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.56139014229398666466212500182', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1], 'jinv': [37933056, 5077], 'lmfdb_iso': '5077.a', 'lmfdb_label': '5077.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 1, -7, 6], 'min_quad_twist_disc': 1, 'modell_images': [], 'modm_images': ['10154.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 1, 'num_int_pts': 36, 'optimality': 1, 'potential_good_reduction': False, 'rank': 3, 'regulator': {'__RealLiteral__': 0, 'data': '0.41714355875838396981711954462', 'prec': 103}, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.56139014229398666466212500182', 'prec': 107}, '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, -2, -3, 2, -4, 6, -4, 0, 6, 8, -6, -6, -4, 8, 12, -4, -4, -12, -7, -8], 'aplist': [-2, -3, -4, -4, -6, -4, -4, -7, -6, -6, -2, 0, 0, -8, -9, -9, -11, -2, -12, -8, -14, 9, -2, 11, 6], 'class_deg': 1, 'class_size': 1, 'conductor': 5077, 'isogeny_matrix': [[1]], 'lmfdb_iso': '5077.a', 'trace_hash': 129556073554127214}
• 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': '3.0733872268190258735445164242', 'prec': 100}, 'conductor': 5077, 'gens': [[1, 0, 1], [2, 0, 1], [0, 2, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.66820516565192793503314205089', 'prec': 103}, {'__RealLiteral__': 0, 'data': '0.76704335533154620579545064655', 'prec': 103}, {'__RealLiteral__': 0, 'data': '0.99090633315308797388259855289', 'prec': 103}], 'lmfdb_label': '5077.a1', 'ngens': 3, 'rank_bounds': [3, 3], 'real_period': {'__RealLiteral__': 0, 'data': '4.1516879830869330498841756835', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.7318499001193006897919750850614576885', 'prec': 130}, 'tamagawa_product': 1, 'torsion_generators': [], 'xcoord_integral_points': [-3, -2, -1, 0, 1, 2, 3, 4, 8, 11, 14, 21, 37, 52, 93, 342, 406, 816]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 3, 0], '3': [3, 3, 0], '5': [3, 0], '7': [3, 0], '11': [3, 0], '13': [3, 0], '17': [3, 0], '19': [3, 0], '23': [3, 0], '29': [3, 0], '31': [3, 0], '37': [3, 3, 0], '41': [3, 3, 0], '43': [3, 0], '47': [3, 0], '5077': 'o?'}, 'iwp0': 0, 'lmfdb_label': '5077.a1'}
• ec_torsion_growth •

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

  
  
  • id: 266153
    {'degree': 3, 'field': [-50, -28, 0, 1], 'lmfdb_label': '5077.a1', 'torsion': [2]}
  • id: 266154
    {'degree': 6, 'field': [4483, 6274, 2095, -284, -163, -2, 1], 'lmfdb_label': '5077.a1', 'torsion': [2, 2]}
  • id: 266155
    {'degree': 8, 'field': [-1323, 0, 675, 0, -126, 0, 0, 0, 1], 'lmfdb_label': '5077.a1', 'torsion': [3]}
  • id: 266156
    {'degree': 12, 'field': [-1592603, -434580, 2586290, -543124, -507293, 139192, 38264, -16016, 547, 468, -66, -4, 1], 'lmfdb_label': '5077.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

  
  {'conductor': 5077, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '5077.a1', 'prime': 5077, 'reduction_type': -1, '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

  
  {'adelic_gens': [[5079, 2, 5079, 3], [1, 2, 0, 1], [1, 0, 2, 1], [1, 1, 10153, 0], [10153, 2, 10152, 3]], 'adelic_image': '10154.2.0.?', 'conductor': 5077, 'lmfdb_label': '5077.a1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 187272
    {'lmfdb_iso': '5077.a', 'p': 5, 'prec': 20, 'unit': 15578877570356, 'val': 1}
  • id: 187273
    {'lmfdb_iso': '5077.a', 'p': 7, 'prec': 20, 'unit': 8563723151992870, 'val': 3}
  • id: 187271
    {'lmfdb_iso': '5077.a', 'p': 11, 'prec': 20, 'unit': 6872444289905743280, 'val': 3}
  • id: 187277
    {'lmfdb_iso': '5077.a', 'p': 13, 'prec': 20, 'unit': 253588997770278844663, 'val': 3}
  • id: 187279
    {'lmfdb_iso': '5077.a', 'p': 17, 'prec': 20, 'unit': 231308078294920924422900, 'val': 3}
  • id: 187280
    {'lmfdb_iso': '5077.a', 'p': 19, 'prec': 20, 'unit': 178254631836083532414348, 'val': 3}
  • id: 187283
    {'lmfdb_iso': '5077.a', 'p': 23, 'prec': 20, 'unit': 27545375191099737165182066, 'val': 3}
  • id: 187276
    {'lmfdb_iso': '5077.a', 'p': 29, 'prec': 20, 'unit': 3460531074954580993948008065, 'val': 3}
  • id: 187289
    {'lmfdb_iso': '5077.a', 'p': 31, 'prec': 20, 'unit': 1108130732959734326936337190, 'val': 3}
  • id: 187275
    {'lmfdb_iso': '5077.a', 'p': 43, 'prec': 20, 'unit': 2773117441872388869291928124796, 'val': 3}
  • id: 187287
    {'lmfdb_iso': '5077.a', 'p': 47, 'prec': 20, 'unit': 25745513892549249967775368198691, 'val': 3}
  • id: 187281
    {'lmfdb_iso': '5077.a', 'p': 53, 'prec': 20, 'unit': 143828886250349295293385482257970, 'val': 3}
  • id: 187282
    {'lmfdb_iso': '5077.a', 'p': 59, 'prec': 20, 'unit': 2724677086788190600112021689959623, 'val': 3}
  • id: 187288
    {'lmfdb_iso': '5077.a', 'p': 61, 'prec': 20, 'unit': 3527952747753980223208726254216489, 'val': 3}
  • id: 187270
    {'lmfdb_iso': '5077.a', 'p': 67, 'prec': 20, 'unit': 33186293012279731563653782761911, 'val': 3}
  • id: 187286
    {'lmfdb_iso': '5077.a', 'p': 71, 'prec': 20, 'unit': 119097953090925626735859242400837605, 'val': 3}
  • id: 187274
    {'lmfdb_iso': '5077.a', 'p': 73, 'prec': 20, 'unit': 214485502080729967009075282739629531, 'val': 3}
  • id: 187278
    {'lmfdb_iso': '5077.a', 'p': 79, 'prec': 20, 'unit': 902248296237922498832179922990133102, 'val': 3}
  • id: 187284
    {'lmfdb_iso': '5077.a', 'p': 83, 'prec': 20, 'unit': 2549217168325722652914590943659361272, 'val': 3}
  • id: 187285
    {'lmfdb_iso': '5077.a', 'p': 89, 'prec': 20, 'unit': 1580848649524179578172588853810601405, 'val': 3}
  • id: 187269
    {'lmfdb_iso': '5077.a', 'p': 97, 'prec': 20, 'unit': 9280059319248165208283863813164300330, 'val': 3}