Elliptic curve data - 558.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': '558d', 'Clabel': '558d2', 'Cnumber': 2, 'abc_quality': 1.0100188200478981, 'absD': 125223906474, 'adelic_genus': 1, 'adelic_index': 48, 'adelic_level': 3720, 'ainvs': [1, -1, 0, -12555, 544887], 'analytic_rank': 1, 'bad_primes': [2, 3, 31], 'class_deg': 5, 'class_size': 2, 'cm': 0, 'conductor': 558, 'degree': 800, 'elladic_images': ['5.12.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0756464544271708897368236094', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 5, 'iso_nlabel': 0, 'isogeny_degrees': [1, 5], 'jinv': [-300238092661681, 171774906], 'lmfdb_iso': '558.a', 'lmfdb_label': '558.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -1395, -20181], 'min_quad_twist_disc': -3, 'modell_images': ['5B.4.2'], 'modm_images': ['5.12.0.a.2', '15.24.0-5.a.2.1', '744.2.0.?', '1240.24.0.?', '3720.48.1.?'], 'nonmax_primes': [5], 'nonmax_rad': 5, 'num_bad_primes': 3, 'num_int_pts': 6, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.071901717837733599971088942877', 'prec': 107}, 'semistable': False, 'serre_invariants': [[2, 4, 279], [3, 8, 62], [5, 2, 18], [31, 32, 18]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.52634031009311604403920099094', 'prec': 103}, 'szpiro_ratio': 6.313408052576593, '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, 0, 1, -1, 0, -2, -1, 0, 1, 3, 0, -1, 2, 0, 1, -3, 0, -5, -1], 'aplist': [-1, 0, -1, -2, 3, -1, -3, -5, -4, 0, 1, -2, -2, -6, 7, -14, -10, 7, -7, 3, -6, 15, 1, -10, 13], 'class_deg': 5, 'class_size': 2, 'conductor': 558, 'isogeny_matrix': [[1, 5], [5, 1]], 'lmfdb_iso': '558.a', 'trace_hash': 1751053207025237164}
• 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': '0.11633365169081019145566132185', 'prec': 103}, 'conductor': 558, 'gens': [[279, 4185, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.071901717837733599971088942877', 'prec': 107}], 'lmfdb_label': '558.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.0317785645251574897411519203', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4837330243501936888092274811383472867', 'prec': 130}, 'tamagawa_product': 20, 'torsion_generators': [], 'xcoord_integral_points': [63, 93, 279]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': 'a', '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 1, 0], '31': [2, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '558.a1'}
• ec_torsion_growth •

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

  
  
  • id: 25155
    {'degree': 3, 'field': [-6, -6, -1, 1], 'lmfdb_label': '558.a1', 'torsion': [2]}
  • id: 25156
    {'degree': 4, 'field': [1, 4, -4, -1, 1], 'lmfdb_label': '558.a1', 'torsion': [5]}
  • id: 25157
    {'degree': 6, 'field': [888, -696, 214, -20, -3, -2, 1], 'lmfdb_label': '558.a1', 'torsion': [2, 2]}
  • id: 25158
    {'degree': 8, 'field': [-156, 148, -68, 24, 10, -2, -3, -2, 1], 'lmfdb_label': '558.a1', 'torsion': [3]}
  • id: 25159
    {'degree': 10, 'field': [36, 0, 0, 0, 0, -6, 0, 0, 0, 0, 1], 'lmfdb_label': '558.a1', 'torsion': [5]}
  • id: 25160
    {'degree': 12, 'field': [-5994, 23292, -31467, 19476, -4697, 152, -629, 200, 187, -16, 1, -4, 1], 'lmfdb_label': '558.a1', 'torsion': [4]}
  • id: 25161
    {'degree': 12, 'field': [961, -6758, -16368, -8547, -1237, -2066, -299, 78, -119, 29, 7, -1, 1], 'lmfdb_label': '558.a1', 'torsion': [10]}
• 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: 6374
    {'conductor': 558, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '558.a1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 6375
    {'conductor': 558, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '558.a1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 6376
    {'conductor': 558, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '558.a1', 'prime': 31, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 5}
• ec_galrep •

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

  
  
  • id: 1668323
    {'adelic_gens': [[1801, 10, 1565, 51], [6, 13, 3665, 3601], [1, 0, 10, 1], [2479, 3710, 1235, 3669], [2791, 10, 2795, 51], [1861, 10, 1865, 51], [3711, 10, 3710, 11], [937, 1870, 3680, 2361], [1, 10, 0, 1]], 'adelic_image': '3720.48.1.?', 'conductor': 558, 'lmfdb_label': '558.a1', 'prime': 0}
  • id: 2490
    {'conductor': 558, 'elladic_image': '5.12.0.2', 'lmfdb_label': '558.a1', 'modell_image': '5B.4.2', 'prime': 5}
• ec_padic •

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

  
  
  • id: 8942
    {'lmfdb_iso': '558.a', 'p': 5, 'prec': 20, 'unit': 15010452705169, 'val': 1}
  • id: 8943
    {'lmfdb_iso': '558.a', 'p': 7, 'prec': 20, 'unit': 8938406562083338, 'val': 1}
  • id: 8948
    {'lmfdb_iso': '558.a', 'p': 11, 'prec': 20, 'unit': 14484761290053026304, 'val': 1}
  • id: 8946
    {'lmfdb_iso': '558.a', 'p': 13, 'prec': 20, 'unit': 289123215233082763850, 'val': 1}
  • id: 8949
    {'lmfdb_iso': '558.a', 'p': 17, 'prec': 20, 'unit': 99616847652350789112338, 'val': 1}
  • id: 8950
    {'lmfdb_iso': '558.a', 'p': 19, 'prec': 20, 'unit': 18439990101206088519399, 'val': 1}
  • id: 8954
    {'lmfdb_iso': '558.a', 'p': 23, 'prec': 20, 'unit': 1729955158635764401439166, 'val': 1}
  • id: 8959
    {'lmfdb_iso': '558.a', 'p': 37, 'prec': 20, 'unit': 79814844822533765016483332061, 'val': 1}
  • id: 8944
    {'lmfdb_iso': '558.a', 'p': 41, 'prec': 20, 'unit': 1136676752906095854499604976446, 'val': 1}
  • id: 8945
    {'lmfdb_iso': '558.a', 'p': 43, 'prec': 20, 'unit': 6100327870996599092668936976145, 'val': 1}
  • id: 8957
    {'lmfdb_iso': '558.a', 'p': 47, 'prec': 20, 'unit': 1350702597405938960231614105311, 'val': 1}
  • id: 8951
    {'lmfdb_iso': '558.a', 'p': 53, 'prec': 20, 'unit': 469131522714958705011494292635787, 'val': 1}
  • id: 8952
    {'lmfdb_iso': '558.a', 'p': 59, 'prec': 20, 'unit': 2493223992812362684000697865717804, 'val': 1}
  • id: 8958
    {'lmfdb_iso': '558.a', 'p': 61, 'prec': 20, 'unit': 2609186390393596160191447173443760, 'val': 1}
  • id: 8941
    {'lmfdb_iso': '558.a', 'p': 67, 'prec': 20, 'unit': 44315388871201202728714113684769661, 'val': 1}
  • id: 8956
    {'lmfdb_iso': '558.a', 'p': 71, 'prec': 20, 'unit': 123562933587756520732299884039213577, 'val': 1}
  • id: 8953
    {'lmfdb_iso': '558.a', 'p': 73, 'prec': 20, 'unit': 174806483881800798940859570625282815, 'val': 1}
  • id: 8947
    {'lmfdb_iso': '558.a', 'p': 79, 'prec': 20, 'unit': 200805848284964741332122080970931576, 'val': 1}
  • id: 8940
    {'lmfdb_iso': '558.a', 'p': 83, 'prec': 20, 'unit': 46412344257488457501185807022225220156, 'val': -1}
  • id: 8955
    {'lmfdb_iso': '558.a', 'p': 89, 'prec': 20, 'unit': 7019511372572969484281086117312508925, 'val': 1}
  • id: 8939
    {'lmfdb_iso': '558.a', 'p': 97, 'prec': 20, 'unit': 41400495426920317872595522617792324592, 'val': 1}