Elliptic curve data - 5056.h1

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '5056q', 'Clabel': '5056q1', 'Cnumber': 1, 'abc_quality': 0.9406342793009744, 'absD': 82837504, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 316, 'ainvs': [0, -1, 0, -225, -1151], 'analytic_rank': 1, 'bad_primes': [2, 79], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 5056, 'degree': 1536, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.26915565023908741186131398292', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 7, 'isogeny_degrees': [1], 'jinv': [4826809, 316], 'lmfdb_iso': '5056.h', 'lmfdb_label': '5056.h1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -3, 1], 'min_quad_twist_disc': -8, 'modell_images': [], 'modm_images': ['316.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 2, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.5618220465126201833609894058', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.77056512060083055226453419927', 'prec': 107}, 'szpiro_ratio': 3.2675028214236406, '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, 1, 0, 3, 0, -2, 0, 4, 0, 7, 0, -1, 0, -4, 0, -6, 0], 'aplist': [0, -1, 1, 3, 4, 7, -4, -6, -6, -4, -8, -10, -8, -8, 3, -2, 1, 0, -4, 11, -6, 1, 6, -15, 1], 'class_deg': 1, 'class_size': 1, 'conductor': 5056, 'isogeny_matrix': [[1]], 'lmfdb_iso': '5056.h', 'trace_hash': 259867199309137505}
• 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': '0.58373317045040235532238111622', 'prec': 103}, 'conductor': 5056, 'gens': [[-9, 8, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.5618220465126201833609894058', 'prec': 100}], 'lmfdb_label': '5056.h1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.2372987770011245243332194782', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.8648810160869167496670600527531115475', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': [-9]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [1, 0], '7': [1, 0], '11': [3, 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], '79': [2, 0]}, 'iwp0': 0, 'lmfdb_label': '5056.h1'}
• ec_torsion_growth •

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

  
  
  • id: 265096
    {'degree': 3, 'field': [2, -4, -1, 1], 'lmfdb_label': '5056.h1', 'torsion': [2]}
  • id: 265097
    {'degree': 6, 'field': [8, -8, -34, 54, -17, -2, 1], 'lmfdb_label': '5056.h1', 'torsion': [2, 2]}
  • id: 265098
    {'degree': 8, 'field': [-972, 0, 378, 0, -108, 0, 0, 0, 1], 'lmfdb_label': '5056.h1', 'torsion': [3]}
  • id: 265099
    {'degree': 12, 'field': [5056, 0, 7360, 0, -2783, 0, -100, 0, 135, 0, -20, 0, 1], 'lmfdb_label': '5056.h1', '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: 98295
    {'conductor': 5056, 'conductor_valuation': 6, 'discriminant_valuation': 20, 'j_denominator_valuation': 2, 'kodaira_symbol': -14, 'lmfdb_label': '5056.h1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 98296
    {'conductor': 5056, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '5056.h1', 'prime': 79, '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': [[1, 1, 315, 0], [315, 2, 314, 3], [161, 2, 161, 3], [159, 2, 159, 3], [1, 0, 2, 1], [1, 2, 0, 1]], 'adelic_image': '316.2.0.?', 'conductor': 5056, 'lmfdb_label': '5056.h1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 186347
    {'lmfdb_iso': '5056.h', 'p': 5, 'prec': 20, 'unit': 36925729913094, 'val': -1}
  • id: 186348
    {'lmfdb_iso': '5056.h', 'p': 7, 'prec': 20, 'unit': 11052833828556838, 'val': 1}
  • id: 186354
    {'lmfdb_iso': '5056.h', 'p': 11, 'prec': 20, 'unit': 4106433861542555462, 'val': 2}
  • id: 186352
    {'lmfdb_iso': '5056.h', 'p': 13, 'prec': 20, 'unit': 607659100355793068139, 'val': 1}
  • id: 186355
    {'lmfdb_iso': '5056.h', 'p': 17, 'prec': 20, 'unit': 86324988301608170635154, 'val': 1}
  • id: 186356
    {'lmfdb_iso': '5056.h', 'p': 19, 'prec': 20, 'unit': 976313997538887298103148, 'val': 1}
  • id: 186359
    {'lmfdb_iso': '5056.h', 'p': 23, 'prec': 20, 'unit': 36035724384045950755576610, 'val': 1}
  • id: 186363
    {'lmfdb_iso': '5056.h', 'p': 29, 'prec': 20, 'unit': 3541920110139925099609104461, 'val': 1}
  • id: 186349
    {'lmfdb_iso': '5056.h', 'p': 31, 'prec': 20, 'unit': 3270450035268573312331614705, 'val': 1}
  • id: 186364
    {'lmfdb_iso': '5056.h', 'p': 37, 'prec': 20, 'unit': 167612882983457792376546831281, 'val': 1}
  • id: 186350
    {'lmfdb_iso': '5056.h', 'p': 41, 'prec': 20, 'unit': 4291127511205976559006543823520, 'val': 1}
  • id: 186351
    {'lmfdb_iso': '5056.h', 'p': 43, 'prec': 20, 'unit': 5366176753855799449372372579158, 'val': 1}
  • id: 186353
    {'lmfdb_iso': '5056.h', 'p': 47, 'prec': 20, 'unit': 52900823226195709370434273915981, 'val': 1}
  • id: 186357
    {'lmfdb_iso': '5056.h', 'p': 53, 'prec': 20, 'unit': 413541135089790172299248631413153, 'val': 1}
  • id: 186362
    {'lmfdb_iso': '5056.h', 'p': 59, 'prec': 20, 'unit': 168208072182120078187400721389550594, 'val': -1}
  • id: 186346
    {'lmfdb_iso': '5056.h', 'p': 67, 'prec': 20, 'unit': 30434814160250739778552534552616848, 'val': 1}
  • id: 186361
    {'lmfdb_iso': '5056.h', 'p': 71, 'prec': 20, 'unit': 3246556103312177679444010003691255, 'val': 1}
  • id: 186358
    {'lmfdb_iso': '5056.h', 'p': 73, 'prec': 20, 'unit': 180483162608377076467902327137717377, 'val': 1}
  • id: 186345
    {'lmfdb_iso': '5056.h', 'p': 83, 'prec': 20, 'unit': 2843688748063586255473457356887430424, 'val': 1}
  • id: 186360
    {'lmfdb_iso': '5056.h', 'p': 89, 'prec': 20, 'unit': 6639127392058772551594947484151648047, 'val': 1}
  • id: 186344
    {'lmfdb_iso': '5056.h', 'p': 97, 'prec': 20, 'unit': 2621429867800617834857942021088011398083, 'val': -1}