Elliptic curve data - 56144.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': '56144n', 'Clabel': '56144n1', 'Cnumber': 1, 'abc_quality': 1.0288286671023683, 'absD': 21413882874712064, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 58, 'ainvs': [0, 1, 0, -1015109, 393255091], 'analytic_rank': 1, 'bad_primes': [2, 11, 29], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 56144, 'degree': 696960, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1359873217641736026242416710', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1], 'jinv': [131753070592, 24389], 'lmfdb_iso': '56144.a', 'lmfdb_label': '56144.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 1, -524, 4795], 'min_quad_twist_disc': 44, 'modell_images': [], 'modm_images': ['58.2.0.a.1'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.8962841347821558119019166509', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 3509], [3, 2, 1936], [11, 42, 464], [29, 30, 1936]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.15575670732801873616761950244', 'prec': 107}, 'szpiro_ratio': 4.8561358310631935, '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, -2, 0, -2, 0, -1, 0, 1, 0, 0, 0, 7, 0, 4, 0, -2, 0, 0, 0], 'aplist': [0, -2, -2, -1, 0, 7, -2, 0, 1, -1, -4, 6, 10, 0, -8, -3, 7, 12, -8, 3, 4, 10, -9, -6, 2], 'class_deg': 1, 'class_size': 1, 'conductor': 56144, 'isogeny_matrix': [[1]], 'lmfdb_iso': '56144.a', 'trace_hash': 679173275649256367}
• 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': '0.013954201356790119461948985003', 'prec': 107}, 'conductor': 56144, 'gens': [[766, 8107, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.8962841347821558119019166509', 'prec': 100}], 'lmfdb_label': '56144.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.37109816188454018534864142239', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.2244171561390415884444025154434159952', 'prec': 130}, 'tamagawa_product': 3, 'torsion_generators': [], 'xcoord_integral_points': [766]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 0], '5': [5, 0], '7': [1, 0], '11': 'a', '13': [1, 0], '17': [3, 0], '19': [1, 1, 0], '23': [1, 0], '29': [3, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '56144.a1'}
• ec_torsion_growth •

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

  
  
  • id: 2709846
    {'degree': 3, 'field': [-31, -29, -1, 1], 'lmfdb_label': '56144.a1', 'torsion': [2]}
  • id: 2709847
    {'degree': 6, 'field': [-225, -225, 194, 61, -28, -3, 1], 'lmfdb_label': '56144.a1', 'torsion': [2, 2]}
  • id: 2709848
    {'degree': 8, 'field': [-3, 0, -19, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '56144.a1', 'torsion': [3]}
  • id: 2709849
    {'degree': 12, 'field': [12895, 38176, -39104, -10790, 9623, 7568, -5136, 396, 67, 68, -8, -6, 1], 'lmfdb_label': '56144.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: 1349996
    {'conductor': 56144, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '56144.a1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1349997
    {'conductor': 56144, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '56144.a1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
  • id: 1349998
    {'conductor': 56144, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '56144.a1', 'prime': 29, '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, 2, 0, 1], [31, 2, 31, 3], [1, 0, 2, 1], [1, 1, 57, 0], [57, 2, 56, 3]], 'adelic_image': '58.2.0.?', 'conductor': 56144, 'lmfdb_label': '56144.a1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 2843430
    {'lmfdb_iso': '56144.a', 'p': 5, 'prec': 20, 'unit': 2441913716377, 'val': 2}
  • id: 2843431
    {'lmfdb_iso': '56144.a', 'p': 7, 'prec': 20, 'unit': 443986082270292, 'val': 1}
  • id: 2843435
    {'lmfdb_iso': '56144.a', 'p': 13, 'prec': 20, 'unit': 415616010673619347711, 'val': 1}
  • id: 2843437
    {'lmfdb_iso': '56144.a', 'p': 17, 'prec': 20, 'unit': 6460050205018463728497, 'val': 2}
  • id: 2843442
    {'lmfdb_iso': '56144.a', 'p': 23, 'prec': 20, 'unit': 508228582168680580571700889, 'val': -1}
  • id: 2843432
    {'lmfdb_iso': '56144.a', 'p': 31, 'prec': 20, 'unit': 9411079838032598260153613488, 'val': 1}
  • id: 2843446
    {'lmfdb_iso': '56144.a', 'p': 37, 'prec': 20, 'unit': 206309234642757348076995247271, 'val': 1}
  • id: 2843433
    {'lmfdb_iso': '56144.a', 'p': 41, 'prec': 20, 'unit': 1583286763441429184998518813383, 'val': 1}
  • id: 2843444
    {'lmfdb_iso': '56144.a', 'p': 47, 'prec': 20, 'unit': 42270578886498951985063781531041, 'val': 1}
  • id: 2843439
    {'lmfdb_iso': '56144.a', 'p': 53, 'prec': 20, 'unit': 406174632009610732688395795303882, 'val': 1}
  • id: 2843440
    {'lmfdb_iso': '56144.a', 'p': 59, 'prec': 20, 'unit': 3358508909664241717513159308650551, 'val': 1}
  • id: 2843445
    {'lmfdb_iso': '56144.a', 'p': 61, 'prec': 20, 'unit': 7885449784715422072363912349848991, 'val': 1}
  • id: 2843429
    {'lmfdb_iso': '56144.a', 'p': 67, 'prec': 20, 'unit': 41778098568361730432744652813282363, 'val': 1}
  • id: 2843434
    {'lmfdb_iso': '56144.a', 'p': 71, 'prec': 20, 'unit': 76710223490691822041676513326956056, 'val': 1}
  • id: 2843441
    {'lmfdb_iso': '56144.a', 'p': 73, 'prec': 20, 'unit': 200319757648407878876411653815206729, 'val': 1}
  • id: 2843436
    {'lmfdb_iso': '56144.a', 'p': 79, 'prec': 20, 'unit': 819501392028400060834987510930772756, 'val': 1}
  • id: 2843438
    {'lmfdb_iso': '56144.a', 'p': 83, 'prec': 20, 'unit': 2288895142143008736631399470585048844, 'val': 1}
  • id: 2843443
    {'lmfdb_iso': '56144.a', 'p': 89, 'prec': 20, 'unit': 5079541284355457704327828185051287126, 'val': 1}
  • id: 2843428
    {'lmfdb_iso': '56144.a', 'p': 97, 'prec': 20, 'unit': 31453031673586259341092226997203714890, 'val': 1}