Elliptic curve data - 68445.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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '68445k', 'Clabel': '68445k1', 'Cnumber': 1, 'abc_quality': 0.7777818305444921, 'absD': 1425091223205, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 10, 'ainvs': [0, 0, 1, -4563, 103808], 'analytic_rank': 1, 'bad_primes': [3, 5, 13], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 68445, 'degree': 155520, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0592835654349327190744929865', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1], 'jinv': [36864, 5], 'lmfdb_iso': '68445.a', 'lmfdb_label': '68445.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 1, -3, -2], 'min_quad_twist_disc': -39, 'modell_images': [], 'modm_images': ['10.2.0.a.1'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 3, 'num_int_pts': 4, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.4639582210342366133372140467', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1387013538525937251149550984', 'prec': 103}, 'szpiro_ratio': 3.313411134157904, '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, 0, 2, -1, 0, 0, 0, 0, 2, -5, 0, 0, 0, 0, -4, -4, 0, 5, -2], 'aplist': [-2, 0, -1, 0, -5, 0, -4, 5, 6, -5, 9, 10, -7, -2, -2, 8, 1, -2, -6, -1, 8, 12, -6, 9, -14], 'class_deg': 1, 'class_size': 1, 'conductor': 68445, 'isogeny_matrix': [[1]], 'lmfdb_iso': '68445.a', 'trace_hash': 1381321782826190692}
• 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': '0.12020374140476916323255462778', 'prec': 103}, 'conductor': 68445, 'gens': [[52, 84, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.4639582210342366133372140467', 'prec': 100}], 'lmfdb_label': '68445.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.82036460120467988243432375692', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.4019590043581282464200483647568822286', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': [52, 337]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 3, 0], '3': 'a', '5': [3, 0], '7': [1, 1, 0], '11': [1, 0], '13': 'a', '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': '68445.a1'}
• ec_torsion_growth •

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

  
  
  • id: 3256806
    {'degree': 3, 'field': [-14, -12, 0, 1], 'lmfdb_label': '68445.a1', 'torsion': [2]}
  • id: 3256807
    {'degree': 6, 'field': [-20, 0, 36, 0, -12, 0, 1], 'lmfdb_label': '68445.a1', 'torsion': [2, 2]}
  • id: 3256808
    {'degree': 8, 'field': [-285, -402, -13, -135, -120, -14, -3, 0, 1], 'lmfdb_label': '68445.a1', 'torsion': [3]}
  • id: 3256809
    {'degree': 12, 'field': [46786962, 7084116, 17403552, -87564, -975102, 1792740, -404084, 6528, 1362, 34, 12, -6, 1], 'lmfdb_label': '68445.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: 1656356
    {'conductor': 68445, 'conductor_valuation': 4, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '68445.a1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1656357
    {'conductor': 68445, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '68445.a1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1656358
    {'conductor': 68445, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '68445.a1', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
• 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], [9, 2, 8, 3], [1, 0, 2, 1], [7, 2, 7, 3], [1, 1, 9, 0]], 'adelic_image': '10.2.0.?', 'conductor': 68445, 'lmfdb_label': '68445.a1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 3500862
    {'lmfdb_iso': '68445.a', 'p': 11, 'prec': 20, 'unit': 30187112910162577348, 'val': 1}
  • id: 3500863
    {'lmfdb_iso': '68445.a', 'p': 17, 'prec': 20, 'unit': 216885176392504300814766, 'val': 1}
  • id: 3500864
    {'lmfdb_iso': '68445.a', 'p': 19, 'prec': 20, 'unit': 476296792032076240132153, 'val': 1}
  • id: 3500868
    {'lmfdb_iso': '68445.a', 'p': 23, 'prec': 20, 'unit': 64670125972708573500126009, 'val': 1}
  • id: 3500860
    {'lmfdb_iso': '68445.a', 'p': 29, 'prec': 20, 'unit': 5008005498108113012449970132, 'val': 1}
  • id: 3500872
    {'lmfdb_iso': '68445.a', 'p': 31, 'prec': 20, 'unit': 1771379279151466751656522797, 'val': 1}
  • id: 3500856
    {'lmfdb_iso': '68445.a', 'p': 37, 'prec': 20, 'unit': 75447941353715646550042723362, 'val': 1}
  • id: 3500858
    {'lmfdb_iso': '68445.a', 'p': 41, 'prec': 20, 'unit': 1184575403393664401429763404940, 'val': 1}
  • id: 3500859
    {'lmfdb_iso': '68445.a', 'p': 43, 'prec': 20, 'unit': 5961923371378025965723938621636, 'val': 1}
  • id: 3500870
    {'lmfdb_iso': '68445.a', 'p': 47, 'prec': 20, 'unit': 56945440503515522052098604035101, 'val': 1}
  • id: 3500865
    {'lmfdb_iso': '68445.a', 'p': 53, 'prec': 20, 'unit': 359394444089983492076174654387446, 'val': 1}
  • id: 3500866
    {'lmfdb_iso': '68445.a', 'p': 59, 'prec': 20, 'unit': 199187800992237698942183220213343666, 'val': 0}
  • id: 3500871
    {'lmfdb_iso': '68445.a', 'p': 61, 'prec': 20, 'unit': 4836136604483761896773927954826926, 'val': 1}
  • id: 3500855
    {'lmfdb_iso': '68445.a', 'p': 67, 'prec': 20, 'unit': 37484006262450780429241083263109180, 'val': 1}
  • id: 3500857
    {'lmfdb_iso': '68445.a', 'p': 71, 'prec': 20, 'unit': 111874497135598112280389149794446627, 'val': 1}
  • id: 3500867
    {'lmfdb_iso': '68445.a', 'p': 73, 'prec': 20, 'unit': 80511245437881326287275253315261241, 'val': 1}
  • id: 3500861
    {'lmfdb_iso': '68445.a', 'p': 79, 'prec': 20, 'unit': 3248018720806551145257296685828635, 'val': 2}
  • id: 3500854
    {'lmfdb_iso': '68445.a', 'p': 83, 'prec': 20, 'unit': 1283555679127625742634245937634011947, 'val': 1}
  • id: 3500869
    {'lmfdb_iso': '68445.a', 'p': 89, 'prec': 20, 'unit': 4962404735084636993602964379353535511, 'val': 1}
  • id: 3500853
    {'lmfdb_iso': '68445.a', 'p': 97, 'prec': 20, 'unit': 54682637957114273209331186338752397404, 'val': 1}