Elliptic curve data - 16731.e1

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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': '16731a', 'Clabel': '16731a2', 'Cnumber': 2, 'abc_quality': 0.9632317793377989, 'absD': 55487721345361016283, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 156, 'ainvs': [1, -1, 1, -2735804, 1705120876], 'analytic_rank': 1, 'bad_primes': [3, 11, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 16731, 'degree': 483840, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.5725102633805725744527507562', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2], 'jinv': [23835655373139, 584043889], 'lmfdb_iso': '16731.e', 'lmfdb_label': '16731.e1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -1799, -28284], 'min_quad_twist_disc': -39, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '12.6.0.a.1', '52.6.0.e.1', '156.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.9143148660434873686809265229', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.46607636814872193787957310773', 'prec': 103}, 'szpiro_ratio': 5.766509345774998, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
• 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, 2, 0, 2, 3, 0, -2, -1, 0, 0, -2, 0, -1, 4, 0, -6, -2], 'aplist': [-1, 0, 2, 2, -1, 0, 4, -6, 8, 0, -10, 6, 2, 0, -8, 0, 4, -6, 10, 0, -10, -4, -12, -18, 10], 'class_deg': 2, 'class_size': 2, 'conductor': 16731, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '16731.e', 'trace_hash': 737493821749449583}
• 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': '0.0058283547255343373571989758634', 'prec': 110}, 'conductor': 16731, 'gens': [[-1112, 58619, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '4.9143148660434873686809265229', 'prec': 100}], 'lmfdb_label': '16731.e1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.19830287687657450352952913121', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.8980911032549656006758178156754821069', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[3355, -3359, 2]], 'xcoord_integral_points': [-1112]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 0], '3': 'a', '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': 'a', '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '16731.e1'}
• ec_torsion_growth •

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

  
  
  • id: 857085
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '16731.e1', 'torsion': [2, 2]}
  • id: 857086
    {'degree': 4, 'field': [12, 0, -3, 0, 1], 'lmfdb_label': '16731.e1', 'torsion': [4]}
  • id: 857088
    {'degree': 8, 'field': [1, 0, 1, 0, 12, 0, 1, 0, 1], 'lmfdb_label': '16731.e1', 'torsion': [2, 4]}
  • id: 857089
    {'degree': 8, 'field': [217, 1024, 1015, 327, -33, -24, -2, -2, 1], 'lmfdb_label': '16731.e1', 'torsion': [6]}
  • id: 857087
    {'degree': 8, 'field': [2831998, 264316, -254086, -20288, 9715, 512, -166, -4, 1], 'lmfdb_label': '16731.e1', 'torsion': [2, 4]}
  • id: 857091
    {'degree': 16, 'field': [154449, 0, -325233, 0, -71343, 0, -50409, 0, 2901, 0, 1908, 0, 310, 0, 25, 0, 1], 'lmfdb_label': '16731.e1', 'torsion': [2, 6]}
  • id: 857090
    {'degree': 16, 'field': [273529, 0, 739142, 0, 4644317, 0, -174310, 0, -3668, 0, 3814, 0, 5, 0, -14, 0, 1], 'lmfdb_label': '16731.e1', 'torsion': [8]}
• 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: 372235
    {'conductor': 16731, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '16731.e1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 372236
    {'conductor': 16731, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '16731.e1', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 372237
    {'conductor': 16731, 'conductor_valuation': 2, 'discriminant_valuation': 12, 'j_denominator_valuation': 6, 'kodaira_symbol': -10, 'lmfdb_label': '16731.e1', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 1775468
    {'adelic_gens': [[145, 4, 134, 9], [1, 2, 2, 5], [40, 121, 117, 40], [3, 4, 8, 11], [153, 4, 152, 5], [56, 1, 103, 0], [1, 4, 0, 1], [1, 0, 4, 1]], 'adelic_image': '156.12.0.?', 'conductor': 16731, 'lmfdb_label': '16731.e1', 'prime': 0}
  • id: 78508
    {'conductor': 16731, 'elladic_image': '2.3.0.1', 'lmfdb_label': '16731.e1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 761347
    {'lmfdb_iso': '16731.e', 'p': 5, 'prec': 20, 'unit': 13364380816039, 'val': 1}
  • id: 761348
    {'lmfdb_iso': '16731.e', 'p': 7, 'prec': 20, 'unit': 11297936059550286, 'val': 1}
  • id: 761353
    {'lmfdb_iso': '16731.e', 'p': 17, 'prec': 20, 'unit': 11161933449817210583757, 'val': 1}
  • id: 761344
    {'lmfdb_iso': '16731.e', 'p': 19, 'prec': 20, 'unit': 1888355716057260425087937, 'val': 1}
  • id: 761351
    {'lmfdb_iso': '16731.e', 'p': 23, 'prec': 20, 'unit': 44913994117373288888253183, 'val': 1}
  • id: 761349
    {'lmfdb_iso': '16731.e', 'p': 31, 'prec': 20, 'unit': 17833975803192202220444675961, 'val': 1}
  • id: 761360
    {'lmfdb_iso': '16731.e', 'p': 37, 'prec': 20, 'unit': 100235527554780404797573967853, 'val': 1}
  • id: 761350
    {'lmfdb_iso': '16731.e', 'p': 41, 'prec': 20, 'unit': 2774030982610623407137342021411, 'val': 1}
  • id: 761358
    {'lmfdb_iso': '16731.e', 'p': 47, 'prec': 20, 'unit': 32205570321532493301864358458407, 'val': 1}
  • id: 761355
    {'lmfdb_iso': '16731.e', 'p': 59, 'prec': 20, 'unit': 3821133121936384283880029632301492, 'val': 1}
  • id: 761359
    {'lmfdb_iso': '16731.e', 'p': 61, 'prec': 20, 'unit': 2094843568327813922294984499223270, 'val': 1}
  • id: 761346
    {'lmfdb_iso': '16731.e', 'p': 67, 'prec': 20, 'unit': 19139965226403730654669300750260993, 'val': 1}
  • id: 761356
    {'lmfdb_iso': '16731.e', 'p': 73, 'prec': 20, 'unit': 184747581775071348438151585557714687, 'val': 1}
  • id: 761352
    {'lmfdb_iso': '16731.e', 'p': 79, 'prec': 20, 'unit': 587541185359991696390360636490823592, 'val': 1}
  • id: 761354
    {'lmfdb_iso': '16731.e', 'p': 83, 'prec': 20, 'unit': 1701024105384701726526131938415383606, 'val': 1}
  • id: 761357
    {'lmfdb_iso': '16731.e', 'p': 89, 'prec': 20, 'unit': 1636410093402310970240821764750128206, 'val': 1}
  • id: 761345
    {'lmfdb_iso': '16731.e', 'p': 97, 'prec': 20, 'unit': 42808039716843585856146175641358629686, 'val': 1}