Elliptic curve data - 51714.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': '51714j', 'Clabel': '51714j1', 'Cnumber': 1, 'abc_quality': 0.9154342309315725, 'absD': 2587993811290368, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 68, 'ainvs': [1, -1, 0, 34191, 254749], 'analytic_rank': 1, 'bad_primes': [2, 3, 13, 17], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 51714, 'degree': 449280, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6468784334206745398315887711', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1], 'jinv': [7433231, 4352], 'lmfdb_iso': '51714.a', 'lmfdb_label': '51714.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 23, 5], 'min_quad_twist_disc': -39, 'modell_images': [], 'modm_images': ['68.2.0.a.1'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.0251856304663701009382535670', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.61239394922107146323502547507', 'prec': 107}, 'szpiro_ratio': 3.9556644204691813, '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, -4, 0, -1, -1, 0, 4, -4, 0, 0, 1, 0, 1, 1, 0, 2, -4], 'aplist': [-1, 0, -4, -1, -4, 0, 1, 2, 7, -10, -5, 2, 2, 6, 4, -11, 0, 6, 8, -12, 2, -1, 0, -1, -12], 'class_deg': 1, 'class_size': 1, 'conductor': 51714, 'isogeny_matrix': [[1]], 'lmfdb_iso': '51714.a', 'trace_hash': 624333790150648504}
• 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': '0.037114154217105039936707485591', 'prec': 107}, 'conductor': 51714, 'gens': [[66, 1639, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '4.0251856304663701009382535670', 'prec': 100}], 'lmfdb_label': '51714.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.27635230127478246855380250377', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.2247386240751350488774633595281325260', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': [66]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 0], '3': 'a', '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': 'a', '17': [2, 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': '51714.a1'}
• ec_torsion_growth •

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

  
  
  • id: 2504544
    {'degree': 3, 'field': [-40, -4, -1, 1], 'lmfdb_label': '51714.a1', 'torsion': [2]}
  • id: 2504545
    {'degree': 6, 'field': [272, 0, 120, 0, 49, 0, 1], 'lmfdb_label': '51714.a1', 'torsion': [2, 2]}
  • id: 2504546
    {'degree': 8, 'field': [-34, 85, -136, 95, -29, -25, 13, -4, 1], 'lmfdb_label': '51714.a1', 'torsion': [3]}
  • id: 2504547
    {'degree': 12, 'field': [412192, 527104, 116030, -45474, 25781, 2796, -11886, 168, 990, -52, -8, -6, 1], 'lmfdb_label': '51714.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: 1237684
    {'conductor': 51714, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '51714.a1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1237685
    {'conductor': 51714, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '51714.a1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 1237686
    {'conductor': 51714, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '51714.a1', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1237687
    {'conductor': 51714, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '51714.a1', 'prime': 17, '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], [1, 0, 2, 1], [35, 2, 35, 3], [1, 1, 67, 0], [67, 2, 66, 3], [37, 2, 37, 3]], 'adelic_image': '68.2.0.?', 'conductor': 51714, 'lmfdb_label': '51714.a1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 2602457
    {'lmfdb_iso': '51714.a', 'p': 5, 'prec': 20, 'unit': 10403398317926, 'val': -1}
  • id: 2602458
    {'lmfdb_iso': '51714.a', 'p': 7, 'prec': 20, 'unit': 5855440634256214, 'val': 1}
  • id: 2602464
    {'lmfdb_iso': '51714.a', 'p': 11, 'prec': 20, 'unit': 8955625039810325012, 'val': 1}
  • id: 2602465
    {'lmfdb_iso': '51714.a', 'p': 19, 'prec': 20, 'unit': 1785337724780346143823156, 'val': 1}
  • id: 2602468
    {'lmfdb_iso': '51714.a', 'p': 23, 'prec': 20, 'unit': 981358902892991685385968, 'val': 1}
  • id: 2602462
    {'lmfdb_iso': '51714.a', 'p': 29, 'prec': 20, 'unit': 2437077160290095262050188953, 'val': 1}
  • id: 2602459
    {'lmfdb_iso': '51714.a', 'p': 31, 'prec': 20, 'unit': 8793216953439420308034627933, 'val': 1}
  • id: 2602473
    {'lmfdb_iso': '51714.a', 'p': 37, 'prec': 20, 'unit': 97380976058260102717956090608, 'val': 1}
  • id: 2602460
    {'lmfdb_iso': '51714.a', 'p': 41, 'prec': 20, 'unit': 1472360979306062809412244512073, 'val': 1}
  • id: 2602461
    {'lmfdb_iso': '51714.a', 'p': 43, 'prec': 20, 'unit': 9258386512449093568153176191926, 'val': 1}
  • id: 2602463
    {'lmfdb_iso': '51714.a', 'p': 47, 'prec': 20, 'unit': 1379290889694496690991560814705, 'val': 1}
  • id: 2602466
    {'lmfdb_iso': '51714.a', 'p': 53, 'prec': 20, 'unit': 412691752145324821834917444671102, 'val': 1}
  • id: 2602472
    {'lmfdb_iso': '51714.a', 'p': 61, 'prec': 20, 'unit': 6749341351655819191116642409939992, 'val': 1}
  • id: 2602456
    {'lmfdb_iso': '51714.a', 'p': 67, 'prec': 20, 'unit': 10297465215289222685929584625615365, 'val': 1}
  • id: 2602470
    {'lmfdb_iso': '51714.a', 'p': 71, 'prec': 20, 'unit': 134285052934647657461089386188329915, 'val': 1}
  • id: 2602467
    {'lmfdb_iso': '51714.a', 'p': 73, 'prec': 20, 'unit': 66437896723634418810154142038580693, 'val': 1}
  • id: 2602471
    {'lmfdb_iso': '51714.a', 'p': 79, 'prec': 20, 'unit': 319128904883489234014010760004795980, 'val': 1}
  • id: 2602469
    {'lmfdb_iso': '51714.a', 'p': 89, 'prec': 20, 'unit': 4914006002585700303028719681795465190, 'val': 1}
  • id: 2602455
    {'lmfdb_iso': '51714.a', 'p': 97, 'prec': 20, 'unit': 14607578242125388906094052228583886976, 'val': 1}