Elliptic curve data - 86700.i1

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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': '86700v', 'Clabel': '86700v1', 'Cnumber': 1, 'abc_quality': 0.8232444987185115, 'absD': 199424595078000, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 510, 'ainvs': [0, -1, 0, -11078, 817977], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 17], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 86700, 'degree': 276480, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4366926481081428331468178680', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 8, 'isogeny_degrees': [1], 'jinv': [-3114752, 4131], 'lmfdb_iso': '86700.i', 'lmfdb_label': '86700.i1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -38, 153], 'min_quad_twist_disc': 17, 'modell_images': [], 'modm_images': ['510.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 4, 'num_int_pts': 4, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.41435374108042253860830380021', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 4335], [3, 4, 28900], [5, 10, 1156], [17, 162, 300]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.61332256221513873710054998140', 'prec': 107}, 'szpiro_ratio': 3.5833355875956214, '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, 0, 0, -1, 0, 1, 0, 5, 0, -4, 0, 0, 0, 0, 0, 1, 0], 'aplist': [0, -1, 0, -1, 5, -4, 0, 1, 0, -9, 6, -3, -5, -2, -9, -3, -6, 0, 14, 8, 7, 6, -12, -6, -2], 'class_deg': 1, 'class_size': 1, 'conductor': 86700, 'isogeny_matrix': [[1]], 'lmfdb_iso': '86700.i', 'trace_hash': 465211022655893412}
• 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': '0.056507308443303969005869025077', 'prec': 107}, 'conductor': 86700, 'gens': [[142, 1445, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.41435374108042253860830380021', 'prec': 103}], 'lmfdb_label': '86700.i1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.50959737865981271999159372105', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.0676859270192819619486771143413045575', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [], 'xcoord_integral_points': [6, 142]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': 'a', '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': 'a', '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '86700.i1'}
• ec_torsion_growth •

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

  
  
  • id: 4061834
    {'degree': 3, 'field': [-3, 0, -1, 1], 'lmfdb_label': '86700.i1', 'torsion': [2]}
  • id: 4061835
    {'degree': 6, 'field': [81, -27, 48, 21, -2, -2, 1], 'lmfdb_label': '86700.i1', 'torsion': [2, 2]}
  • id: 4061836
    {'degree': 8, 'field': [-87584, 56236, 1819, -1938, 459, 204, 1, -2, 1], 'lmfdb_label': '86700.i1', 'torsion': [3]}
  • id: 4061837
    {'degree': 12, 'field': [8551, 43554, -191284, 253980, -120316, 14238, 3392, 3462, -259, -24, -4, 0, 1], 'lmfdb_label': '86700.i1', '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: 2116267
    {'conductor': 86700, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '86700.i1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
  • id: 2116268
    {'conductor': 86700, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '86700.i1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 2116269
    {'conductor': 86700, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '86700.i1', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2116270
    {'conductor': 86700, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '86700.i1', 'prime': 17, '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

  
  {'adelic_gens': [[307, 2, 307, 3], [509, 2, 508, 3], [1, 1, 509, 0], [241, 2, 241, 3], [341, 2, 341, 3], [1, 0, 2, 1], [1, 2, 0, 1]], 'adelic_image': '510.2.0.?', 'conductor': 86700, 'lmfdb_label': '86700.i1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 4480424
    {'lmfdb_iso': '86700.i', 'p': 7, 'prec': 20, 'unit': 11369069979209949, 'val': 1}
  • id: 4480429
    {'lmfdb_iso': '86700.i', 'p': 11, 'prec': 20, 'unit': 21534979826856229057, 'val': 1}
  • id: 4480427
    {'lmfdb_iso': '86700.i', 'p': 13, 'prec': 20, 'unit': 457842650752451288939, 'val': 1}
  • id: 4480431
    {'lmfdb_iso': '86700.i', 'p': 19, 'prec': 20, 'unit': 14858611264644702753905633, 'val': -1}
  • id: 4480437
    {'lmfdb_iso': '86700.i', 'p': 29, 'prec': 20, 'unit': 5562504399936560275860440309, 'val': 1}
  • id: 4480438
    {'lmfdb_iso': '86700.i', 'p': 31, 'prec': 20, 'unit': 11548597273366353439689672773, 'val': 1}
  • id: 4480423
    {'lmfdb_iso': '86700.i', 'p': 37, 'prec': 20, 'unit': 533384869313869104457625669514, 'val': 1}
  • id: 4480425
    {'lmfdb_iso': '86700.i', 'p': 41, 'prec': 20, 'unit': 3131794097172994285390305038889, 'val': 1}
  • id: 4480426
    {'lmfdb_iso': '86700.i', 'p': 43, 'prec': 20, 'unit': 3248772932268015552284736416244, 'val': 1}
  • id: 4480436
    {'lmfdb_iso': '86700.i', 'p': 47, 'prec': 20, 'unit': 2156610674002671596275090902175, 'val': 1}
  • id: 4480432
    {'lmfdb_iso': '86700.i', 'p': 53, 'prec': 20, 'unit': 505318750052509523495798533386934, 'val': 1}
  • id: 4480430
    {'lmfdb_iso': '86700.i', 'p': 59, 'prec': 20, 'unit': 3880109287701203561552156493325314, 'val': 1}
  • id: 4480422
    {'lmfdb_iso': '86700.i', 'p': 67, 'prec': 20, 'unit': 28519369285529336223949341617739453, 'val': 1}
  • id: 4480435
    {'lmfdb_iso': '86700.i', 'p': 71, 'prec': 20, 'unit': 119783262508980378331819124398185847, 'val': 1}
  • id: 4480433
    {'lmfdb_iso': '86700.i', 'p': 73, 'prec': 20, 'unit': 17161328957477046338577444700664220, 'val': 1}
  • id: 4480428
    {'lmfdb_iso': '86700.i', 'p': 79, 'prec': 20, 'unit': 326719364777750430253418516767046955, 'val': 1}
  • id: 4480421
    {'lmfdb_iso': '86700.i', 'p': 83, 'prec': 20, 'unit': 1537532017227659291801194575787803290, 'val': 1}
  • id: 4480434
    {'lmfdb_iso': '86700.i', 'p': 89, 'prec': 20, 'unit': 5797525336495072480877503355153386154, 'val': 1}
  • id: 4480420
    {'lmfdb_iso': '86700.i', 'p': 97, 'prec': 20, 'unit': 3204500695563513707451897700092401156, 'val': 1}