Elliptic curve data - 86700.u1

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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': '86700r', 'Clabel': '86700r1', 'Cnumber': 1, 'abc_quality': 0.9724522688602968, 'absD': 4668330346180902000, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 510, 'ainvs': [0, -1, 0, -2219038, 1277296297], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 17], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 86700, 'degree': 2115072, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4407008804338503597079402307', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 20, 'isogeny_degrees': [1], 'jinv': [-5095042816, 19683], 'lmfdb_iso': '86700.u', 'lmfdb_label': '86700.u1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -7678, 257273], 'min_quad_twist_disc': 17, 'modell_images': [], 'modm_images': ['510.2.0.?'], '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': '2.0519730786041703443977661060', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 255], [3, 4, 28900], [5, 10, 3468], [17, 98, 300]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.31761766590348523060181127316', 'prec': 107}, 'szpiro_ratio': 4.877483697844016, '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, 3, 0, -4, 0, 0, 0, 0, 0, 1, 0], 'aplist': [0, -1, 0, 1, 3, -4, 0, 1, 2, 9, 4, 11, -7, -6, -13, -11, -14, 14, 4, -8, 1, 14, 12, 10, 10], 'class_deg': 1, 'class_size': 1, 'conductor': 86700, 'isogeny_matrix': [[1]], 'lmfdb_iso': '86700.u', 'trace_hash': 1200968241151072902}
• 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': '0.0075863722909298588709121249252', 'prec': 110}, 'conductor': 86700, 'gens': [[771, 4913, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.0519730786041703443977661060', 'prec': 100}], 'lmfdb_label': '86700.u1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.24537833144533519757886968246', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.0421167623836675816167448438919421816', 'prec': 130}, 'tamagawa_product': 12, 'torsion_generators': [], 'xcoord_integral_points': [771]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [3, 0], '5': 'a', '7': [1, 0], '11': [5, 0], '13': [1, 0], '17': 'a', '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': '86700.u1'}
• ec_torsion_growth •

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

  
  
  • id: 4061804
    {'degree': 3, 'field': [-3, 0, -1, 1], 'lmfdb_label': '86700.u1', 'torsion': [2]}
  • id: 4061805
    {'degree': 6, 'field': [81, -27, 48, 21, -2, -2, 1], 'lmfdb_label': '86700.u1', 'torsion': [2, 2]}
  • id: 4061806
    {'degree': 8, 'field': [-9094, -4691, 5042, -703, 355, -7, 7, -4, 1], 'lmfdb_label': '86700.u1', 'torsion': [3]}
  • id: 4061807
    {'degree': 12, 'field': [-262733589, 138724352, -21732052, 3655510, -888096, -62136, 6234, 7238, -229, 118, -46, -4, 1], 'lmfdb_label': '86700.u1', '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: 2116247
    {'conductor': 86700, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '86700.u1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
  • id: 2116248
    {'conductor': 86700, 'conductor_valuation': 1, 'discriminant_valuation': 9, 'j_denominator_valuation': 9, 'kodaira_symbol': 13, 'lmfdb_label': '86700.u1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 2116249
    {'conductor': 86700, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '86700.u1', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2116250
    {'conductor': 86700, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '86700.u1', 'prime': 17, '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': [[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.u1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 4480344
    {'lmfdb_iso': '86700.u', 'p': 7, 'prec': 20, 'unit': 62729704238029636, 'val': -1}
  • id: 4480342
    {'lmfdb_iso': '86700.u', 'p': 11, 'prec': 20, 'unit': 2750865345043964217, 'val': 2}
  • id: 4480348
    {'lmfdb_iso': '86700.u', 'p': 13, 'prec': 20, 'unit': 441824836468061760690, 'val': 1}
  • id: 4480351
    {'lmfdb_iso': '86700.u', 'p': 19, 'prec': 20, 'unit': 1919638543171041815605402, 'val': -1}
  • id: 4480354
    {'lmfdb_iso': '86700.u', 'p': 23, 'prec': 20, 'unit': 46921498141741327211658266, 'val': 1}
  • id: 4480347
    {'lmfdb_iso': '86700.u', 'p': 29, 'prec': 20, 'unit': 4064865225978594754479697393, 'val': 1}
  • id: 4480360
    {'lmfdb_iso': '86700.u', 'p': 31, 'prec': 20, 'unit': 17307622608153936629416199368, 'val': 1}
  • id: 4480343
    {'lmfdb_iso': '86700.u', 'p': 37, 'prec': 20, 'unit': 372106024273168112832399083223, 'val': 1}
  • id: 4480345
    {'lmfdb_iso': '86700.u', 'p': 41, 'prec': 20, 'unit': 1897515572998903580399595995113, 'val': 1}
  • id: 4480346
    {'lmfdb_iso': '86700.u', 'p': 43, 'prec': 20, 'unit': 8374282128138826560001173812772, 'val': 1}
  • id: 4480357
    {'lmfdb_iso': '86700.u', 'p': 47, 'prec': 20, 'unit': 19262917226093227381897995893837, 'val': 1}
  • id: 4480352
    {'lmfdb_iso': '86700.u', 'p': 53, 'prec': 20, 'unit': 351887465278552645227757422946985, 'val': 1}
  • id: 4480350
    {'lmfdb_iso': '86700.u', 'p': 59, 'prec': 20, 'unit': 1381834065247655897771434759499757, 'val': 1}
  • id: 4480358
    {'lmfdb_iso': '86700.u', 'p': 61, 'prec': 20, 'unit': 2574272424622068815695485649060652, 'val': 1}
  • id: 4480341
    {'lmfdb_iso': '86700.u', 'p': 67, 'prec': 20, 'unit': 3395010416620915450825773291876385, 'val': 1}
  • id: 4480356
    {'lmfdb_iso': '86700.u', 'p': 71, 'prec': 20, 'unit': 116871156766252146524297940439708311, 'val': 1}
  • id: 4480353
    {'lmfdb_iso': '86700.u', 'p': 73, 'prec': 20, 'unit': 17182121738633475475781983186781217102, 'val': -1}
  • id: 4480349
    {'lmfdb_iso': '86700.u', 'p': 79, 'prec': 20, 'unit': 752816714668361730265811600066906478, 'val': 1}
  • id: 4480359
    {'lmfdb_iso': '86700.u', 'p': 83, 'prec': 20, 'unit': 2618944010708555343236652862863760015, 'val': 1}
  • id: 4480355
    {'lmfdb_iso': '86700.u', 'p': 89, 'prec': 20, 'unit': 7707952734836841462153869389964521754, 'val': 1}
  • id: 4480340
    {'lmfdb_iso': '86700.u', 'p': 97, 'prec': 20, 'unit': 29104799095625010340253686872599872139, 'val': 1}