Elliptic curve data - 86700.x1

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '86700bb', 'Clabel': '86700bb1', 'Cnumber': 1, 'abc_quality': 1.1322361776649692, 'absD': 205955750566804500000000, 'adelic_genus': 0, 'adelic_index': 30, 'adelic_level': 10, 'ainvs': [0, -1, 0, -568270333, -5213879671463], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 17], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 86700, 'degree': 19094400, 'elladic_images': ['5.5.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.6320505108401406113573524738', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 23, 'isogeny_degrees': [1], 'jinv': [5818717724672, 59049], 'lmfdb_iso': '86700.x', 'lmfdb_label': '86700.x1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -78653, -8464023], 'min_quad_twist_disc': 85, 'modell_images': ['5S4'], 'modm_images': ['5.5.0.a.1', '10.30.0.a.1'], 'nonmax_primes': [5], 'nonmax_rad': 5, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 1445], [3, 4, 28900], [5, 14, 1156], [17, 114, 300]], 'sha': 9, 'sha_primes': [3], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.074065060103791070628938480993', 'prec': 107}, 'szpiro_ratio': 6.340070389915232, '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, 2, 0, 1, 0, 1, 0, 4, 0, 0, 0, 0, 0, 7, 0], 'aplist': [0, -1, 0, 2, 1, 4, 0, 7, 6, 3, 0, 0, -1, -4, 0, 0, 3, 9, 10, 1, 10, -3, 0, 3, -8], 'class_deg': 1, 'class_size': 1, 'conductor': 86700, 'isogeny_matrix': [[1]], 'lmfdb_iso': '86700.x', 'trace_hash': 68676963726131079}
• 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': '0.00070023047880328424895759770071', 'prec': 113}, 'conductor': 86700, 'gens': [], 'heights': [], 'lmfdb_label': '86700.x1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.030921537003020310254866934418', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '9.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.3395259963261935075256289171952838102', 'prec': 130}, 'tamagawa_product': 12, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [6, 0], '5': 'a', '7': [0, 0], '11': [2, 0], '13': [0, 0], '17': 'a', '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0, 0], '37': [0, 0, 0], '41': [0, 0], '43': [0, 0], '47': [0, 0, 0]}, 'iwp0': 0, 'lmfdb_label': '86700.x1'}
• ec_torsion_growth •

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

  
  
  • id: 4061870
    {'degree': 3, 'field': [5, -11, -1, 1], 'lmfdb_label': '86700.x1', 'torsion': [2]}
  • id: 4061871
    {'degree': 6, 'field': [-125, -25, 130, 15, -26, -1, 1], 'lmfdb_label': '86700.x1', 'torsion': [2, 2]}
  • id: 4061872
    {'degree': 8, 'field': [-274, 124, -178, 107, -50, -7, 7, -4, 1], 'lmfdb_label': '86700.x1', 'torsion': [3]}
  • id: 4061873
    {'degree': 12, 'field': [59991, -60920, -8294, 34646, -12579, -2188, -68, 548, -11, -20, 6, -6, 1], 'lmfdb_label': '86700.x1', '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: 2116295
    {'conductor': 86700, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '86700.x1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 2116296
    {'conductor': 86700, 'conductor_valuation': 1, 'discriminant_valuation': 10, 'j_denominator_valuation': 10, 'kodaira_symbol': 14, 'lmfdb_label': '86700.x1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2116297
    {'conductor': 86700, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '86700.x1', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 2116298
    {'conductor': 86700, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '86700.x1', 'prime': 17, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
• ec_galrep •

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

  
  
  • id: 2235153
    {'adelic_gens': [[3, 1, 3, 8], [7, 0, 0, 7], [9, 4, 2, 1], [9, 0, 0, 9], [3, 0, 4, 7], [6, 7, 5, 2]], 'adelic_image': '10.30.0.?', 'conductor': 86700, 'lmfdb_label': '86700.x1', 'prime': 0}
  • id: 353395
    {'conductor': 86700, 'elladic_image': '5.5.0.1', 'lmfdb_label': '86700.x1', 'modell_image': '5S4', 'prime': 5}
• lmfdb_iso 86700.x does not appear in ec_padic