Elliptic curve data - 163370.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
  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': '163370n', 'Clabel': '163370n1', 'Cnumber': 1, 'abc_quality': 0.8860591221810037, 'absD': 158264687500, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 10540, 'ainvs': [1, 1, 0, -5057, 135001], 'analytic_rank': 2, 'bad_primes': [2, 5, 17, 31], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 163370, 'degree': 186368, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.96338339277858993801558825751', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 4, 'isogeny_degrees': [1], 'jinv': [480232637191, 5312500], 'lmfdb_iso': '163370.e', 'lmfdb_label': '163370.e1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -5057, 135001], 'min_quad_twist_disc': 1, 'modell_images': [], 'modm_images': ['10540.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 4, 'num_int_pts': 18, 'optimality': 1, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '0.29390088012270453430718441729', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 4, 2635], [5, 6, 32674], [7, 2, 32674], [17, 18, 9610], [31, 272, 170]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.10488659165730337653329717637', 'prec': 103}, 'szpiro_ratio': 3.098983842404223, '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, -1, 1, 1, 1, -2, -1, -2, -1, 2, -1, 1, 2, -1, 1, 1, 2, 2, 1], 'aplist': [-1, -1, 1, -2, 2, 1, 1, 2, -5, 3, 0, -4, 0, -8, -3, -1, -8, -14, -9, -9, -16, 4, -6, 6, 14], 'class_deg': 1, 'class_size': 1, 'conductor': 163370, 'isogeny_matrix': [[1]], 'lmfdb_iso': '163370.e', 'trace_hash': 1611001796108424691}
• 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': '0.14561825321970787547374558418', 'prec': 103}, 'conductor': 163370, 'gens': [[-3, 389, 1], [152, 1629, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.18860538407482067566996919985', 'prec': 103}, {'__RealLiteral__': 0, 'data': '1.5649247411682819437499082945', 'prec': 100}], 'lmfdb_label': '163370.e1', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '1.0281828956105658172374490697', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '0.99999999999999999999999999999', 'prec': 103}, 'special_value': {'__RealLiteral__': 0, 'data': '8.4611480225175717624303454712869240737', 'prec': 130}, 'tamagawa_product': 28, 'torsion_generators': [], 'xcoord_integral_points': [-78, -3, 32, 36, 47, 87, 152, 1020, 86952]}
• lmfdb_label 163370.e1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7299493
    {'degree': 3, 'field': [-4, -22, 0, 1], 'lmfdb_label': '163370.e1', 'torsion': [2]}
  • id: 7299494
    {'degree': 6, 'field': [-544, -2992, 438, 526, -117, -2, 1], 'lmfdb_label': '163370.e1', 'torsion': [2, 2]}
  • id: 7299495
    {'degree': 8, 'field': [1464768, -160611, 82430, -40455, -13443, -2945, -177, 0, 1], 'lmfdb_label': '163370.e1', 'torsion': [3]}
  • id: 7299496
    {'degree': 12, 'field': [10128940, 0, 2859936, 0, -1114760, 0, -19220, 0, -465, 0, 0, 0, 1], 'lmfdb_label': '163370.e1', '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: 4044518
    {'conductor': 163370, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '163370.e1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4044519
    {'conductor': 163370, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '163370.e1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 7}
  • id: 4044520
    {'conductor': 163370, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '163370.e1', 'prime': 17, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 4044521
    {'conductor': 163370, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '163370.e1', 'prime': 31, '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': [[1, 0, 2, 1], [1, 2, 0, 1], [1, 1, 10539, 0], [10539, 2, 10538, 3], [4217, 2, 4217, 3], [9861, 2, 9861, 3], [5271, 2, 5271, 3], [8061, 2, 8061, 3]], 'adelic_image': '10540.2.0.?', 'conductor': 163370, 'lmfdb_label': '163370.e1', 'prime': 0}
• lmfdb_iso 163370.e does not appear in ec_padic