Elliptic curve data - 165825.be1

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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': '165825bb', 'Clabel': '165825bb2', 'Cnumber': 2, 'abc_quality': 0.8461141554463657, 'absD': 25310595234375, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 44220, 'ainvs': [1, -1, 0, -66942, 6678841], 'analytic_rank': 0, 'bad_primes': [3, 5, 11, 67], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 165825, 'degree': 466944, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5041375420178808710362266642', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 30, 'isogeny_degrees': [1, 2], 'jinv': [2912566550041, 2222055], 'lmfdb_iso': '165825.be', 'lmfdb_label': '165825.be1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -298, -1999], 'min_quad_twist_disc': -15, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '220.6.0.?', '804.6.0.?', '44220.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 2475], [3, 8, 18425], [5, 18, 6633], [11, 12, 15075], [67, 68, 2475]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.15011244146677583803822437913', 'prec': 103}, 'szpiro_ratio': 3.7398720966861827, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
• 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, 0, 0, -2, -3, 0, 0, 1, 0, 2, -2, 0, -1, 2, 0, -4, 0], 'aplist': [1, 0, 0, -2, 1, 2, 2, -4, 0, 4, 2, 10, 6, -10, 0, 6, 6, -12, 1, 14, 6, 0, 14, 2, -16], 'class_deg': 2, 'class_size': 2, 'conductor': 165825, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '165825.be', 'trace_hash': 722496054681888485}
• 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': '0.049376776135871431739846590384', 'prec': 107}, 'conductor': 165825, 'gens': [], 'heights': [], 'lmfdb_label': '165825.be1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.66540836021154562209509772876', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.6616334408461824883803909150398446713', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[611, -611, 2]], 'xcoord_integral_points': []}
• lmfdb_label 165825.be1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7396842
    {'degree': 2, 'field': [-55, 0, 1], 'lmfdb_label': '165825.be1', 'torsion': [2, 2]}
  • id: 7396843
    {'degree': 4, 'field': [55, 0, -32, 0, 1], 'lmfdb_label': '165825.be1', 'torsion': [4]}
  • id: 7396845
    {'degree': 8, 'field': [-143391, -332532, -134720, 13028, 11102, 308, -208, -4, 1], 'lmfdb_label': '165825.be1', 'torsion': [2, 4]}
  • id: 7396846
    {'degree': 8, 'field': [-855, 236520, -37386, 32847, -3060, 825, -110, -3, 1], 'lmfdb_label': '165825.be1', 'torsion': [6]}
  • id: 7396844
    {'degree': 8, 'field': [123859681, 35726108, 4255856, 193644, -20206, -3348, -16, -4, 1], 'lmfdb_label': '165825.be1', 'torsion': [2, 4]}
  • id: 7396848
    {'degree': 16, 'field': [-478728579657275, 28871985221100, 208028403825, -7149366670320, 1184102068516, 324467393616, -53443199546, -7407867720, 1246172730, 102546906, -17230004, -877896, 142765, 4620, -651, -6, 1], 'lmfdb_label': '165825.be1', 'torsion': [2, 6]}
  • id: 7396847
    {'degree': 16, 'field': [11454891107625625, 0, -1988350014311375, 0, 59644290704350, 0, -172712946725, 0, -4976595470, 0, 12938035, 0, 105934, 0, -119, 0, 1], 'lmfdb_label': '165825.be1', 'torsion': [8]}
• 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: 4105696
    {'conductor': 165825, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '165825.be1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4105697
    {'conductor': 165825, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '165825.be1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4105698
    {'conductor': 165825, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '165825.be1', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 4105699
    {'conductor': 165825, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '165825.be1', 'prime': 67, 'reduction_type': 1, '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

  
  
  • id: 2735784
    {'adelic_gens': [[44217, 4, 44216, 5], [1, 2, 2, 5], [1, 4, 0, 1], [11056, 33169, 33165, 11056], [13201, 4, 26402, 9], [14741, 4, 29482, 9], [1, 0, 4, 1], [3, 4, 8, 11], [26534, 1, 8843, 0], [28142, 1, 8039, 0]], 'adelic_image': '44220.12.0.?', 'conductor': 165825, 'lmfdb_label': '165825.be1', 'prime': 0}
  • id: 628987
    {'conductor': 165825, 'elladic_image': '2.3.0.1', 'lmfdb_label': '165825.be1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 165825.be does not appear in ec_padic