Elliptic curve data - 250050.bt2

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '250050bt', 'Clabel': '250050bt2', 'Cnumber': 2, 'abc_quality': 0.8728527956422452, 'absD': 3126250125000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 40008, 'ainvs': [1, 0, 0, -1538, -88308], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 1667], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 250050, 'degree': 393216, 'elladic_images': ['8.6.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0804854721253855880450441985', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 45, 'isogeny_degrees': [1, 2], 'jinv': [-25750777177, 200080008], 'lmfdb_iso': '250050.bt', 'lmfdb_label': '250050.bt2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -61, -731], 'min_quad_twist_disc': 5, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.a.1', '20004.6.0.?', '40008.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '9.0228033840058374917260431170', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.27576651590833540074466453189', 'prec': 103}, 'szpiro_ratio': 2.920282990977792, '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, 1, 1, 0, 1, 2, 1, 1, 0, 0, 1, 2, 2, 0, 1, -6, 1, 4, 0], 'aplist': [1, 1, 0, 2, 0, 2, -6, 4, -2, 2, 8, 0, 6, -4, -2, 4, -4, -6, 0, -10, -14, 2, 12, -6, -2], 'class_deg': 2, 'class_size': 2, 'conductor': 250050, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '250050.bt', 'trace_hash': 1309452066753226248}
• 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': '0.11521320111761532800308517210', 'prec': 103}, 'conductor': 250050, 'gens': [[63322, 15630326, 9]], 'heights': [{'__RealLiteral__': 0, 'data': '9.0228033840058374917260431170', 'prec': 100}], 'lmfdb_label': '250050.bt2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.33637054945266180863029018643', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '18.210031991288279250097543136515663945', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [[223, -223, 2]], 'xcoord_integral_points': []}
• lmfdb_label 250050.bt2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 10763558
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '250050.bt2', 'torsion': [2, 2]}
  • id: 10763559
    {'degree': 4, 'field': [-3200, 0, -335, 0, 1], 'lmfdb_label': '250050.bt2', 'torsion': [4]}
  • id: 10763562
    {'degree': 8, 'field': [-7500, 0, 8375, 0, 300, 0, 0, 0, 1], 'lmfdb_label': '250050.bt2', 'torsion': [6]}
  • id: 10763560
    {'degree': 8, 'field': [506944, 0, -17024, 0, 1010, 0, -32, 0, 1], 'lmfdb_label': '250050.bt2', 'torsion': [2, 4]}
  • id: 10763561
    {'degree': 8, 'field': [6380676, 0, 2672412, 0, 104509, 0, -662, 0, 1], 'lmfdb_label': '250050.bt2', 'torsion': [2, 4]}
  • id: 10763564
    {'degree': 16, 'field': [530565156, 0, 198524124, 0, 75365217, 0, 5514392, 0, -400180, 0, 14798, 0, 712, 0, 16, 0, 1], 'lmfdb_label': '250050.bt2', 'torsion': [2, 6]}
  • id: 10763563
    {'degree': 16, 'field': [27779470248001536, 0, -2041890934118400, 0, 24620191825668, 0, 73921272, 0, 1740947008, 0, -4996792, 0, 36189, 0, 542, 0, 1], 'lmfdb_label': '250050.bt2', '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: 6200723
    {'conductor': 250050, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '250050.bt2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 6200724
    {'conductor': 250050, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '250050.bt2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 6200725
    {'conductor': 250050, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '250050.bt2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6200726
    {'conductor': 250050, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '250050.bt2', 'prime': 1667, '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: 3251469
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [15004, 25009, 5001, 35008], [1, 2, 2, 5], [1, 4, 0, 1], [13337, 4, 26674, 9], [40005, 4, 40004, 5], [2, 1, 20003, 0], [21673, 4, 3338, 9]], 'adelic_image': '40008.12.0.?', 'conductor': 250050, 'lmfdb_label': '250050.bt2', 'prime': 0}
  • id: 902554
    {'conductor': 250050, 'elladic_image': '8.6.0.5', 'lmfdb_label': '250050.bt2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 250050.bt does not appear in ec_padic