Elliptic curve data - 216225.y2

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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': '216225bk', 'Clabel': '216225bk2', 'Cnumber': 2, 'absD': 10082964732901941301875, 'ainvs': [0, 0, 1, 0, 4831169231], 'analytic_rank': 1, 'bad_primes': [3, 5, 31], 'class_deg': 3, 'class_size': 2, 'cm': -3, 'conductor': 216225, 'degree': 7298640, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.9009770959553663500311214467', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 24, 'isogeny_degrees': [1, 3], 'jinv': [0, 1], 'lmfdb_iso': '216225.y', 'lmfdb_label': '216225.y2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 1, 0, 6006], 'min_quad_twist_disc': 93, 'modell_images': [], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '24.631128526905221162944330127', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 72075], [3, 2, 24025], [5, 14, 8649], [31, 212, 225]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.3211174284280379149898691959', 'prec': 103}, 'szpiro_ratio': 4.731317183862617, '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, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, -5, 0, 0, 4, 0, 0, 8, 0], 'aplist': [0, 0, 0, -1, 0, -5, 0, 8, 0, 0, 0, 1, 0, -5, 0, 0, 0, 1, 11, 0, 7, 4, 0, 0, 5], 'class_deg': 3, 'class_size': 2, 'conductor': 216225, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '216225.y', 'trace_hash': 2250396062721406429}
• 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': '0.0030216440995322452158600650064', 'prec': 110}, 'conductor': 216225, 'gens': [[217016883321, 102223821064433971, 6016]], 'heights': [{'__RealLiteral__': 0, 'data': '24.631128526905221162944330127', 'prec': 100}], 'lmfdb_label': '216225.y2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.10230973661172780446713246103', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.0400085440745764990278658854181551262', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 216225.y2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9426153
    {'degree': 2, 'field': [-23, -1, 1], 'lmfdb_label': '216225.y2', 'torsion': [3]}
  • id: 9426154
    {'degree': 3, 'field': [-620, 0, 0, 1], 'lmfdb_label': '216225.y2', 'torsion': [2]}
  • id: 9426157
    {'degree': 6, 'field': [-2309, -533, 526, 13, -4, -3, 1], 'lmfdb_label': '216225.y2', 'torsion': [6]}
  • id: 9426155
    {'degree': 6, 'field': [14283, 0, -413, 0, 1, 0, 1], 'lmfdb_label': '216225.y2', 'torsion': [2, 2]}
  • id: 9426156
    {'degree': 6, 'field': [19375, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '216225.y2', 'torsion': [3]}
  • id: 9426158
    {'degree': 12, 'field': [-2293215947, 654229234, 305398440, -74611054, -20914721, 4261152, 501832, -80628, -5025, 502, 16, -6, 1], 'lmfdb_label': '216225.y2', 'torsion': [4]}
  • id: 9426161
    {'degree': 12, 'field': [5331481, 1230697, 1498623, -220324, 274369, 9501, -3944, 2571, -471, -14, 13, -3, 1], 'lmfdb_label': '216225.y2', 'torsion': [2, 6]}
  • id: 9426160
    {'degree': 12, 'field': [99830827, -37656354, 41043897, -5124958, 5386920, -24816, 98418, 8988, -2703, 110, -18, -3, 1], 'lmfdb_label': '216225.y2', 'torsion': [7]}
  • id: 9426159
    {'degree': 12, 'field': [375429376, -116256, -290604, 774950, -290535, -116376, 38891, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '216225.y2', 'torsion': [3, 3]}
  • id: 9426162
    {'degree': 18, 'field': [1404928, 84747264, 13208832, -33986274816, -5204092080, -6816133872, 1659720921, -4256427, -49127742, -6445973, -10472118, 1704726, -163095, -36249, 9144, -240, -141, 0, 1], 'lmfdb_label': '216225.y2', 'torsion': [9]}
  • id: 9426163
    {'degree': 18, 'field': [20777573564, -30549572724, 6184732542, 2495557827, 286839993, 1013426874, 46681548, 64553169, 18440355, 49433, 1628685, -64059, 32163, 4221, -753, 114, 6, -9, 1], 'lmfdb_label': '216225.y2', 'torsion': [6]}
• 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: 5358602
    {'conductor': 216225, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '216225.y2', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5358603
    {'conductor': 216225, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '216225.y2', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 5358604
    {'conductor': 216225, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '216225.y2', 'prime': 31, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
• lmfdb_label 216225.y2 does not appear in ec_galrep
• lmfdb_iso 216225.y does not appear in ec_padic