Elliptic curve data - 21168.bv2

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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': '21168cx', 'Clabel': '21168cx3', 'Cnumber': 3, 'abc_quality': 1.23864473399791, 'absD': 117099343872, 'ainvs': [0, 0, 0, -23520, 1388464], 'analytic_rank': 0, 'bad_primes': [2, 3, 7], 'class_deg': 27, 'class_size': 4, 'cm': -27, 'conductor': 21168, 'degree': 27216, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1689440431606463155264732250', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'intrinsic_torsion': 1, 'iso_nlabel': 47, 'isogeny_degrees': [1, 3, 9, 27], 'jinv': [-12288000, 1], 'lmfdb_iso': '21168.bv', 'lmfdb_label': '21168.bv2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 1, -30, 63], 'min_quad_twist_disc': 28, 'modell_images': [], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 1323], [3, 8, 56], [7, 26, 432]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.95491333220533468452478745023', 'prec': 107}, 'szpiro_ratio': 4.197744044768404, '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, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, -7, 0], 'aplist': [0, 0, 0, 0, 0, -5, 0, -7, 0, 0, -4, 11, 0, -8, 0, 0, 0, 1, -5, 0, 7, -17, 0, 0, 19], 'class_deg': 27, 'class_size': 4, 'conductor': 21168, 'isogeny_matrix': [[1, 27, 3, 9], [27, 1, 9, 3], [3, 9, 1, 3], [9, 3, 3, 1]], 'lmfdb_iso': '21168.bv', 'trace_hash': 501869113937929739}
• 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': '0.096531288857889221914836940719', 'prec': 107}, 'conductor': 21168, 'gens': [], 'heights': [], 'lmfdb_label': '21168.bv2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.0015900263739798047581918017', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.0015900263739798047581918016907099415', 'prec': 130}, 'tamagawa_product': 1, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [0, 0, 0], '7': 'a', '11': [0, 0, 0], '13': [0, 0], '17': [0, 0, 0], '19': [0, 0], '23': [0, 0, 0], '29': [0, 0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0, 0], '43': [0, 0], '47': [0, 0, 0]}, 'iwp0': 0, 'lmfdb_label': '21168.bv2'}
• ec_torsion_growth •

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

  
  
  • id: 1077256
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '21168.bv2', 'torsion': [3]}
  • id: 1077257
    {'degree': 3, 'field': [-2, 0, 0, 1], 'lmfdb_label': '21168.bv2', 'torsion': [2]}
  • id: 1077260
    {'degree': 6, 'field': [-111, -36, 156, -2, -27, 0, 1], 'lmfdb_label': '21168.bv2', 'torsion': [9]}
  • id: 1077261
    {'degree': 6, 'field': [-54, 0, 0, -22, 0, 0, 1], 'lmfdb_label': '21168.bv2', 'torsion': [6]}
  • id: 1077258
    {'degree': 6, 'field': [1, -3, 0, 5, 0, -3, 1], 'lmfdb_label': '21168.bv2', 'torsion': [2, 2]}
  • id: 1077259
    {'degree': 6, 'field': [1029, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '21168.bv2', 'torsion': [3]}
  • id: 1077262
    {'degree': 12, 'field': [-479, -36, 1488, 538, -285, -1704, -852, -228, 69, 16, 12, -6, 1], 'lmfdb_label': '21168.bv2', 'torsion': [4]}
  • id: 1077265
    {'degree': 12, 'field': [1029, 0, 2205, 0, 1596, 0, 195, 0, -51, 0, -6, 0, 1], 'lmfdb_label': '21168.bv2', 'torsion': [7]}
  • id: 1077266
    {'degree': 12, 'field': [16041, -7272, 9885, -5568, 3714, -1332, 823, -366, 150, -50, 21, -6, 1], 'lmfdb_label': '21168.bv2', 'torsion': [2, 6]}
  • id: 1077264
    {'degree': 12, 'field': [116629, 42840, -95109, -16482, 36456, 1764, -6845, 0, 735, -6, -42, 0, 1], 'lmfdb_label': '21168.bv2', 'torsion': [9]}
  • id: 1077263
    {'degree': 12, 'field': [119716, 0, -96432, 0, 36645, 0, -6854, 0, 735, 0, -42, 0, 1], 'lmfdb_label': '21168.bv2', 'torsion': [3, 3]}
  • id: 1077267
    {'degree': 18, 'field': [-1330671, -11988, 6097788, -30474, -9569043, -9756, 6651561, -486, -2308842, -2, 431892, 0, -45297, 0, 2655, 0, -81, 0, 1], 'lmfdb_label': '21168.bv2', 'torsion': [27]}
  • id: 1077269
    {'degree': 18, 'field': [-873199, 495768, 1328724, -593142, -805155, 609618, -87129, -72600, 80379, -44766, 8850, 3558, -2952, 1056, -189, -24, 21, -6, 1], 'lmfdb_label': '21168.bv2', 'torsion': [18]}
  • id: 1077268
    {'degree': 18, 'field': [24137569, 0, 0, -4520262, 0, 0, 775779, 0, 0, -58466, 0, 0, 2253, 0, 0, -60, 0, 0, 1], 'lmfdb_label': '21168.bv2', '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: 481615
    {'conductor': 21168, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '21168.bv2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 481616
    {'conductor': 21168, 'conductor_valuation': 3, 'discriminant_valuation': 5, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '21168.bv2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 481617
    {'conductor': 21168, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '21168.bv2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
• lmfdb_label 21168.bv2 does not appear in ec_galrep
• lmfdb_iso 21168.bv does not appear in ec_padic