Elliptic curve data - 216384.d1

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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': '216384gw', 'Clabel': '216384gw2', 'Cnumber': 2, 'abc_quality': 1.1220416108192128, 'absD': 705096403118456832, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 184, 'ainvs': [0, -1, 0, -227425, 10587361], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 23], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 216384, 'degree': 3538944, 'elladic_images': ['8.6.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1157159758085802010899389152', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 3, 'isogeny_degrees': [1, 2], 'jinv': [42180533641, 22862322], 'lmfdb_iso': '216384.d', 'lmfdb_label': '216384.d1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -72, -90], 'min_quad_twist_disc': -56, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.b.1', '92.6.0.?', '184.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 5, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.0091496141959770976770876360', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.10304013044100558441141436129', 'prec': 103}, 'szpiro_ratio': 3.957516254523652, '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, 0, -1, 0, -4, 0, 0, 0, 1, 0, -2, 0, 2, 0, 4, 0, -2, 0, -2, 0], 'aplist': [0, -1, -4, 0, -2, 2, -2, -2, 1, 6, 0, -4, 10, 10, 8, 0, 0, -4, -2, 8, 2, -8, -6, -6, 2], 'class_deg': 2, 'class_size': 2, 'conductor': 216384, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '216384.d', 'trace_hash': 489698610414686015}
• 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': '0.014531567141850302755889080405', 'prec': 107}, 'conductor': 216384, 'gens': [[-296, 7203, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.0091496141959770976770876360', 'prec': 100}], 'lmfdb_label': '216384.d1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.24939586504587216295326989607', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.0085888483118882103621117339496208591', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[47, 0, 1]], 'xcoord_integral_points': [-296, 47, 691]}
• lmfdb_label 216384.d1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9434076
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '216384.d1', 'torsion': [2, 2]}
  • id: 9434077
    {'degree': 4, 'field': [392, 0, 21, 0, 1], 'lmfdb_label': '216384.d1', 'torsion': [4]}
  • id: 9434080
    {'degree': 8, 'field': [-9408, 0, -4298, 0, 336, 0, 0, 0, 1], 'lmfdb_label': '216384.d1', 'torsion': [6]}
  • id: 9434078
    {'degree': 8, 'field': [324, 0, -3456, 0, -198, 0, -24, 0, 1], 'lmfdb_label': '216384.d1', 'torsion': [2, 4]}
  • id: 9434079
    {'degree': 8, 'field': [3364, 0, -76, 0, 533, 0, 32, 0, 1], 'lmfdb_label': '216384.d1', 'torsion': [2, 4]}
  • id: 9434081
    {'degree': 16, 'field': [12960000, 0, 17994600, 0, 12580012, 0, 1993662, 0, -59623, 0, -16992, 0, 830, 0, 66, 0, 1], 'lmfdb_label': '216384.d1', 'torsion': [8]}
  • id: 9434082
    {'degree': 16, 'field': [61653074, -13706084, 15981805, -4542804, 2223676, 136262, -194873, 164752, -89403, 35986, -11221, 2408, -553, 42, 14, -8, 1], 'lmfdb_label': '216384.d1', 'torsion': [2, 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: 5363350
    {'conductor': 216384, 'conductor_valuation': 6, 'discriminant_valuation': 19, 'j_denominator_valuation': 1, 'kodaira_symbol': -13, 'lmfdb_label': '216384.d1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5363351
    {'conductor': 216384, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '216384.d1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5363352
    {'conductor': 216384, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '216384.d1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5363353
    {'conductor': 216384, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '216384.d1', 'prime': 23, '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: 3046451
    {'adelic_gens': [[2, 1, 91, 0], [1, 2, 2, 5], [25, 162, 160, 23], [3, 4, 8, 11], [181, 4, 180, 5], [1, 4, 0, 1], [97, 4, 10, 9], [1, 0, 4, 1]], 'adelic_image': '184.12.0.?', 'conductor': 216384, 'lmfdb_label': '216384.d1', 'prime': 0}
  • id: 795504
    {'conductor': 216384, 'elladic_image': '8.6.0.6', 'lmfdb_label': '216384.d1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 216384.d does not appear in ec_padic