Elliptic curve data - 54720.cf1

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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': '54720t', 'Clabel': '54720t4', 'Cnumber': 4, 'abc_quality': 1.0531544430296054, 'absD': 720030384000000000000000000, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 2280, 'ainvs': [0, 0, 0, -266821068, -1071201902992], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 19], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 54720, 'degree': 26542080, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.8553863362595932956628848657', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 6, 'iso_nlabel': 57, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [10993009831928446009969, 3767761230468750000], 'lmfdb_iso': '54720.cf', 'lmfdb_label': '54720.cf1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -463231, 77449961], 'min_quad_twist_disc': -24, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '24.24.0-6.a.1.11', '60.24.0.t.1', '76.6.0.?', '120.48.0.?', '228.24.0.?', '456.48.0.?', '1140.48.1.?', '2280.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 25, 'sha_primes': [5], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.2663594210856204858394140651', 'prec': 100}, 'szpiro_ratio': 6.399630467051713, '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, 0, 0, -1, 0, 2, 0, 0, 0, 6, 0, 4, 0, 0, 0, 6, 0, -1, 0], 'aplist': [0, 0, -1, 2, 6, 4, 6, -1, 0, 0, 8, -8, 12, -2, 0, -6, -12, -2, 16, 0, -10, 8, 0, 12, 8], 'class_deg': 6, 'class_size': 4, 'conductor': 54720, 'isogeny_matrix': [[1, 3, 6, 2], [3, 1, 2, 6], [6, 2, 1, 3], [2, 6, 3, 1]], 'lmfdb_iso': '54720.cf', 'trace_hash': 1775890224888868236}
• 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': '0.00044797520524364949945576842566', 'prec': 113}, 'conductor': 54720, 'gens': [], 'heights': [], 'lmfdb_label': '54720.cf1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.038395847824297820471994154129', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '25.000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.8395847824297820471994154129058905381', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-4316, 0, 1]], 'xcoord_integral_points': [-4316]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [2, 0], '19': [0, 0]}, 'iwp0': 7, 'lmfdb_label': '54720.cf1'}
• ec_torsion_growth •

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

  
  
  • id: 2644374
    {'degree': 2, 'field': [-19, 0, 1], 'lmfdb_label': '54720.cf1', 'torsion': [2, 2]}
  • id: 2644375
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '54720.cf1', 'torsion': [6]}
  • id: 2644377
    {'degree': 4, 'field': [81, 0, -20, 0, 1], 'lmfdb_label': '54720.cf1', 'torsion': [2, 6]}
  • id: 2644376
    {'degree': 4, 'field': [304, 0, 34, 0, 1], 'lmfdb_label': '54720.cf1', 'torsion': [4]}
  • id: 2644378
    {'degree': 6, 'field': [96, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '54720.cf1', 'torsion': [6]}
  • id: 2644381
    {'degree': 8, 'field': [46, -96, 229, -82, 53, 4, -9, -2, 1], 'lmfdb_label': '54720.cf1', 'torsion': [12]}
  • id: 2644379
    {'degree': 8, 'field': [3600, 0, -240, 0, 169, 0, 4, 0, 1], 'lmfdb_label': '54720.cf1', 'torsion': [2, 4]}
  • id: 2644380
    {'degree': 8, 'field': [28900, 0, -12840, 0, 1564, 0, -72, 0, 1], 'lmfdb_label': '54720.cf1', 'torsion': [2, 4]}
  • id: 2644382
    {'degree': 12, 'field': [289, 102, 291, -770, 360, -18, 105, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '54720.cf1', 'torsion': [3, 6]}
  • id: 2644383
    {'degree': 12, 'field': [76527504, 0, 0, 0, 0, 0, 37680, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '54720.cf1', 'torsion': [2, 6]}
  • id: 2644384
    {'degree': 16, 'field': [1296, 0, -39960, 0, 2247129, 0, -453360, 0, 81976, 0, -3760, 0, 84, 0, -10, 0, 1], 'lmfdb_label': '54720.cf1', 'torsion': [8]}
  • id: 2644385
    {'degree': 16, 'field': [65536, 0, 61440, 0, 108304, 0, -60720, 0, 32601, 0, 240, 0, 634, 0, 0, 0, 1], 'lmfdb_label': '54720.cf1', 'torsion': [2, 12]}
  • id: 2644386
    {'degree': 16, 'field': [5701417, 6390896, -3904414, -4491496, 1132134, 1100120, -19574, -208316, -50865, 55708, 998, -5644, 152, 336, -28, -8, 1], 'lmfdb_label': '54720.cf1', 'torsion': [2, 12]}
  • id: 2644387
    {'degree': 18, 'field': [-304946208, 0, 364068432, 0, -77538384, 0, 19372788, 0, -4192560, 0, 519912, 0, -41102, 0, 1872, 0, -48, 0, 1], 'lmfdb_label': '54720.cf1', 'torsion': [18]}
• 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: 1314079
    {'conductor': 54720, 'conductor_valuation': 6, 'discriminant_valuation': 22, 'j_denominator_valuation': 4, 'kodaira_symbol': -16, 'lmfdb_label': '54720.cf1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1314080
    {'conductor': 54720, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '54720.cf1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1314081
    {'conductor': 54720, 'conductor_valuation': 1, 'discriminant_valuation': 18, 'j_denominator_valuation': 18, 'kodaira_symbol': 22, 'lmfdb_label': '54720.cf1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1314082
    {'conductor': 54720, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '54720.cf1', 'prime': 19, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 2027722
    {'adelic_gens': [[1, 6, 6, 37], [2269, 2278, 1190, 1149], [1, 12, 0, 1], [1614, 1223, 1615, 1234], [970, 3, 573, 1132], [457, 12, 462, 73], [1139, 0, 0, 2279], [11, 2, 2230, 2271], [1519, 2268, 1514, 2207], [2269, 12, 2268, 13], [1151, 2268, 1152, 2267], [1, 0, 12, 1]], 'adelic_image': '2280.96.1.?', 'conductor': 54720, 'lmfdb_label': '54720.cf1', 'prime': 0}
  • id: 233323
    {'conductor': 54720, 'elladic_image': '2.3.0.1', 'lmfdb_label': '54720.cf1', 'modell_image': '2B', 'prime': 2}
  • id: 233324
    {'conductor': 54720, 'elladic_image': '3.4.0.1', 'lmfdb_label': '54720.cf1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 54720.cf does not appear in ec_padic