Elliptic curve data - 3648.bf4

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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': '3648bf', 'Clabel': '3648bf4', 'Cnumber': 4, 'abc_quality': 0.9747386105988611, 'absD': 102488604672, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 456, 'ainvs': [0, 1, 0, 543, -14433], 'analytic_rank': 1, 'bad_primes': [2, 3, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 3648, 'degree': 3072, 'elladic_images': ['8.12.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.79471210863709187045641581232', 'prec': 103}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 31, 'isogeny_degrees': [1, 2, 4], 'jinv': [67419143, 390963], 'lmfdb_iso': '3648.bf', 'lmfdb_label': '3648.bf4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 8, 29], 'min_quad_twist_disc': -8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '6.6.0.a.1', '8.12.0-4.c.1.4', '12.12.0.g.1', '24.24.0-12.g.1.1', '152.24.0.?', '456.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '8.4255002443428089193767528379', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 3], [3, 4, 1216], [19, 20, 192]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.24500866220282609366943236987', 'prec': 107}, 'szpiro_ratio': 3.9871821090729087, '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, 2, 0, 0, 0, 1, 0, 0, 0, -6, 0, 2, 0, -6, 0, -1, 0], 'aplist': [0, 1, 2, 0, 0, -6, -6, -1, -4, -2, -8, 10, -2, -4, -12, 6, -12, 2, -4, 0, 10, 0, 16, -2, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 3648, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '3648.bf', 'trace_hash': 1851139363558986978}
• 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': '0.20404306238858564706910178575', 'prec': 103}, 'conductor': 3648, 'gens': [[4501, 234676, 15]], 'heights': [{'__RealLiteral__': 0, 'data': '8.4255002443428089193767528379', 'prec': 100}], 'lmfdb_label': '3648.bf4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.53176054913281958440990935702', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.4803486366504376560690804486840264928', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[17, 0, 1]], 'xcoord_integral_points': [17]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [1, 0], '7': [1, 1, 0], '11': [3, 1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '3648.bf4'}
• ec_torsion_growth •

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

  
  
  • id: 190790
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '3648.bf4', 'torsion': [4]}
  • id: 190789
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '3648.bf4', 'torsion': [2, 2]}
  • id: 190791
    {'degree': 2, 'field': [6, 0, 1], 'lmfdb_label': '3648.bf4', 'torsion': [4]}
  • id: 190792
    {'degree': 4, 'field': [4, 0, 2, 0, 1], 'lmfdb_label': '3648.bf4', 'torsion': [2, 4]}
  • id: 190796
    {'degree': 8, 'field': [-48, 0, -88, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '3648.bf4', 'torsion': [6]}
  • id: 190793
    {'degree': 8, 'field': [1, 0, -4, 0, 3, 0, 2, 0, 1], 'lmfdb_label': '3648.bf4', 'torsion': [2, 4]}
  • id: 190794
    {'degree': 8, 'field': [9, 0, -188, 0, 30, 0, 12, 0, 1], 'lmfdb_label': '3648.bf4', 'torsion': [8]}
  • id: 190795
    {'degree': 8, 'field': [16, 0, 56, 0, 0, 0, 14, 0, 1], 'lmfdb_label': '3648.bf4', 'torsion': [8]}
  • id: 190797
    {'degree': 16, 'field': [1, -12, 68, -232, 488, -564, 194, 396, -665, 444, -62, -152, 162, -92, 34, -8, 1], 'lmfdb_label': '3648.bf4', 'torsion': [4, 4]}
  • id: 190799
    {'degree': 16, 'field': [81, 0, 1692, 0, 35074, 0, 5856, 0, 3147, 0, -736, 0, 114, 0, -12, 0, 1], 'lmfdb_label': '3648.bf4', 'torsion': [2, 8]}
  • id: 190801
    {'degree': 16, 'field': [1089, 0, -9378, 0, 6597, 0, -3740, 0, 1394, 0, -518, 0, 100, 0, -16, 0, 1], 'lmfdb_label': '3648.bf4', 'torsion': [12]}
  • id: 190802
    {'degree': 16, 'field': [1089, 0, -5184, 0, 43612, 0, 768, 0, -5142, 0, 1816, 0, -291, 0, 12, 0, 1], 'lmfdb_label': '3648.bf4', 'torsion': [12]}
  • id: 190800
    {'degree': 16, 'field': [2304, 0, -4224, 0, 6592, 0, -2112, 0, 624, 0, -176, 0, 24, 0, 0, 0, 1], 'lmfdb_label': '3648.bf4', 'torsion': [2, 6]}
  • id: 190798
    {'degree': 16, 'field': [2439, -6498, 2655, 11862, -9987, -5196, 9126, -1032, -3422, 1272, 718, -492, -57, 90, -5, -6, 1], 'lmfdb_label': '3648.bf4', 'torsion': [2, 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: 67322
    {'conductor': 3648, 'conductor_valuation': 6, 'discriminant_valuation': 18, 'j_denominator_valuation': 0, 'kodaira_symbol': -12, 'lmfdb_label': '3648.bf4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 67323
    {'conductor': 3648, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '3648.bf4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 67324
    {'conductor': 3648, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '3648.bf4', 'prime': 19, '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: 1687660
    {'adelic_gens': [[277, 284, 238, 51], [7, 6, 450, 451], [97, 8, 388, 33], [1, 0, 8, 1], [449, 8, 448, 9], [53, 54, 158, 389], [160, 3, 157, 2], [1, 8, 0, 1], [1, 4, 4, 17]], 'adelic_image': '456.48.0.?', 'conductor': 3648, 'lmfdb_label': '3648.bf4', 'prime': 0}
  • id: 18242
    {'conductor': 3648, 'elladic_image': '8.12.0.8', 'lmfdb_label': '3648.bf4', 'modell_image': '2B', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 123826
    {'lmfdb_iso': '3648.bf', 'p': 5, 'prec': 20, 'unit': 2065575017452, 'val': 1}
  • id: 123831
    {'lmfdb_iso': '3648.bf', 'p': 13, 'prec': 20, 'unit': 1091727876847595279762, 'val': 1}
  • id: 123833
    {'lmfdb_iso': '3648.bf', 'p': 17, 'prec': 20, 'unit': 32134093798555827558510, 'val': 1}
  • id: 123837
    {'lmfdb_iso': '3648.bf', 'p': 23, 'prec': 20, 'unit': 55810185189078822755224223, 'val': 1}
  • id: 123830
    {'lmfdb_iso': '3648.bf', 'p': 29, 'prec': 20, 'unit': 5521665255761359022237279726, 'val': 1}
  • id: 123827
    {'lmfdb_iso': '3648.bf', 'p': 31, 'prec': 20, 'unit': 9064989474425118344799384993, 'val': 1}
  • id: 123841
    {'lmfdb_iso': '3648.bf', 'p': 37, 'prec': 20, 'unit': 587864302614253588320803464151, 'val': 1}
  • id: 123828
    {'lmfdb_iso': '3648.bf', 'p': 41, 'prec': 20, 'unit': 2241809301459497604554938023445, 'val': 1}
  • id: 123829
    {'lmfdb_iso': '3648.bf', 'p': 43, 'prec': 20, 'unit': 4488924985845082939792941315817, 'val': 1}
  • id: 123832
    {'lmfdb_iso': '3648.bf', 'p': 47, 'prec': 20, 'unit': 8207030753152009724083296624491, 'val': 1}
  • id: 123835
    {'lmfdb_iso': '3648.bf', 'p': 53, 'prec': 20, 'unit': 492467216998140805664843055615801, 'val': 1}
  • id: 123839
    {'lmfdb_iso': '3648.bf', 'p': 59, 'prec': 20, 'unit': 3280340097702353715392930419658908, 'val': 1}
  • id: 123840
    {'lmfdb_iso': '3648.bf', 'p': 61, 'prec': 20, 'unit': 1480601356385745660061608549649861, 'val': 1}
  • id: 123825
    {'lmfdb_iso': '3648.bf', 'p': 67, 'prec': 20, 'unit': 30517228596257917179233278671745765, 'val': 1}
  • id: 123836
    {'lmfdb_iso': '3648.bf', 'p': 73, 'prec': 20, 'unit': 221063627406277688390680453933532572, 'val': 1}
  • id: 123834
    {'lmfdb_iso': '3648.bf', 'p': 83, 'prec': 20, 'unit': 2780033148262961793959722172719602074, 'val': 1}
  • id: 123838
    {'lmfdb_iso': '3648.bf', 'p': 89, 'prec': 20, 'unit': 2690306237434735129649281431959977870, 'val': 1}
  • id: 123824
    {'lmfdb_iso': '3648.bf', 'p': 97, 'prec': 20, 'unit': 10992687297977768326892810221181655099, 'val': 1}