Elliptic curve data - 6336.b1

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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': '6336e', 'Clabel': '6336e2', 'Cnumber': 2, 'abc_quality': 0.9412039603715836, 'absD': 624333422592, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 132, 'ainvs': [0, 0, 0, -9612, -360720], 'analytic_rank': 1, 'bad_primes': [2, 3, 11], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 6336, 'degree': 12288, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1003363414795531194188466610', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [19034163, 121], 'lmfdb_iso': '6336.b', 'lmfdb_label': '6336.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -17, 30], 'min_quad_twist_disc': -24, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '12.6.0.a.1', '44.6.0.e.1', '132.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 5, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.8351541653209892856026311362', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 3], [3, 2, 704], [11, 12, 576]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.76334364586144711325343544888', 'prec': 107}, 'szpiro_ratio': 4.469487401425304, '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, -4, 0, -2, 0, 0, 0, -1, 0, 2, 0, 0, 0, -2, 0, 6, 0], 'aplist': [0, 0, -4, -2, -1, 2, -2, 6, -4, -6, 4, 6, 10, -6, 8, 0, 4, 6, -8, 0, -2, -10, 12, 0, 2], 'class_deg': 2, 'class_size': 2, 'conductor': 6336, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '6336.b', 'trace_hash': 286444877604722863}
• 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': '0.11072864802961361563170465082', 'prec': 103}, 'conductor': 6336, 'gens': [[-56, 44, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.8351541653209892856026311362', 'prec': 100}], 'lmfdb_label': '6336.b1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.48235016690192447879089938787', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.7350741696705311360872623926714230046', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-60, 0, 1]], 'xcoord_integral_points': [-60, -56, 237]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [3, 0], '19': [1, 0], '23': [1, 0], '29': [5, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '6336.b1'}
• ec_torsion_growth •

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

  
  
  • id: 329633
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '6336.b1', 'torsion': [2, 2]}
  • id: 329634
    {'degree': 4, 'field': [48, 0, 18, 0, 1], 'lmfdb_label': '6336.b1', 'torsion': [4]}
  • id: 329637
    {'degree': 8, 'field': [-48, 0, 152, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '6336.b1', 'torsion': [6]}
  • id: 329636
    {'degree': 8, 'field': [1, -8, -82, 16, 4, -4, 2, -4, 1], 'lmfdb_label': '6336.b1', 'torsion': [2, 4]}
  • id: 329635
    {'degree': 8, 'field': [36, 0, 252, 0, 165, 0, 24, 0, 1], 'lmfdb_label': '6336.b1', 'torsion': [2, 4]}
  • id: 329639
    {'degree': 16, 'field': [9, 0, 0, 0, -252, 0, -780, 0, -546, 0, 120, 0, 109, 0, 20, 0, 1], 'lmfdb_label': '6336.b1', 'torsion': [2, 6]}
  • id: 329638
    {'degree': 16, 'field': [6724, 0, 11710, 0, 12245, 0, 6562, 0, 1492, 0, -4, 0, -4, 0, 8, 0, 1], 'lmfdb_label': '6336.b1', 'torsion': [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: 126687
    {'conductor': 6336, 'conductor_valuation': 6, 'discriminant_valuation': 18, 'j_denominator_valuation': 0, 'kodaira_symbol': -12, 'lmfdb_label': '6336.b1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 126688
    {'conductor': 6336, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '6336.b1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 126689
    {'conductor': 6336, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '6336.b1', 'prime': 11, '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: 1705460
    {'adelic_gens': [[1, 2, 2, 5], [92, 1, 43, 0], [3, 4, 8, 11], [100, 37, 33, 100], [1, 4, 0, 1], [13, 4, 26, 9], [1, 0, 4, 1], [129, 4, 128, 5]], 'adelic_image': '132.12.0.?', 'conductor': 6336, 'lmfdb_label': '6336.b1', 'prime': 0}
  • id: 31062
    {'conductor': 6336, 'elladic_image': '2.3.0.1', 'lmfdb_label': '6336.b1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 248049
    {'lmfdb_iso': '6336.b', 'p': 5, 'prec': 20, 'unit': 77751921263439, 'val': -1}
  • id: 248050
    {'lmfdb_iso': '6336.b', 'p': 7, 'prec': 20, 'unit': 1813046020947057, 'val': 1}
  • id: 248055
    {'lmfdb_iso': '6336.b', 'p': 13, 'prec': 20, 'unit': 650757190476796410962, 'val': 1}
  • id: 248057
    {'lmfdb_iso': '6336.b', 'p': 17, 'prec': 20, 'unit': 551483662101168509778, 'val': 2}
  • id: 248058
    {'lmfdb_iso': '6336.b', 'p': 19, 'prec': 20, 'unit': 947552261292210240020769, 'val': 1}
  • id: 248061
    {'lmfdb_iso': '6336.b', 'p': 23, 'prec': 20, 'unit': 30837640860161766011514564, 'val': 1}
  • id: 248054
    {'lmfdb_iso': '6336.b', 'p': 29, 'prec': 20, 'unit': 95965737869670062400053347, 'val': 2}
  • id: 248051
    {'lmfdb_iso': '6336.b', 'p': 31, 'prec': 20, 'unit': 19618361375498586421833079645, 'val': 1}
  • id: 248064
    {'lmfdb_iso': '6336.b', 'p': 37, 'prec': 20, 'unit': 163304856971867326236081497848, 'val': 1}
  • id: 248052
    {'lmfdb_iso': '6336.b', 'p': 41, 'prec': 20, 'unit': 1702076174602810519292674149135, 'val': 1}
  • id: 248053
    {'lmfdb_iso': '6336.b', 'p': 43, 'prec': 20, 'unit': 7538521270462065143176010431343, 'val': 1}
  • id: 248062
    {'lmfdb_iso': '6336.b', 'p': 47, 'prec': 20, 'unit': 32759979866454841302089538602199, 'val': 1}
  • id: 248059
    {'lmfdb_iso': '6336.b', 'p': 59, 'prec': 20, 'unit': 1705336795591294357827608762307978, 'val': 1}
  • id: 248063
    {'lmfdb_iso': '6336.b', 'p': 61, 'prec': 20, 'unit': 3765326908178000159011188067463218, 'val': 1}
  • id: 248048
    {'lmfdb_iso': '6336.b', 'p': 67, 'prec': 20, 'unit': 22577086030399093966860000113506406, 'val': 1}
  • id: 248060
    {'lmfdb_iso': '6336.b', 'p': 73, 'prec': 20, 'unit': 163572846070570994645163697451424798, 'val': 1}
  • id: 248056
    {'lmfdb_iso': '6336.b', 'p': 79, 'prec': 20, 'unit': 759373163110823150414569922196460913, 'val': 1}
  • id: 248047
    {'lmfdb_iso': '6336.b', 'p': 83, 'prec': 20, 'unit': 2094071609811202262868900351256938287, 'val': 1}
  • id: 248046
    {'lmfdb_iso': '6336.b', 'p': 97, 'prec': 20, 'unit': 4732254315791175404879494101587787397, 'val': 1}