Elliptic curve data - 6378.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
  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': '6378c', 'Clabel': '6378c1', 'Cnumber': 1, 'abc_quality': 1.0028179074165748, 'absD': 10662541623558144, 'adelic_genus': 2, 'adelic_index': 96, 'adelic_level': 59528, 'ainvs': [1, 0, 0, -1144386, 471132612], 'analytic_rank': 1, 'bad_primes': [2, 3, 1063], 'class_deg': 7, 'class_size': 2, 'cm': 0, 'conductor': 6378, 'degree': 98784, 'elladic_images': ['7.48.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1329871270028769668398963931', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 3, 'isogeny_degrees': [1, 7], 'jinv': [-165745346665991446425889, 10662541623558144], 'lmfdb_iso': '6378.d', 'lmfdb_label': '6378.d1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -1144386, 471132612], 'min_quad_twist_disc': 1, 'modell_images': ['7B.1.1'], 'modm_images': ['7.48.0-7.a.1.2', '8504.2.0.?', '59528.96.2.?'], 'nonmax_primes': [7], 'nonmax_rad': 7, 'num_bad_primes': 3, 'num_int_pts': 14, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.8838911563792701481661813536', 'prec': 100}, 'semistable': True, 'serre_invariants': [[2, 4, 1063], [3, 4, 1063], [7, 2, 1063], [1063, 1064, 6]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.1329871270028769668398963931', 'prec': 100}, 'szpiro_ratio': 6.102868589624617, 'torsion': 7, 'torsion_primes': [7], 'torsion_structure': [7]}
• 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, 1, 1, 1, -1, 1, 1, 1, 1, -1, -2, 1, 0, 1, -1, 1, -3, 1, -8, -1], 'aplist': [1, 1, -1, 1, -2, 0, -3, -8, -4, 9, 4, -4, 0, -12, -8, 5, -3, -1, 12, 9, -17, 10, -14, -1, -7], 'class_deg': 7, 'class_size': 2, 'conductor': 6378, 'isogeny_matrix': [[1, 7], [7, 1]], 'lmfdb_iso': '6378.d', 'trace_hash': 2030625377114053298}
• 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': '0.014038183711849622526616059561', 'prec': 107}, 'conductor': 6378, 'gens': [[596, 638, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.8838911563792701481661813536', 'prec': 100}], 'lmfdb_label': '6378.d1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.38469467116915853371925052478', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.6565053605458060817276492800664085181', 'prec': 130}, 'tamagawa_product': 294, 'torsion_generators': [[612, -18, 1]], 'xcoord_integral_points': [-774, 36, 432, 596, 612, 684, 4644]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 0], '3': [8, 0], '5': [1, 0], '7': [3, 0], '11': [1, 0], '13': [1, 1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 1, 0], '43': [1, 0], '47': [1, 0], '1063': 'o?'}, 'iwp0': 0, 'lmfdb_label': '6378.d1'}
• ec_torsion_growth •

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

  
  
  • id: 333000
    {'degree': 3, 'field': [54, -2, -1, 1], 'lmfdb_label': '6378.d1', 'torsion': [14]}
  • id: 333001
    {'degree': 6, 'field': [14226, -4472, 2127, -220, 2, 0, 1], 'lmfdb_label': '6378.d1', 'torsion': [2, 14]}
  • id: 333002
    {'degree': 8, 'field': [-3468, 0, 1583, 0, -204, 0, 0, 0, 1], 'lmfdb_label': '6378.d1', 'torsion': [21]}
  • id: 333003
    {'degree': 12, 'field': [-566060256, 0, -22373940, 0, -4131071, 0, -42780, 0, -638, 0, 0, 0, 1], 'lmfdb_label': '6378.d1', 'torsion': [28]}
• 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: 127983
    {'conductor': 6378, 'conductor_valuation': 1, 'discriminant_valuation': 21, 'j_denominator_valuation': 21, 'kodaira_symbol': 25, 'lmfdb_label': '6378.d1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 21}
  • id: 127984
    {'conductor': 6378, 'conductor_valuation': 1, 'discriminant_valuation': 14, 'j_denominator_valuation': 14, 'kodaira_symbol': 18, 'lmfdb_label': '6378.d1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 14}
  • id: 127985
    {'conductor': 6378, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '6378.d1', 'prime': 1063, '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: 1705871
    {'adelic_gens': [[1, 14, 0, 1], [2129, 14, 14903, 99], [14883, 29778, 0, 57403], [59515, 14, 59514, 15], [1, 0, 14, 1], [8, 5, 91, 57], [44647, 14, 0, 1], [29765, 14, 29771, 99]], 'adelic_image': '59528.96.2.?', 'conductor': 6378, 'lmfdb_label': '6378.d1', 'prime': 0}
  • id: 31421
    {'conductor': 6378, 'elladic_image': '7.48.0.1', 'lmfdb_label': '6378.d1', 'modell_image': '7B.1.1', 'prime': 7}
• ec_padic •

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

  
  
  • id: 250842
    {'lmfdb_iso': '6378.d', 'p': 5, 'prec': 20, 'unit': 11972286975474, 'val': 1}
  • id: 250843
    {'lmfdb_iso': '6378.d', 'p': 7, 'prec': 20, 'unit': 47323611902780027, 'val': 0}
  • id: 250849
    {'lmfdb_iso': '6378.d', 'p': 11, 'prec': 20, 'unit': 254439840389711637, 'val': 1}
  • id: 250850
    {'lmfdb_iso': '6378.d', 'p': 17, 'prec': 20, 'unit': 231196853099251670937420, 'val': 1}
  • id: 250851
    {'lmfdb_iso': '6378.d', 'p': 19, 'prec': 20, 'unit': 1311259932961766126350990, 'val': 1}
  • id: 250854
    {'lmfdb_iso': '6378.d', 'p': 23, 'prec': 20, 'unit': 2992343631725224215891736, 'val': 1}
  • id: 250847
    {'lmfdb_iso': '6378.d', 'p': 29, 'prec': 20, 'unit': 3187235187517580534567902931, 'val': 1}
  • id: 250844
    {'lmfdb_iso': '6378.d', 'p': 31, 'prec': 20, 'unit': 1050036501322761380310596286, 'val': 1}
  • id: 250859
    {'lmfdb_iso': '6378.d', 'p': 37, 'prec': 20, 'unit': 492317159508249714550192720875, 'val': 1}
  • id: 250846
    {'lmfdb_iso': '6378.d', 'p': 43, 'prec': 20, 'unit': 6464603529649968402146788975278, 'val': 1}
  • id: 250857
    {'lmfdb_iso': '6378.d', 'p': 47, 'prec': 20, 'unit': 20128784239090422220130000424739, 'val': 1}
  • id: 250852
    {'lmfdb_iso': '6378.d', 'p': 53, 'prec': 20, 'unit': 478920568552224353413303310065431, 'val': 1}
  • id: 250853
    {'lmfdb_iso': '6378.d', 'p': 59, 'prec': 20, 'unit': 3591436573830996325907197226304022, 'val': 1}
  • id: 250858
    {'lmfdb_iso': '6378.d', 'p': 61, 'prec': 20, 'unit': 2468367122215467110944854576305824, 'val': 1}
  • id: 250841
    {'lmfdb_iso': '6378.d', 'p': 67, 'prec': 20, 'unit': 9365876212552197484309972006208736, 'val': 1}
  • id: 250856
    {'lmfdb_iso': '6378.d', 'p': 71, 'prec': 20, 'unit': 22241677889957754465530279271332352, 'val': 1}
  • id: 250845
    {'lmfdb_iso': '6378.d', 'p': 73, 'prec': 20, 'unit': 80717931490923706406170448946296759, 'val': 1}
  • id: 250848
    {'lmfdb_iso': '6378.d', 'p': 79, 'prec': 20, 'unit': 287504294655993279599733290781390437, 'val': 1}
  • id: 250840
    {'lmfdb_iso': '6378.d', 'p': 83, 'prec': 20, 'unit': 1840926555712326894542746879496572116, 'val': 1}
  • id: 250855
    {'lmfdb_iso': '6378.d', 'p': 89, 'prec': 20, 'unit': 10512380231358237252984047946789129325, 'val': 1}
  • id: 250839
    {'lmfdb_iso': '6378.d', 'p': 97, 'prec': 20, 'unit': 38339294815886891222353261646434320960, 'val': 1}