Elliptic curve data - 8450.c3

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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': '8450c', 'Clabel': '8450c1', 'Cnumber': 1, 'abc_quality': 0.8441470072585473, 'absD': 1960891156250, 'adelic_genus': 3, 'adelic_index': 144, 'adelic_level': 4680, 'ainvs': [1, 1, 0, 2025, 58375], 'analytic_rank': 1, 'bad_primes': [2, 5, 13], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 8450, 'degree': 12096, 'elladic_images': ['9.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0429677724130855197050886612', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 2, 'isogeny_degrees': [1, 3, 9], 'jinv': [12167, 26], 'lmfdb_iso': '8450.c', 'lmfdb_label': '8450.c3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 0, 0], 'min_quad_twist_disc': 65, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '9.12.0.a.1', '104.2.0.?', '117.36.0.?', '120.8.0.?', '195.8.0.?', '312.8.0.?', '360.24.0.?', '585.72.0.?', '936.72.3.?', '1560.16.0.?', '4680.144.3.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 4, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.88602288337548506424197309138', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 4, 4225], [5, 14, 338], [13, 98, 50]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0442258625347330356220347262', 'prec': 103}, 'szpiro_ratio': 3.919887694020949, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 0, 1, -1, -1, -2, 0, -6, -1, 0, 1, 0, 1, 3, 2, -2, 0], 'aplist': [-1, -1, 0, -1, -6, 0, 3, -2, 0, 6, 4, -7, 0, 1, 3, 0, 6, 8, 14, 3, 2, 8, 12, 6, -10], 'class_deg': 9, 'class_size': 3, 'conductor': 8450, 'isogeny_matrix': [[1, 3, 9], [3, 1, 3], [9, 3, 1]], 'lmfdb_iso': '8450.c', 'trace_hash': 409588078620829567}
• 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': '0.12419087966522973926886705016', 'prec': 103}, 'conductor': 8450, 'gens': [[-21, 95, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.88602288337548506424197309138', 'prec': 103}], 'lmfdb_label': '8450.c3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.57554471791414890180911220021', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.0397831619112976074092639552875277932', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': [-21, 421]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': [1, 0], '5': 'a', '7': [1, 0], '11': [1, 0], '13': 'a', '17': [1, 0], '19': [1, 0], '23': [3, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [3, 1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '8450.c3'}
• ec_torsion_growth •

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

  
  
  • id: 442062
    {'degree': 2, 'field': [-16, -1, 1], 'lmfdb_label': '8450.c3', 'torsion': [3]}
  • id: 442063
    {'degree': 3, 'field': [-2, -1, 0, 1], 'lmfdb_label': '8450.c3', 'torsion': [2]}
  • id: 442067
    {'degree': 6, 'field': [-16, -40, -18, 11, -1, -1, 1], 'lmfdb_label': '8450.c3', 'torsion': [6]}
  • id: 442066
    {'degree': 6, 'field': [-1, -16, 58, 17, -18, -1, 1], 'lmfdb_label': '8450.c3', 'torsion': [9]}
  • id: 442064
    {'degree': 6, 'field': [26, 0, 29, 0, 8, 0, 1], 'lmfdb_label': '8450.c3', 'torsion': [2, 2]}
  • id: 442065
    {'degree': 6, 'field': [1221, -471, 58, -35, 8, -1, 1], 'lmfdb_label': '8450.c3', 'torsion': [3]}
  • id: 442071
    {'degree': 12, 'field': [16, 0, 642, 0, 489, 0, 380, 0, 118, 0, 18, 0, 1], 'lmfdb_label': '8450.c3', 'torsion': [2, 6]}
  • id: 442069
    {'degree': 12, 'field': [32761, -62626, 97091, -12842, -14706, -5294, 6511, -742, 342, -154, 11, -2, 1], 'lmfdb_label': '8450.c3', 'torsion': [3, 3]}
  • id: 442070
    {'degree': 12, 'field': [67900, 126400, 77820, 3190, -44, 6630, 2903, 130, 443, -30, 33, 0, 1], 'lmfdb_label': '8450.c3', 'torsion': [9]}
  • id: 442068
    {'degree': 12, 'field': [130624, -24560, -4298, -39692, 375, -1468, 1992, 36, 37, -96, 8, 0, 1], 'lmfdb_label': '8450.c3', 'torsion': [4]}
  • id: 442073
    {'degree': 18, 'field': [6241, 11613, -9053, -26637, 13904, 29274, -22284, -14129, 18011, 2697, -5221, -970, 479, 163, 37, 13, -15, -3, 1], 'lmfdb_label': '8450.c3', 'torsion': [18]}
  • id: 442072
    {'degree': 18, 'field': [3802111, 4751292, 12775438, -31494470, 11917802, 8450520, -6684845, 313404, 912860, -247448, -9542, 11440, -4119, 1664, -52, -98, 26, 0, 1], 'lmfdb_label': '8450.c3', 'torsion': [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: 176137
    {'conductor': 8450, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '8450.c3', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 176138
    {'conductor': 8450, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '8450.c3', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 176139
    {'conductor': 8450, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '8450.c3', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 1719871
    {'adelic_gens': [[1, 18, 0, 1], [1, 18, 10, 181], [10, 9, 81, 73], [946, 945, 1395, 3736], [4663, 18, 4662, 19], [1, 0, 18, 1], [3164, 3735, 1305, 3764], [3521, 4230, 4050, 541], [3743, 0, 0, 4679], [3286, 945, 225, 3736]], 'adelic_image': '4680.144.3.?', 'conductor': 8450, 'lmfdb_label': '8450.c3', 'prime': 0}
  • id: 41405
    {'conductor': 8450, 'elladic_image': '9.12.0.1', 'lmfdb_label': '8450.c3', 'modell_image': '3B', 'prime': 3}
• ec_padic •

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

  
  
  • id: 349531
    {'lmfdb_iso': '8450.c', 'p': 7, 'prec': 20, 'unit': 2548956418430903, 'val': 1}
  • id: 349536
    {'lmfdb_iso': '8450.c', 'p': 11, 'prec': 20, 'unit': 15637811554547374732, 'val': 1}
  • id: 349537
    {'lmfdb_iso': '8450.c', 'p': 17, 'prec': 20, 'unit': 204702037861928789383027, 'val': 1}
  • id: 349538
    {'lmfdb_iso': '8450.c', 'p': 19, 'prec': 20, 'unit': 1176110499365714274582967, 'val': 1}
  • id: 349534
    {'lmfdb_iso': '8450.c', 'p': 29, 'prec': 20, 'unit': 5839821818803257217091232073, 'val': 1}
  • id: 349544
    {'lmfdb_iso': '8450.c', 'p': 31, 'prec': 20, 'unit': 4704275885185233805138521929, 'val': 1}
  • id: 349530
    {'lmfdb_iso': '8450.c', 'p': 37, 'prec': 20, 'unit': 244654100781271150779671966282, 'val': 1}
  • id: 349533
    {'lmfdb_iso': '8450.c', 'p': 43, 'prec': 20, 'unit': 75880198887033758121155144885861, 'val': -1}
  • id: 349542
    {'lmfdb_iso': '8450.c', 'p': 47, 'prec': 20, 'unit': 10037477199553389571606436952855, 'val': 1}
  • id: 349539
    {'lmfdb_iso': '8450.c', 'p': 59, 'prec': 20, 'unit': 3672354122838056849382124424760735, 'val': 1}
  • id: 349543
    {'lmfdb_iso': '8450.c', 'p': 61, 'prec': 20, 'unit': 7176163722124674689595500241368664, 'val': 1}
  • id: 349529
    {'lmfdb_iso': '8450.c', 'p': 67, 'prec': 20, 'unit': 30045255387176314445272803162002063, 'val': 1}
  • id: 349541
    {'lmfdb_iso': '8450.c', 'p': 71, 'prec': 20, 'unit': 45902649025218297459758628919399594, 'val': 1}
  • id: 349532
    {'lmfdb_iso': '8450.c', 'p': 73, 'prec': 20, 'unit': 125258888232955899402928203167244405, 'val': 1}
  • id: 349535
    {'lmfdb_iso': '8450.c', 'p': 79, 'prec': 20, 'unit': 1063867042350057393795228721383942785, 'val': 1}
  • id: 349528
    {'lmfdb_iso': '8450.c', 'p': 83, 'prec': 20, 'unit': 672078313306954026494346226192141607, 'val': 1}
  • id: 349540
    {'lmfdb_iso': '8450.c', 'p': 89, 'prec': 20, 'unit': 2006937642046394246810359867722175833, 'val': 1}
  • id: 349527
    {'lmfdb_iso': '8450.c', 'p': 97, 'prec': 20, 'unit': 12155258545916044948217509414388961558, 'val': 1}