Elliptic curve data - 663.b2

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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': '663c', 'Clabel': '663c1', 'Cnumber': 1, 'abc_quality': 0.8649118085872727, 'absD': 232713, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 884, 'ainvs': [1, 0, 0, -33, -72], 'analytic_rank': 1, 'bad_primes': [3, 13, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 663, 'degree': 64, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.21667716360867550877926228915', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [3981876625, 232713], 'lmfdb_iso': '663.b', 'lmfdb_label': '663.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -33, -72], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '34.6.0.a.1', '52.6.0.c.1', '884.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 9, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.40838404957597395562472267840', 'prec': 103}, 'semistable': True, 'serre_invariants': [[2, 2, 17], [3, 4, 221], [13, 14, 51], [17, 18, 39]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.21667716360867550877926228915', 'prec': 107}, 'szpiro_ratio': 3.4024603118203043, '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, -1, 1, -1, 0, -1, -2, 3, 1, 0, -2, -1, -1, 2, 0, -1, 1, -1, 0, 0], 'aplist': [-1, 1, 0, -2, -2, -1, 1, 0, -8, -6, 6, 4, -12, -4, 0, -6, 0, -2, 0, 10, -4, 12, -4, -10, 16], 'class_deg': 2, 'class_size': 2, 'conductor': 663, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '663.b', 'trace_hash': 130407521823932222}
• 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': '1.5424226462124116497809591325', 'prec': 100}, 'conductor': 663, 'gens': [[-3, 3, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.40838404957597395562472267840', 'prec': 103}], 'lmfdb_label': '663.b2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.9988726758581976937440939139', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.6326154359074678518357905581944850886', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-4, 2, 1]], 'xcoord_integral_points': [-4, -3, 9, 12, 321]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 0], '3': [2, 0], '5': [1, 1, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [2, 0], '19': [1, 1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '663.b2'}
• ec_torsion_growth •

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

  
  
  • id: 30719
    {'degree': 2, 'field': [-4, -1, 1], 'lmfdb_label': '663.b2', 'torsion': [2, 2]}
  • id: 30720
    {'degree': 4, 'field': [4, -2, 1, -1, 1], 'lmfdb_label': '663.b2', 'torsion': [4]}
  • id: 30723
    {'degree': 8, 'field': [-177, -1020, 1092, -145, 76, -7, 7, -4, 1], 'lmfdb_label': '663.b2', 'torsion': [6]}
  • id: 30721
    {'degree': 8, 'field': [-72, 48, 130, -166, 45, 24, -12, -2, 1], 'lmfdb_label': '663.b2', 'torsion': [2, 4]}
  • id: 30722
    {'degree': 8, 'field': [17, -34, 123, -2, -38, -4, 1, 0, 1], 'lmfdb_label': '663.b2', 'torsion': [2, 4]}
  • id: 30725
    {'degree': 16, 'field': [-57781, -45112, 48793, 188479, 103610, -85278, -154913, -59663, 19853, 29302, 8145, -125, -106, 21, -1, -4, 1], 'lmfdb_label': '663.b2', 'torsion': [2, 6]}
  • id: 30724
    {'degree': 16, 'field': [14556, -62320, 98114, -89362, 101033, -104896, 109346, -90004, 59330, -31094, 13294, -4556, 1366, -308, 64, -8, 1], 'lmfdb_label': '663.b2', '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: 8105
    {'conductor': 663, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '663.b2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 8106
    {'conductor': 663, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '663.b2', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 8107
    {'conductor': 663, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '663.b2', 'prime': 17, '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: 1668916
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [881, 4, 880, 5], [210, 1, 779, 0], [613, 4, 342, 9], [665, 222, 220, 663]], 'adelic_image': '884.12.0.?', 'conductor': 663, 'lmfdb_label': '663.b2', 'prime': 0}
  • id: 3025
    {'conductor': 663, 'elladic_image': '2.3.0.1', 'lmfdb_label': '663.b2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 11856
    {'lmfdb_iso': '663.b', 'p': 7, 'prec': 20, 'unit': 9188754292165713, 'val': 1}
  • id: 11858
    {'lmfdb_iso': '663.b', 'p': 11, 'prec': 20, 'unit': 18838390907676017178, 'val': 1}
  • id: 11864
    {'lmfdb_iso': '663.b', 'p': 23, 'prec': 20, 'unit': 42128054463797023512369409, 'val': 1}
  • id: 11859
    {'lmfdb_iso': '663.b', 'p': 29, 'prec': 20, 'unit': 3528367191908930761804274318, 'val': 1}
  • id: 11868
    {'lmfdb_iso': '663.b', 'p': 31, 'prec': 20, 'unit': 2765621821528149124121955987, 'val': 1}
  • id: 11855
    {'lmfdb_iso': '663.b', 'p': 37, 'prec': 20, 'unit': 263120159084647960031322129743, 'val': 1}
  • id: 11857
    {'lmfdb_iso': '663.b', 'p': 41, 'prec': 20, 'unit': 895553504957689360913041667262, 'val': 1}
  • id: 11854
    {'lmfdb_iso': '663.b', 'p': 43, 'prec': 20, 'unit': 6224825528604973206329443285807, 'val': 1}
  • id: 11862
    {'lmfdb_iso': '663.b', 'p': 53, 'prec': 20, 'unit': 11206079757818793106573917649354, 'val': 1}
  • id: 11867
    {'lmfdb_iso': '663.b', 'p': 61, 'prec': 20, 'unit': 3624308934808493069936424649354716, 'val': 1}
  • id: 11866
    {'lmfdb_iso': '663.b', 'p': 71, 'prec': 20, 'unit': 33917623836487036440152761358681630, 'val': 1}
  • id: 11863
    {'lmfdb_iso': '663.b', 'p': 73, 'prec': 20, 'unit': 207484457475686743357794043062478295, 'val': 1}
  • id: 11860
    {'lmfdb_iso': '663.b', 'p': 79, 'prec': 20, 'unit': 1090309620136714204012395636064633644, 'val': 1}
  • id: 11861
    {'lmfdb_iso': '663.b', 'p': 83, 'prec': 20, 'unit': 2285376761081058850526938580233256010, 'val': 1}
  • id: 11865
    {'lmfdb_iso': '663.b', 'p': 89, 'prec': 20, 'unit': 205785379909945360252849315949505676, 'val': 1}
  • id: 11853
    {'lmfdb_iso': '663.b', 'p': 97, 'prec': 20, 'unit': 18520588788559558256563082597796354490, 'val': 1}