Elliptic curve data - 4005.d2

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '4005c', 'Clabel': '4005c2', 'Cnumber': 2, 'abc_quality': 1.0430832737057658, 'absD': 11693178225, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 5340, 'ainvs': [1, -1, 0, -1350, 18711], 'analytic_rank': 0, 'bad_primes': [3, 5, 89], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 4005, 'degree': 3584, 'elladic_images': ['2.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.69579681352445902954747040463', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 3, 'isogeny_degrees': [1, 2], 'jinv': [373403541601, 16040025], 'lmfdb_iso': '4005.d', 'lmfdb_label': '4005.d2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -150, -693], 'min_quad_twist_disc': -3, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '12.12.0-2.a.1.1', '20.12.0.a.1', '60.24.0-20.a.1.2', '356.12.0.?', '1068.24.0.?', '1780.24.0.?', '5340.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.14649066919040418384984778617', 'prec': 103}, 'szpiro_ratio': 4.006799495437202, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, 0, -1, -1, 0, 0, -3, 0, -1, -4, 0, -6, 0, 0, -1, 6, 0, 8, 1], 'aplist': [1, 0, -1, 0, -4, -6, 6, 8, -8, -6, -4, 2, 6, 4, 0, 2, 0, 14, 12, 0, -6, 16, -12, -1, -6], 'class_deg': 4, 'class_size': 4, 'conductor': 4005, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '4005.d', 'trace_hash': 1077079177859272692}
• 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': '0.24867868760274127490991924358', 'prec': 103}, 'conductor': 4005, 'gens': [], 'heights': [], 'lmfdb_label': '4005.d2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.2596399894209752026018094496', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2596399894209752026018094496462017723', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-42, 21, 1], [18, -9, 1]], 'xcoord_integral_points': [-42, 18]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 0], '3': 'a', '5': [0, 0], '89': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '4005.d2'}
• ec_torsion_growth •

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

  
  
  • id: 208558
    {'degree': 4, 'field': [25, 0, -5, 0, 1], 'lmfdb_label': '4005.d2', 'torsion': [2, 4]}
  • id: 208557
    {'degree': 4, 'field': [358, 50, -49, -2, 1], 'lmfdb_label': '4005.d2', 'torsion': [2, 4]}
  • id: 208556
    {'degree': 4, 'field': [1959, 177, -20, -1, 1], 'lmfdb_label': '4005.d2', 'torsion': [2, 4]}
  • id: 208559
    {'degree': 8, 'field': [-17, 65, -68, 5, 1, -7, 7, -4, 1], 'lmfdb_label': '4005.d2', 'torsion': [2, 6]}
  • id: 208563
    {'degree': 16, 'field': [36, -264, 1156, -3608, 8562, -14264, 17522, -13728, 6031, 1372, -1178, 456, -63, -8, 6, -4, 1], 'lmfdb_label': '4005.d2', 'torsion': [2, 8]}
  • id: 208562
    {'degree': 16, 'field': [5560164, 0, 33639624, 0, -14936760, 0, -1578276, 0, 843493, 0, 18732, 0, -2890, 0, -24, 0, 1], 'lmfdb_label': '4005.d2', 'torsion': [2, 8]}
  • id: 208561
    {'degree': 16, 'field': [100000000, 0, -20000000, 0, 36650000, 0, 2910000, 0, 1123025, 0, 29100, 0, 3665, 0, -20, 0, 1], 'lmfdb_label': '4005.d2', 'torsion': [2, 8]}
  • id: 208560
    {'degree': 16, 'field': [78017427856, 0, 25486994668, 0, 3705635873, 0, 313232760, 0, 16851656, 0, 591090, 0, 13208, 0, 172, 0, 1], 'lmfdb_label': '4005.d2', 'torsion': [4, 4]}
• 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: 74889
    {'conductor': 4005, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '4005.d2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 74890
    {'conductor': 4005, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '4005.d2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 74891
    {'conductor': 4005, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '4005.d2', 'prime': 89, '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: 1690004
    {'adelic_gens': [[1, 0, 4, 1], [3559, 0, 0, 5339], [2851, 1782, 4626, 3559], [2671, 3564, 1782, 1789], [1, 4, 0, 1], [5337, 4, 5336, 5], [181, 1782, 0, 1]], 'adelic_image': '5340.48.0.?', 'conductor': 4005, 'lmfdb_label': '4005.d2', 'prime': 0}
  • id: 19851
    {'conductor': 4005, 'elladic_image': '2.6.0.1', 'lmfdb_label': '4005.d2', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 4005.d does not appear in ec_padic