Elliptic curve data - 133518.d4

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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': '133518ce', 'Clabel': '133518ce1', 'Cnumber': 1, 'abc_quality': 0.8617725193907065, 'absD': 388252604264448, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 31416, 'ainvs': [1, 1, 0, 17479, -320859], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 11, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 133518, 'degree': 774144, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4882113952398863239327897485', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 3, 'isogeny_degrees': [1, 2, 4], 'jinv': [24464768327, 16084992], 'lmfdb_iso': '133518.d', 'lmfdb_label': '133518.d4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 60, -62], 'min_quad_twist_disc': 17, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '12.12.0-4.c.1.2', '136.12.0.?', '408.24.0.?', '616.12.0.?', '1848.24.0.?', '5236.12.0.?', '7854.6.0.?', '10472.24.0.?', '15708.24.0.?', '31416.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 66759], [3, 4, 22253], [7, 8, 19074], [11, 12, 12138], [17, 162, 462]], 'sha': 4, 'sha_primes': [2], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.071604723211778283808022439562', 'prec': 107}, 'szpiro_ratio': 3.4671927768995365, '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, -2, 1, -1, -1, 1, 2, 1, -1, 6, 1, 2, 1, 0, -1, -4, -2], 'aplist': [-1, -1, -2, -1, 1, 6, 0, -4, 0, 6, 8, -2, -10, 4, 8, -6, 12, 6, -4, 0, -10, -8, 16, 14, -6], 'class_deg': 4, 'class_size': 4, 'conductor': 133518, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '133518.d', 'trace_hash': 371293600658019052}
• 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': '0.050974855845036908150420185702', 'prec': 107}, 'conductor': 133518, 'gens': [], 'heights': [], 'lmfdb_label': '133518.d4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.30465648835492880410911647256', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2186259534197152164364658902445138331', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[18, -9, 1]], 'xcoord_integral_points': [18]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [10, 0], '3': [0, 0], '7': [0, 0], '11': [1, 0], '17': 'a'}, 'iwp0': 3, 'lmfdb_label': '133518.d4'}
• ec_torsion_growth •

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

  
  
  • id: 6054395
    {'degree': 2, 'field': [-327, -1, 1], 'lmfdb_label': '133518.d4', 'torsion': [4]}
  • id: 6054396
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '133518.d4', 'torsion': [4]}
  • id: 6054394
    {'degree': 2, 'field': [982, -1, 1], 'lmfdb_label': '133518.d4', 'torsion': [2, 2]}
  • id: 6054397
    {'degree': 4, 'field': [106929, 327, 328, -1, 1], 'lmfdb_label': '133518.d4', 'torsion': [2, 4]}
  • id: 6054401
    {'degree': 8, 'field': [11484, -16170, -1991, 2544, 30, -118, -12, 0, 1], 'lmfdb_label': '133518.d4', 'torsion': [6]}
  • id: 6054400
    {'degree': 8, 'field': [226576, 388416, 205768, -27744, 1632, 0, 34, 0, 1], 'lmfdb_label': '133518.d4', 'torsion': [8]}
  • id: 6054399
    {'degree': 8, 'field': [2446096, 0, -41072, 0, 5708, 0, -188, 0, 1], 'lmfdb_label': '133518.d4', 'torsion': [8]}
  • id: 6054398
    {'degree': 8, 'field': [113294174464, 0, -569285216, 0, 1355889, 0, -1637, 0, 1], 'lmfdb_label': '133518.d4', 'torsion': [2, 4]}
  • id: 6054407
    {'degree': 16, 'field': [20736, -73008, 198009, -92094, -53426, -45138, 96885, -26830, -3717, 5850, -1071, -18, 267, -70, 12, 0, 1], 'lmfdb_label': '133518.d4', 'torsion': [12]}
  • id: 6054406
    {'degree': 16, 'field': [478559376, 0, -436325388, 0, 38570401, 0, -552252, 0, -360132, 0, 18254, 0, -804, 0, 0, 0, 1], 'lmfdb_label': '133518.d4', 'torsion': [12]}
  • id: 6054405
    {'degree': 16, 'field': [3869835264, 0, 4875925248, 0, 1764343296, 0, 67721184, 0, 622080, 0, -78381, 0, -1728, 0, 0, 0, 1], 'lmfdb_label': '133518.d4', 'torsion': [2, 6]}
  • id: 6054403
    {'degree': 16, 'field': [4294967296, 0, 637534208, 0, -219938816, 0, 41713664, 0, 22604800, 0, 162944, 0, -3356, 0, 38, 0, 1], 'lmfdb_label': '133518.d4', 'torsion': [2, 8]}
  • id: 6054404
    {'degree': 16, 'field': [4294967296, 0, 1509949440, 0, 107216896, 0, 137134080, 0, 39644160, 0, 535680, 0, 1636, 0, 90, 0, 1], 'lmfdb_label': '133518.d4', 'torsion': [2, 8]}
  • id: 6054402
    {'degree': 16, 'field': [1667703876764041216, 1503606567429734400, 677827982868480000, 203710546944000000, 34384885864127488, 1760245168742400, 53170013520000, 1831534635024, 151921031313, 5982455550, 65081250, -10108284, -246161, -36, 18, -6, 1], 'lmfdb_label': '133518.d4', '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: 3293324
    {'conductor': 133518, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '133518.d4', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 3293325
    {'conductor': 133518, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '133518.d4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 3293326
    {'conductor': 133518, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '133518.d4', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 3293327
    {'conductor': 133518, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '133518.d4', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 3293328
    {'conductor': 133518, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '133518.d4', 'prime': 17, 'reduction_type': 0, '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: 2532852
    {'adelic_gens': [[20948, 1, 10495, 6], [9236, 31415, 29545, 31410], [1, 0, 8, 1], [25712, 3, 19997, 2], [1, 8, 0, 1], [31409, 8, 31408, 9], [1, 4, 4, 17], [7, 6, 31410, 31411], [19643, 19638, 11786, 27491], [8984, 3, 13469, 2], [27497, 27492, 27494, 11783]], 'adelic_image': '31416.48.0.?', 'conductor': 133518, 'lmfdb_label': '133518.d4', 'prime': 0}
  • id: 518193
    {'conductor': 133518, 'elladic_image': '4.6.0.1', 'lmfdb_label': '133518.d4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 133518.d does not appear in ec_padic