Elliptic curve data - 221778.b1

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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': '221778p', 'Clabel': '221778p2', 'Cnumber': 2, 'abc_quality': 1.0060683766058514, 'absD': 5454128834101476, 'adelic_genus': 1, 'adelic_index': 128, 'adelic_level': 444, 'ainvs': [1, -1, 0, -76236, -8827804], 'analytic_rank': 1, 'bad_primes': [2, 3, 37], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 221778, 'degree': 1870128, 'elladic_images': ['4.8.0.2', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7569586147135777251878797218', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 1, 'isogeny_degrees': [1, 3], 'jinv': [-35937, 4], 'lmfdb_iso': '221778.b', 'lmfdb_label': '221778.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -6, 8], 'min_quad_twist_disc': -111, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '4.8.0.b.1', '12.64.1.b.2', '111.8.0.?', '148.16.0.?', '444.128.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '11.223779092423384246060539382', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 110889], [3, 2, 2738], [37, 686, 162]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1471126302766441883914133506', 'prec': 103}, 'szpiro_ratio': 3.697513576002974, '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, 0, 1, -3, 0, -4, -1, 0, 3, 0, 0, 1, 4, 0, 1, -3, 0, 4, -3], 'aplist': [-1, 0, -3, -4, 0, 1, -3, 4, 0, 9, 4, 0, -6, -8, 12, 6, 0, 1, -4, 12, 11, 16, 12, -3, -2], 'class_deg': 3, 'class_size': 2, 'conductor': 221778, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '221778.b', 'trace_hash': 1018525008062564479}
• 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': '0.029780030444083315629606503028', 'prec': 107}, 'conductor': 221778, 'gens': [[92800, 26923706, 9]], 'heights': [{'__RealLiteral__': 0, 'data': '11.223779092423384246060539382', 'prec': 100}], 'lmfdb_label': '221778.b1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.14276245030877239132506478178', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.2046684099174637646616781798745492922', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 221778.b1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9654236
    {'degree': 2, 'field': [28, -1, 1], 'lmfdb_label': '221778.b1', 'torsion': [3]}
  • id: 9654237
    {'degree': 3, 'field': [-4, -3, 0, 1], 'lmfdb_label': '221778.b1', 'torsion': [2]}
  • id: 9654241
    {'degree': 6, 'field': [-669, -357, 222, 49, -24, -3, 1], 'lmfdb_label': '221778.b1', 'torsion': [3]}
  • id: 9654239
    {'degree': 6, 'field': [-181, -453, 228, 57, -30, -3, 1], 'lmfdb_label': '221778.b1', 'torsion': [4]}
  • id: 9654238
    {'degree': 6, 'field': [2, 6, 9, -2, 0, 0, 1], 'lmfdb_label': '221778.b1', 'torsion': [2, 2]}
  • id: 9654240
    {'degree': 6, 'field': [11369, 2370, 1062, -52, 54, 0, 1], 'lmfdb_label': '221778.b1', 'torsion': [4]}
  • id: 9654242
    {'degree': 6, 'field': [11776, 4812, 1062, -52, -57, 0, 1], 'lmfdb_label': '221778.b1', 'torsion': [6]}
  • id: 9654244
    {'degree': 12, 'field': [264196, 0, -253728, 0, 97500, 0, -17321, 0, 1515, 0, -63, 0, 1], 'lmfdb_label': '221778.b1', 'torsion': [3, 3]}
  • id: 9654246
    {'degree': 12, 'field': [339556, 163068, -66138, -167082, 26019, 43602, -7103, -5010, 834, 276, -45, -6, 1], 'lmfdb_label': '221778.b1', 'torsion': [12]}
  • id: 9654243
    {'degree': 12, 'field': [672289, 379992, 356133, 91144, 98526, 6792, 15725, 0, 1338, -16, 57, 0, 1], 'lmfdb_label': '221778.b1', 'torsion': [4, 4]}
  • id: 9654247
    {'degree': 12, 'field': [1173652, 99804, 471945, 60428, 100635, 6060, 14429, 0, 1185, -8, 51, 0, 1], 'lmfdb_label': '221778.b1', 'torsion': [12]}
  • id: 9654245
    {'degree': 12, 'field': [26604964, 7798896, 1143072, -813400, -25623, -40824, 1568, -1512, 1458, -56, 0, 0, 1], 'lmfdb_label': '221778.b1', 'torsion': [2, 6]}
  • id: 9654249
    {'degree': 18, 'field': [-414170889, 153411777, 430682427, -38287614, -191908620, -8900946, 47928042, 5805060, -7621077, -1194103, 818313, 128208, -59886, -7662, 2874, 240, -81, -3, 1], 'lmfdb_label': '221778.b1', 'torsion': [12]}
  • id: 9654248
    {'degree': 18, 'field': [21885993540, -5615308476, -1411921044, 246655206, 521568126, -69301440, 12256245, 1988118, 879822, -1069359, 188865, 12744, -675, -720, 603, -63, -18, 0, 1], 'lmfdb_label': '221778.b1', 'torsion': [9]}
• 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: 5501452
    {'conductor': 221778, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '221778.b1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5501453
    {'conductor': 221778, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '221778.b1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 5501454
    {'conductor': 221778, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '221778.b1', 'prime': 37, 'reduction_type': 0, '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: 3080449
    {'adelic_gens': [[1, 333, 0, 223], [297, 148, 296, 149], [1, 333, 333, 334], [37, 408, 36, 37], [35, 0, 0, 443], [1, 0, 408, 1], [369, 296, 296, 369]], 'adelic_image': '444.128.1.?', 'conductor': 221778, 'lmfdb_label': '221778.b1', 'prime': 0}
  • id: 813343
    {'conductor': 221778, 'elladic_image': '4.8.0.2', 'lmfdb_label': '221778.b1', 'modell_image': '2G', 'prime': 2}
  • id: 813344
    {'conductor': 221778, 'elladic_image': '3.4.0.1', 'lmfdb_label': '221778.b1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 221778.b does not appear in ec_padic