Elliptic curve data - 198744.w2

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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': '198744dp', 'Clabel': '198744dp1', 'Cnumber': 1, 'abc_quality': 1.047777044202656, 'absD': 8062987458691607118768, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 156, 'ainvs': [0, -1, 0, 4278517, 2655860544], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 198744, 'degree': 7225344, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.8906902412112860332150003100', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 22, 'isogeny_degrees': [1, 2], 'jinv': [953312000000, 887416803], 'lmfdb_iso': '198744.w', 'lmfdb_label': '198744.w2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, 517, -3354], 'min_quad_twist_disc': -91, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '6.6.0.a.1', '52.6.0.c.1', '156.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 24843], [3, 4, 66248], [7, 32, 1352], [13, 98, 1176]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.40421142776621257616316951034', 'prec': 103}, 'szpiro_ratio': 4.706723196629934, '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, 0, -1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0], 'aplist': [0, -1, 0, 0, 2, 0, 2, 0, -8, 2, -4, -6, -8, -4, 6, -2, -2, -2, 4, 6, -2, 0, -6, 4, -2], 'class_deg': 2, 'class_size': 2, 'conductor': 198744, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '198744.w', 'trace_hash': 728810942423150797}
• 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': '0.0030844544326849871144188891356', 'prec': 110}, 'conductor': 198744, 'gens': [], 'heights': [], 'lmfdb_label': '198744.w2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.085899305925372111402198393584', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.68719444740297689121758714866640809332', 'prec': 133}, 'tamagawa_product': 32, 'torsion_generators': [[-576, 0, 1]], 'xcoord_integral_points': [-576]}
• lmfdb_label 198744.w2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8721067
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '198744.w2', 'torsion': [2, 2]}
  • id: 8721068
    {'degree': 4, 'field': [-13, 13, -3, -1, 1], 'lmfdb_label': '198744.w2', 'torsion': [4]}
  • id: 8721071
    {'degree': 8, 'field': [-1917114, -657780, 179846, 17874, -1686, -128, -66, 0, 1], 'lmfdb_label': '198744.w2', 'torsion': [6]}
  • id: 8721070
    {'degree': 8, 'field': [169, -169, 130, -65, 35, -23, 4, -1, 1], 'lmfdb_label': '198744.w2', 'torsion': [2, 4]}
  • id: 8721069
    {'degree': 8, 'field': [130321, 0, -44462, 0, 4611, 0, -122, 0, 1], 'lmfdb_label': '198744.w2', 'torsion': [2, 4]}
  • id: 8721072
    {'degree': 16, 'field': [36507, 98154, -57154, -108070, 128095, -114524, 83088, -42312, 14224, -722, -1488, 776, -8, -84, 32, -8, 1], 'lmfdb_label': '198744.w2', 'torsion': [8]}
  • id: 8721073
    {'degree': 16, 'field': [3675326088996, -1261039246920, 777459812844, 49766110608, 40869489232, -1241923836, 791563440, -59318492, 18917418, -1917396, 264800, -26322, 6042, -256, 66, 0, 1], 'lmfdb_label': '198744.w2', 'torsion': [2, 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: 4920424
    {'conductor': 198744, 'conductor_valuation': 3, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '198744.w2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4920425
    {'conductor': 198744, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '198744.w2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 4920426
    {'conductor': 198744, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '198744.w2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4920427
    {'conductor': 198744, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '198744.w2', '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: 2937754
    {'adelic_gens': [[1, 2, 2, 5], [145, 4, 134, 9], [106, 1, 103, 0], [3, 4, 8, 11], [153, 4, 152, 5], [1, 4, 0, 1], [41, 118, 116, 39], [1, 0, 4, 1]], 'adelic_image': '156.12.0.?', 'conductor': 198744, 'lmfdb_label': '198744.w2', 'prime': 0}
  • id: 737602
    {'conductor': 198744, 'elladic_image': '2.3.0.1', 'lmfdb_label': '198744.w2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 198744.w does not appear in ec_padic