Elliptic curve data - 198550.t4

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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': '198550cn', 'Clabel': '198550cn3', 'Cnumber': 3, 'abc_quality': 1.0830002448778728, 'absD': 1278044544013574218750000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 8360, 'ainvs': [1, -1, 0, 413458, -54391517884], 'analytic_rank': 0, 'bad_primes': [2, 5, 11, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 198550, 'degree': 26542080, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.3045013459930808851098073703', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 19, 'isogeny_degrees': [1, 2, 4], 'jinv': [10633486599, 1738618750000], 'lmfdb_iso': '198550.t', 'lmfdb_label': '198550.t4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, 46, 63428], 'min_quad_twist_disc': -95, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '20.12.0-4.c.1.1', '38.6.0.b.1', '76.12.0.?', '88.12.0.?', '380.24.0.?', '440.24.0.?', '1672.24.0.?', '8360.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 9025], [5, 18, 7942], [11, 12, 18050], [19, 200, 550]], 'sha': 4, 'sha_primes': [2], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.0275629001928104678049139877', 'prec': 100}, 'szpiro_ratio': 5.161336301606129, '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, 0, 1, 0, 0, 0, -1, -3, 0, -1, 0, 2, 0, 0, 1, 6, 3, 0, 0], 'aplist': [-1, 0, 0, 0, -1, 2, 6, 0, -8, -2, 4, -10, 2, 12, 0, 6, 0, -2, 8, 12, -2, 0, 4, 6, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 198550, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '198550.t', 'trace_hash': 209276227028956496}
• 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': '0.0013481760259258983144944071093', 'prec': 110}, 'conductor': 198550, 'gens': [], 'heights': [], 'lmfdb_label': '198550.t4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.039572193150074935602244701727', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2663101808023979392718304552685579049', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[15011, -15011, 2]], 'xcoord_integral_points': []}
• lmfdb_label 198550.t4 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8712873
    {'degree': 2, 'field': [-95, 0, 1], 'lmfdb_label': '198550.t4', 'torsion': [4]}
  • id: 8712872
    {'degree': 2, 'field': [5, -1, 1], 'lmfdb_label': '198550.t4', 'torsion': [2, 2]}
  • id: 8712874
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '198550.t4', 'torsion': [4]}
  • id: 8712875
    {'degree': 4, 'field': [5, -20, 21, -2, 1], 'lmfdb_label': '198550.t4', 'torsion': [2, 4]}
  • id: 8712876
    {'degree': 8, 'field': [495, -300, 344, -84, 33, 8, 2, -4, 1], 'lmfdb_label': '198550.t4', 'torsion': [2, 4]}
  • id: 8712877
    {'degree': 8, 'field': [2401, 0, 15640, 0, -382, 0, -40, 0, 1], 'lmfdb_label': '198550.t4', 'torsion': [8]}
  • id: 8712878
    {'degree': 8, 'field': [2235025, 0, 464860, 0, 1366, 0, -132, 0, 1], 'lmfdb_label': '198550.t4', 'torsion': [8]}
  • id: 8712879
    {'degree': 8, 'field': [3960384, -1803264, 336240, -44352, 5040, -432, -48, 0, 1], 'lmfdb_label': '198550.t4', 'torsion': [6]}
  • id: 8712884
    {'degree': 16, 'field': [-4884601646, 37641765366, -67761893899, -24886045110, 6177710392, 1586900154, -265343407, -70415964, 894385, 2433912, 564287, 98580, 9583, -900, -214, 0, 1], 'lmfdb_label': '198550.t4', 'torsion': [12]}
  • id: 8712880
    {'degree': 16, 'field': [900, 0, 1360, 0, 6196, 0, -868, 0, 1349, 0, -124, 0, 14, 0, -8, 0, 1], 'lmfdb_label': '198550.t4', 'torsion': [4, 4]}
  • id: 8712883
    {'degree': 16, 'field': [6895876, 0, 11254043, 0, -3219002, 0, 4841, 0, -11345, 0, 3881, 0, 823, 0, 38, 0, 1], 'lmfdb_label': '198550.t4', 'torsion': [2, 6]}
  • id: 8712882
    {'degree': 16, 'field': [20976400, 0, 9805040, 0, 4495676, 0, 172788, 0, 26689, 0, 6384, 0, 594, 0, 28, 0, 1], 'lmfdb_label': '198550.t4', 'torsion': [2, 8]}
  • id: 8712885
    {'degree': 16, 'field': [39644365549, 11385518052, 8421210424, 1143942240, 18027832, 275165148, 80389432, -8762712, -4571570, -127596, 73168, 11160, 1108, -180, -56, 0, 1], 'lmfdb_label': '198550.t4', 'torsion': [12]}
  • id: 8712881
    {'degree': 16, 'field': [1874736973025, 269126730600, -249763524440, -37884370840, 16861710166, 2428102808, -696724140, -93636720, 19817671, 2314120, -383844, -41520, 5646, 560, -60, -8, 1], 'lmfdb_label': '198550.t4', 'torsion': [2, 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: 4915146
    {'conductor': 198550, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '198550.t4', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4915147
    {'conductor': 198550, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '198550.t4', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 4915148
    {'conductor': 198550, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '198550.t4', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4915149
    {'conductor': 198550, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '198550.t4', 'prime': 19, '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: 2936443
    {'adelic_gens': [[8353, 8, 8352, 9], [6064, 6685, 4835, 5014], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [4811, 4810, 2730, 1891], [3343, 0, 0, 8359], [5651, 2300, 5690, 3141], [761, 1680, 8060, 6721], [7, 6, 8354, 8355]], 'adelic_image': '8360.48.0.?', 'conductor': 198550, 'lmfdb_label': '198550.t4', 'prime': 0}
  • id: 736994
    {'conductor': 198550, 'elladic_image': '4.6.0.1', 'lmfdb_label': '198550.t4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 198550.t does not appear in ec_padic