Elliptic curve data - 198550.j4

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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': '198550ca', 'Clabel': '198550ca4', 'Cnumber': 4, 'abc_quality': 0.9490054959708933, 'absD': 4184548518859460640625000, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 25080, 'ainvs': [1, 0, 1, 33947349, 62377895198], 'analytic_rank': 1, 'bad_primes': [2, 5, 11, 19], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 198550, 'degree': 44789760, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.4115177484519531311510165124', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 6, 'iso_nlabel': 9, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [5885721311824151, 5692551601000], 'lmfdb_iso': '198550.j', 'lmfdb_label': '198550.j4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 3761, -72438], 'min_quad_twist_disc': -95, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '40.6.0.a.1', '120.24.0.?', '264.24.0.?', '285.8.0.?', '456.24.0.?', '570.24.0.?', '660.24.0.?', '836.6.0.?', '1320.48.0.?', '2280.48.0.?', '2508.24.0.?', '5016.48.0.?', '8360.12.0.?', '12540.48.0.?', '25080.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '11.429859413571095611503797598', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 9025], [3, 2, 99275], [5, 18, 7942], [11, 12, 18050], [19, 200, 550]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1345793026516827138461231298', 'prec': 100}, 'szpiro_ratio': 5.216462822361044, '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, -2, 1, 0, 2, 4, -1, 1, 0, 1, -2, 2, -4, 0, 1, 0, -1, 0, 0], 'aplist': [-1, -2, 0, 4, 1, 2, 0, 0, 0, -6, -2, 2, -6, 10, 0, -6, 12, 8, 14, 6, 4, 4, -6, -6, -16], 'class_deg': 6, 'class_size': 4, 'conductor': 198550, 'isogeny_matrix': [[1, 3, 6, 2], [3, 1, 2, 6], [6, 2, 1, 3], [2, 6, 3, 1]], 'lmfdb_iso': '198550.j', 'trace_hash': 1889704695701203133}
• 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': '0.0010884120314047478267794821981', 'prec': 110}, 'conductor': 198550, 'gens': [[2172771, 7923744167, 26]], 'heights': [{'__RealLiteral__': 0, 'data': '11.429859413571095611503797598', 'prec': 100}], 'lmfdb_label': '198550.j4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.051200996952108059567897360727', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.6817615759782182360741167233188034332', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-6777, 6773, 2]], 'xcoord_integral_points': []}
• lmfdb_label 198550.j4 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8712657
    {'degree': 2, 'field': [-71, -1, 1], 'lmfdb_label': '198550.j4', 'torsion': [6]}
  • id: 8712656
    {'degree': 2, 'field': [10, 0, 1], 'lmfdb_label': '198550.j4', 'torsion': [2, 2]}
  • id: 8712658
    {'degree': 4, 'field': [-160, 0, 14, 0, 1], 'lmfdb_label': '198550.j4', 'torsion': [4]}
  • id: 8712659
    {'degree': 4, 'field': [676, 0, 62, 0, 1], 'lmfdb_label': '198550.j4', 'torsion': [2, 6]}
  • id: 8712660
    {'degree': 6, 'field': [14726, -3279, 1767, -123, 75, -3, 1], 'lmfdb_label': '198550.j4', 'torsion': [6]}
  • id: 8712663
    {'degree': 8, 'field': [2116, 0, 254, 0, -589, 0, 49, 0, 1], 'lmfdb_label': '198550.j4', 'torsion': [12]}
  • id: 8712662
    {'degree': 8, 'field': [40000, 0, 19840, 0, 756, 0, 68, 0, 1], 'lmfdb_label': '198550.j4', 'torsion': [2, 4]}
  • id: 8712661
    {'degree': 8, 'field': [7372076, -1144560, 278376, -30400, 2736, -440, 76, 0, 1], 'lmfdb_label': '198550.j4', 'torsion': [2, 4]}
  • id: 8712665
    {'degree': 12, 'field': [3400409, -986172, -277044, -477180, 162126, 63096, -14114, 0, 1020, -44, -42, 0, 1], 'lmfdb_label': '198550.j4', 'torsion': [2, 6]}
  • id: 8712664
    {'degree': 12, 'field': [216855076, -48286554, -15269001, -2171397, 1614522, 230331, -97781, -1902, 3489, 21, -66, -3, 1], 'lmfdb_label': '198550.j4', 'torsion': [3, 6]}
  • id: 8712668
    {'degree': 16, 'field': [883600, 0, 95275280, 0, 79037596, 0, 19107244, 0, 2329665, 0, 162680, 0, 6310, 0, 124, 0, 1], 'lmfdb_label': '198550.j4', 'torsion': [2, 12]}
  • id: 8712667
    {'degree': 16, 'field': [2108559340, 3015100720, -1875930200, -2242324320, 1035265656, 91547080, -11531748, -15822336, 3419269, 318376, -25976, -18712, 1602, 672, -76, -8, 1], 'lmfdb_label': '198550.j4', 'torsion': [2, 12]}
  • id: 8712666
    {'degree': 16, 'field': [34477062400, 0, 25652077440, 0, -26743509936, 0, 665157328, 0, 26300404, 0, 1264544, 0, -1896, 0, -20, 0, 1], 'lmfdb_label': '198550.j4', 'torsion': [8]}
  • id: 8712669
    {'degree': 18, 'field': [-439686726447159, 232745513508621, -16907526848781, -20225616201846, 4826097248040, 308485187766, -244715523414, 18014536134, 4119193089, -695328435, 10732659, 4564374, -437744, 72336, -6000, -116, 9, -9, 1], 'lmfdb_label': '198550.j4', 'torsion': [18]}
• 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: 4915046
    {'conductor': 198550, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '198550.j4', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 4915047
    {'conductor': 198550, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '198550.j4', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 4915048
    {'conductor': 198550, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '198550.j4', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4915049
    {'conductor': 198550, 'conductor_valuation': 2, 'discriminant_valuation': 12, 'j_denominator_valuation': 6, 'kodaira_symbol': -10, 'lmfdb_label': '198550.j4', 'prime': 19, '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: 2936423
    {'adelic_gens': [[11, 2, 25030, 25071], [9121, 12, 4566, 73], [16721, 12, 4180, 1], [5226, 1057, 17765, 13586], [1, 0, 12, 1], [25070, 25077, 10059, 8], [1, 6, 6, 37], [2639, 25068, 15834, 25007], [1, 12, 0, 1], [25069, 12, 25068, 13], [10, 3, 12513, 25072]], 'adelic_image': '25080.96.1.?', 'conductor': 198550, 'lmfdb_label': '198550.j4', 'prime': 0}
  • id: 736971
    {'conductor': 198550, 'elladic_image': '2.3.0.1', 'lmfdb_label': '198550.j4', 'modell_image': '2B', 'prime': 2}
  • id: 736972
    {'conductor': 198550, 'elladic_image': '3.4.0.1', 'lmfdb_label': '198550.j4', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 198550.j does not appear in ec_padic