Elliptic curve data - 198450.hw2

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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': '198450v', 'Clabel': '198450v4', 'Cnumber': 4, 'abc_quality': 1.1123490200903752, 'absD': 227641124487168000000, 'adelic_genus': 21, 'adelic_index': 768, 'adelic_level': 2520, 'ainvs': [1, -1, 1, -1043930, -833699303], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 21, 'class_size': 4, 'cm': 0, 'conductor': 198450, 'degree': 6531840, 'elladic_images': ['8.2.0.1', '3.4.0.1', '7.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.5963482539564018673815189075', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 21, 'iso_nlabel': 204, 'isogeny_degrees': [1, 3, 7, 21], 'jinv': [-1159088625, 2097152], 'lmfdb_iso': '198450.hw', 'lmfdb_label': '198450.hw2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -852, 19664], 'min_quad_twist_disc': -35, 'modell_images': ['3B', '7B'], 'modm_images': ['3.4.0.a.1', '7.8.0.a.1', '8.2.0.a.1', '21.64.1.a.1', '24.8.0.a.1', '56.16.0.a.1', '63.192.5.e.3', '105.128.1.?', '168.128.5.?', '315.384.5.?', '504.384.21.?', '840.256.5.?', '2520.768.21.?'], 'nonmax_primes': [2, 3, 7], 'nonmax_rad': 42, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 99225], [3, 4, 35], [5, 14, 7938], [7, 26, 2025]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.096836017345063048634241494935', 'prec': 110}, 'szpiro_ratio': 4.476572307445777, '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, 0, 0, 0, 1, 0, 0, 3, 0, 2, 0, 0, 1, 3, 0, 1, 0], 'aplist': [1, 0, 0, 0, 3, 2, 3, 1, -6, -6, 4, 4, 9, 1, 6, 12, 3, -8, -5, 12, 11, -4, -12, 6, 5], 'class_deg': 21, 'class_size': 4, 'conductor': 198450, 'isogeny_matrix': [[1, 3, 21, 7], [3, 1, 7, 21], [21, 7, 1, 3], [7, 21, 3, 1]], 'lmfdb_iso': '198450.hw', 'trace_hash': 161178993457890801}
• 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': '0.0055570020937198928701792538248', 'prec': 110}, 'conductor': 198450, 'gens': [], 'heights': [], 'lmfdb_label': '198450.hw2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.070430811603466927209528433327', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.9161881746912218856003883994617490405', 'prec': 130}, 'tamagawa_product': 84, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 198450.hw2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8707038
    {'degree': 2, 'field': [-26, -1, 1], 'lmfdb_label': '198450.hw2', 'torsion': [3]}
  • id: 8707039
    {'degree': 3, 'field': [-10, -3, 0, 1], 'lmfdb_label': '198450.hw2', 'torsion': [2]}
  • id: 8707043
    {'degree': 6, 'field': [-6144, 1152, 576, -162, -57, 0, 1], 'lmfdb_label': '198450.hw2', 'torsion': [6]}
  • id: 8707040
    {'degree': 6, 'field': [8, 0, 9, 0, -6, 0, 1], 'lmfdb_label': '198450.hw2', 'torsion': [2, 2]}
  • id: 8707041
    {'degree': 6, 'field': [816, -396, 261, -49, 30, -3, 1], 'lmfdb_label': '198450.hw2', 'torsion': [3]}
  • id: 8707042
    {'degree': 6, 'field': [2304, 1296, 522, 3, -27, -3, 1], 'lmfdb_label': '198450.hw2', 'torsion': [7]}
  • id: 8707044
    {'degree': 12, 'field': [-556528076, 160632552, 32462868, -3782552, -935937, -382986, 143700, 6786, -5328, 310, 12, -6, 1], 'lmfdb_label': '198450.hw2', 'torsion': [4]}
  • id: 8707047
    {'degree': 12, 'field': [50176, -23520, 209916, 26264, -1911, -3528, 3836, 840, 126, -56, 0, 0, 1], 'lmfdb_label': '198450.hw2', 'torsion': [21]}
  • id: 8707045
    {'degree': 12, 'field': [529104, -360792, 458424, -209850, 142605, -48672, 22147, -5406, 1770, -290, 69, -6, 1], 'lmfdb_label': '198450.hw2', 'torsion': [3, 3]}
  • id: 8707046
    {'degree': 12, 'field': [65157184, 0, -7826544, 0, 1111185, 0, -89468, 0, 4374, 0, -108, 0, 1], 'lmfdb_label': '198450.hw2', 'torsion': [2, 6]}
  • id: 8707050
    {'degree': 18, 'field': [26736256, 28555872, 21730032, 7507976, -774468, -1779984, 24316, 495762, 291447, 66736, -5331, -10692, -1550, 816, 342, -6, -21, 0, 1], 'lmfdb_label': '198450.hw2', 'torsion': [14]}
  • id: 8707049
    {'degree': 18, 'field': [487743524, -622906668, 752052150, -557992062, 393927039, -208282221, 107420565, -43560432, 17638218, -5651298, 1854288, -469890, 125538, -24444, 5220, -720, 117, -9, 1], 'lmfdb_label': '198450.hw2', 'torsion': [6]}
  • id: 8707048
    {'degree': 18, 'field': [10065716224, 13882936320, -6439533696, -2608730016, 1023040656, -571455864, 92062812, 26900604, -12646818, 7613173, -1316187, 360666, -16716, 1440, 1890, -354, 90, -9, 1], 'lmfdb_label': '198450.hw2', '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: 4911899
    {'conductor': 198450, 'conductor_valuation': 1, 'discriminant_valuation': 21, 'j_denominator_valuation': 21, 'kodaira_symbol': 25, 'lmfdb_label': '198450.hw2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 21}
  • id: 4911900
    {'conductor': 198450, 'conductor_valuation': 4, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '198450.hw2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 4911901
    {'conductor': 198450, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '198450.hw2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4911902
    {'conductor': 198450, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '198450.hw2', 'prime': 7, '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: 2935861
    {'adelic_gens': [[1, 0, 1470, 1], [281, 1400, 1120, 1401], [1, 930, 1050, 1261], [2311, 1050, 735, 211], [503, 0, 0, 2519], [1439, 1110, 0, 2519], [1, 720, 0, 1], [1, 1680, 0, 1], [1471, 1290, 420, 2311], [2101, 1050, 2205, 1051], [526, 825, 2205, 1681], [505, 2016, 504, 505], [1, 0, 1680, 1], [1, 0, 2016, 1], [841, 1680, 840, 1681], [759, 1790, 560, 159], [1, 0, 420, 1]], 'adelic_image': '2520.768.21.?', 'conductor': 198450, 'lmfdb_label': '198450.hw2', 'prime': 0}
  • id: 736578
    {'conductor': 198450, 'elladic_image': '8.2.0.1', 'lmfdb_label': '198450.hw2', 'modell_image': '2G', 'prime': 2}
  • id: 736579
    {'conductor': 198450, 'elladic_image': '3.4.0.1', 'lmfdb_label': '198450.hw2', 'modell_image': '3B', 'prime': 3}
  • id: 736580
    {'conductor': 198450, 'elladic_image': '7.8.0.1', 'lmfdb_label': '198450.hw2', 'modell_image': '7B', 'prime': 7}
• lmfdb_iso 198450.hw does not appear in ec_padic