Elliptic curve data - 198450.ba4

Formats: - HTML - YAML - JSON - 2025-10-12T23:58:16.204057

• 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': '198450gp', 'Clabel': '198450gp2', 'Cnumber': 2, 'abc_quality': 1.4265653296335434, 'absD': 1953859444031250, 'adelic_genus': 21, 'adelic_index': 768, 'adelic_level': 2520, 'ainvs': [1, -1, 0, 31008, -333334], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 21, 'class_size': 4, 'cm': 0, 'conductor': 198450, 'degree': 933120, 'elladic_images': ['8.2.0.1', '3.4.0.1', '7.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6233931794287452148288425358', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 3, 'iso_nlabel': 26, 'isogeny_degrees': [1, 3, 7, 21], 'jinv': [3375, 2], 'lmfdb_iso': '198450.ba', 'lmfdb_label': '198450.ba4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, 3, -1], 'min_quad_twist_disc': 105, '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.2', '24.8.0.a.1', '35.16.0-7.a.1.2', '56.16.0.a.1', '63.192.5.e.2', '105.128.1.?', '168.128.5.?', '280.32.0.?', '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, 2, 2450], [5, 14, 7938], [7, 26, 4050]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.2528931399840713164194587395', 'prec': 103}, 'szpiro_ratio': 3.4955373124832594, '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.ba', 'trace_hash': 1448179643587337808}
• 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': '0.038899014656039250091254776773', 'prec': 107}, 'conductor': 198450, 'gens': [], 'heights': [], 'lmfdb_label': '198450.ba4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.27331816132630495780823925353', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.0932726453052198312329570141294544009', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 198450.ba4 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8708825
    {'degree': 2, 'field': [-26, -1, 1], 'lmfdb_label': '198450.ba4', 'torsion': [3]}
  • id: 8708826
    {'degree': 3, 'field': [-10, -3, 0, 1], 'lmfdb_label': '198450.ba4', 'torsion': [2]}
  • id: 8708830
    {'degree': 6, 'field': [-6144, 1152, 576, -162, -57, 0, 1], 'lmfdb_label': '198450.ba4', 'torsion': [6]}
  • id: 8708827
    {'degree': 6, 'field': [8, 0, 9, 0, -6, 0, 1], 'lmfdb_label': '198450.ba4', 'torsion': [2, 2]}
  • id: 8708828
    {'degree': 6, 'field': [785, -345, 264, -51, 30, -3, 1], 'lmfdb_label': '198450.ba4', 'torsion': [3]}
  • id: 8708829
    {'degree': 6, 'field': [1299, -306, 267, -41, 24, -3, 1], 'lmfdb_label': '198450.ba4', 'torsion': [7]}
  • id: 8708831
    {'degree': 12, 'field': [-197785846, 362297232, 56430063, -17855702, 19326753, -2245056, 744405, -40674, 10317, -320, 117, -6, 1], 'lmfdb_label': '198450.ba4', 'torsion': [4]}
  • id: 8708834
    {'degree': 12, 'field': [531441, 0, 0, -18954, 0, 0, -53, 0, 0, -26, 0, 0, 1], 'lmfdb_label': '198450.ba4', 'torsion': [21]}
  • id: 8708832
    {'degree': 12, 'field': [996004, 0, 455400, 0, 96960, 0, 12379, 0, 975, 0, 45, 0, 1], 'lmfdb_label': '198450.ba4', 'torsion': [3, 3]}
  • id: 8708833
    {'degree': 12, 'field': [65157184, 0, -7826544, 0, 1111185, 0, -89468, 0, 4374, 0, -108, 0, 1], 'lmfdb_label': '198450.ba4', 'torsion': [2, 6]}
  • id: 8708835
    {'degree': 18, 'field': [-2662233164, 273280320, 1905048180, 69535842, 225739458, 84378078, 6509931, 13627260, -770796, 862229, -138177, 28458, -7455, 1368, -351, -75, -18, 0, 1], 'lmfdb_label': '198450.ba4', 'torsion': [9]}
  • id: 8708838
    {'degree': 18, 'field': [70187849, 2359338, 140603643, -31147779, 103038339, -25881681, 37620315, -8416533, 7831899, -1446192, 990804, -143157, 77391, -8157, 3627, -246, 93, -3, 1], 'lmfdb_label': '198450.ba4', 'torsion': [21]}
  • id: 8708836
    {'degree': 18, 'field': [75746409, -125897463, 136897155, -126191652, 97931232, -53819964, 37061424, -12702846, 8154723, -1807409, 1076547, -157614, 85608, -8256, 3984, -240, 99, -3, 1], 'lmfdb_label': '198450.ba4', 'torsion': [6]}
  • id: 8708837
    {'degree': 18, 'field': [731965301, -133858146, 565500843, -113923873, 211170099, -41624337, 48175287, -8694201, 7303407, -1153826, 761322, -100917, 54639, -5733, 2607, -194, 75, -3, 1], 'lmfdb_label': '198450.ba4', 'torsion': [14]}
• 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: 4912815
    {'conductor': 198450, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '198450.ba4', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 4912816
    {'conductor': 198450, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '198450.ba4', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 4912817
    {'conductor': 198450, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '198450.ba4', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4912818
    {'conductor': 198450, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '198450.ba4', '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: 2935572
    {'adelic_gens': [[1, 0, 1470, 1], [281, 1400, 1120, 1401], [1, 930, 1050, 1261], [2311, 1050, 735, 211], [503, 0, 0, 2519], [1479, 350, 560, 879], [2519, 1470, 0, 1439], [1, 720, 0, 1], [1, 1680, 0, 1], [1471, 1290, 420, 2311], [2101, 1050, 2205, 1051], [505, 2016, 504, 505], [526, 825, 2205, 1681], [1, 0, 1680, 1], [1, 0, 2016, 1], [841, 1680, 840, 1681], [1, 0, 420, 1]], 'adelic_image': '2520.768.21.?', 'conductor': 198450, 'lmfdb_label': '198450.ba4', 'prime': 0}
  • id: 736260
    {'conductor': 198450, 'elladic_image': '8.2.0.1', 'lmfdb_label': '198450.ba4', 'modell_image': '2G', 'prime': 2}
  • id: 736261
    {'conductor': 198450, 'elladic_image': '3.4.0.1', 'lmfdb_label': '198450.ba4', 'modell_image': '3B', 'prime': 3}
  • id: 736262
    {'conductor': 198450, 'elladic_image': '7.8.0.1', 'lmfdb_label': '198450.ba4', 'modell_image': '7B', 'prime': 7}
• lmfdb_iso 198450.ba does not appear in ec_padic