Elliptic curve data - 198744.d1

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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': '198744bi', 'Clabel': '198744bi1', 'Cnumber': 1, 'abc_quality': 0.9643192035105397, 'absD': 1192464, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1092, 'ainvs': [0, -1, 0, -212, -1119], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 13], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 198744, 'degree': 48384, 'elladic_images': ['2.2.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.079792321199993876739664637848', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 3, 'isogeny_degrees': [1], 'jinv': [7990528, 9], 'lmfdb_iso': '198744.d', 'lmfdb_label': '198744.d1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -212, -1119], 'min_quad_twist_disc': 1, 'modell_images': ['2Cn'], 'modm_images': ['2.2.0.a.1', '182.6.0.?', '1092.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 4, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.84249425829768122365863876771', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 8281], [3, 4, 66248], [13, 38, 1176]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.90306665673946289992588610014', 'prec': 107}, 'szpiro_ratio': 2.26955661297059, '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, 0, -1, 0, -3, 0, 0, 0, 1, 0, -4, 0, 0, 0, 3, 0, 3, 0, 4, 0], 'aplist': [0, -1, -3, 0, -4, 0, 3, 4, -1, 9, 1, -7, 9, 1, -3, 9, -11, 2, -8, -3, 3, 3, 0, -15, 7], 'class_deg': 1, 'class_size': 1, 'conductor': 198744, 'isogeny_matrix': [[1]], 'lmfdb_iso': '198744.d', 'trace_hash': 578719591998265418}
• 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': '0.85249780688218800230865351738', 'prec': 103}, 'conductor': 198744, 'gens': [[-8, 1, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.84249425829768122365863876771', 'prec': 103}], 'lmfdb_label': '198744.d1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.2507611434554694852407806416', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.2150363274523017107923032743015560848', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': [-8, 21]}
• lmfdb_label 198744.d1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8720368
    {'degree': 3, 'field': [-27, -30, -1, 1], 'lmfdb_label': '198744.d1', 'torsion': [2, 2]}
  • id: 8720369
    {'degree': 8, 'field': [-1217307, 0, -128492, 0, -3822, 0, 0, 0, 1], 'lmfdb_label': '198744.d1', 'torsion': [3]}
  • id: 8720370
    {'degree': 12, 'field': [6487209, 0, 177624, 0, -483426, 0, -126106, 0, 617, 0, -50, 0, 1], 'lmfdb_label': '198744.d1', 'torsion': [2, 4]}
• 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: 4920060
    {'conductor': 198744, 'conductor_valuation': 3, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '198744.d1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 4920061
    {'conductor': 198744, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '198744.d1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4920062
    {'conductor': 198744, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '198744.d1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 4920063
    {'conductor': 198744, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '198744.d1', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 2937687
    {'adelic_gens': [[157, 3, 157, 4], [1089, 4, 1088, 5], [1, 2, 2, 5], [549, 4, 554, 11], [3, 2, 1084, 1087], [1, 4, 0, 1], [3, 4, 736, 11], [424, 1, 591, 1], [1, 0, 4, 1]], 'adelic_image': '1092.12.0.?', 'conductor': 198744, 'lmfdb_label': '198744.d1', 'prime': 0}
  • id: 737556
    {'conductor': 198744, 'elladic_image': '2.2.0.1', 'lmfdb_label': '198744.d1', 'modell_image': '2Cn', 'prime': 2}
• lmfdb_iso 198744.d does not appear in ec_padic