Elliptic curve data - 397800.j3

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '397800j', 'Clabel': '397800j4', 'Cnumber': 4, 'abc_quality': 0.9632691528300815, 'absD': 3539992675781250000000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 26520, 'ainvs': [0, 0, 0, -19749675, 96621245750], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 13, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 397800, 'degree': 75497472, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.3956896824526952728551960584', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 9, 'isogeny_degrees': [1, 2, 4], 'jinv': [-73039208963041156, 303497314453125], 'lmfdb_iso': '397800.j', 'lmfdb_label': '397800.j3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -87776, -28657776], 'min_quad_twist_disc': -15, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '104.12.0.?', '120.12.0.?', '136.12.0.?', '780.12.0.?', '884.12.0.?', '1020.12.0.?', '1560.24.0.?', '1768.24.0.?', '2040.24.0.?', '13260.24.0.?', '26520.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 4, 'sha_primes': [2], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.4640419314349691486761670054', 'prec': 100}, 'szpiro_ratio': 4.972292780030168, '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, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 4, 0], 'aplist': [0, 0, 0, -4, 0, -1, 1, 4, -8, 10, -4, -10, 10, 4, 8, -10, -4, -2, 12, 12, 2, 8, 4, 6, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 397800, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '397800.j', 'trace_hash': 1224830928225509741}
• 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': '0.0011234181014457167823424396102', 'prec': 110}, 'conductor': 397800, 'gens': [], 'heights': [], 'lmfdb_label': '397800.j3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.068885533738530434921907416780', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.2043370796329739175010373369517381992', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-5990, 0, 1]], 'xcoord_integral_points': [-5990]}
• lmfdb_label 397800.j3 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 16412792
    {'degree': 2, 'field': [-195, 0, 1], 'lmfdb_label': '397800.j3', 'torsion': [4]}
  • id: 16412793
    {'degree': 2, 'field': [64, -1, 1], 'lmfdb_label': '397800.j3', 'torsion': [4]}
  • id: 16412791
    {'degree': 2, 'field': [221, 0, 1], 'lmfdb_label': '397800.j3', 'torsion': [2, 2]}
  • id: 16412794
    {'degree': 4, 'field': [10816, 0, 13, 0, 1], 'lmfdb_label': '397800.j3', 'torsion': [2, 4]}
  • id: 16412798
    {'degree': 8, 'field': [-8167500, 0, -538500, 0, -9900, 0, 0, 0, 1], 'lmfdb_label': '397800.j3', 'torsion': [6]}
  • id: 16412796
    {'degree': 8, 'field': [72361, 0, -250568, 0, -522, 0, -8, 0, 1], 'lmfdb_label': '397800.j3', 'torsion': [8]}
  • id: 16412795
    {'degree': 8, 'field': [29658201, -33846, 60802, -53658, 26195, 758, -248, -4, 1], 'lmfdb_label': '397800.j3', 'torsion': [2, 4]}
  • id: 16412797
    {'degree': 8, 'field': [200052736, 0, -480896, 0, 29376, 0, 34, 0, 1], 'lmfdb_label': '397800.j3', 'torsion': [8]}
  • id: 16412803
    {'degree': 16, 'field': [-37106820413815244, -23958662509444552, -7138284750016720, -1451388588979800, -211158662989420, -21010744231976, -1340846603648, -71460353520, -8232105500, -941313420, -39989468, 2740016, 301820, -1500, -880, -8, 1], 'lmfdb_label': '397800.j3', 'torsion': [12]}
  • id: 16412800
    {'degree': 16, 'field': [556811146789, -440391254368, 238413748218, -94252994056, 22885921528, -3678466324, 764468050, -151162232, 16889985, -2138396, 435206, -22984, 2524, -884, 4, 0, 1], 'lmfdb_label': '397800.j3', 'torsion': [2, 8]}
  • id: 16412799
    {'degree': 16, 'field': [60825330103716, -6958457892504, -10317089318328, 1513607261184, 554178415144, -138456122464, 14774716668, -2683746444, 389139033, -36005006, 3071438, -150838, 24975, -1482, -84, -8, 1], 'lmfdb_label': '397800.j3', 'torsion': [4, 4]}
  • id: 16412801
    {'degree': 16, 'field': [457163239653376, 0, 6722988818432, 0, -156661341952, 0, 641441280, 0, 90787616, 0, 138720, 0, -7327, 0, 68, 0, 1], 'lmfdb_label': '397800.j3', 'torsion': [2, 8]}
  • id: 16412804
    {'degree': 16, 'field': [2852444158925284, 0, -105641723539108, 0, 1778879482060, 0, 24200337644, 0, 468353305, 0, -13211284, 0, 114838, 0, -520, 0, 1], 'lmfdb_label': '397800.j3', 'torsion': [12]}
  • id: 16412802
    {'degree': 16, 'field': [172659961421678025, 33735886040520000, 9858178667443500, 1315770734234340, 236388815349840, 15728745258180, 1695746792916, 66618353628, 8522462010, 394487088, 59013768, 1084020, 255216, -1980, 736, -4, 1], 'lmfdb_label': '397800.j3', 'torsion': [2, 6]}
• 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: 9840224
    {'conductor': 397800, 'conductor_valuation': 3, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '397800.j3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 9840225
    {'conductor': 397800, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '397800.j3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 9840226
    {'conductor': 397800, 'conductor_valuation': 2, 'discriminant_valuation': 22, 'j_denominator_valuation': 16, 'kodaira_symbol': -20, 'lmfdb_label': '397800.j3', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 9840227
    {'conductor': 397800, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '397800.j3', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 9840228
    {'conductor': 397800, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '397800.j3', 'prime': 17, 'reduction_type': 1, '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: 4131863
    {'adelic_gens': [[5303, 0, 0, 26519], [26513, 8, 26512, 9], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [5971, 5970, 21450, 4651], [7, 6, 26514, 26515], [7756, 14145, 13215, 17686], [8839, 0, 0, 26519], [24976, 17025, 21465, 9136], [13216, 15915, 525, 14146]], 'adelic_image': '26520.48.0.?', 'conductor': 397800, 'lmfdb_label': '397800.j3', 'prime': 0}
  • id: 1353470
    {'conductor': 397800, 'elladic_image': '4.6.0.1', 'lmfdb_label': '397800.j3', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 397800.j does not appear in ec_padic