Elliptic curve data - 398544.bf3

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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': '398544bf', 'Clabel': '398544bf2', 'Cnumber': 2, 'abc_quality': 0.9444691501696788, 'absD': 33027996958212096, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 3496, 'ainvs': [0, -1, 0, -98312, 8052720], 'analytic_rank': 0, 'bad_primes': [2, 3, 19, 23], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 398544, 'degree': 2322432, 'elladic_images': ['8.12.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8738073332403827347131307826', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 31, 'isogeny_degrees': [1, 2], 'jinv': [545338513, 171396], 'lmfdb_iso': '398544.bf', 'lmfdb_label': '398544.bf3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -17, 11], 'min_quad_twist_disc': 76, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '8.12.0.a.1', '76.12.0.?', '92.12.0.?', '152.24.0.?', '184.24.0.?', '1748.24.0.?', '3496.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 361], [3, 4, 132848], [19, 182, 1104], [23, 24, 17328]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.29155933690278280470861505480', 'prec': 107}, 'szpiro_ratio': 3.5749723307619328, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, -1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 2, 0, -2, 0, 2, 0, 0, 0], 'aplist': [0, -1, 2, 0, 0, 2, 2, 0, 1, 2, -8, -2, -10, -8, -8, -2, -4, 2, 8, 0, -6, 8, 16, -18, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 398544, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '398544.bf', 'trace_hash': 2103978202970237707}
• 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': '0.023573910482548896037408297746', 'prec': 107}, 'conductor': 398544, 'gens': [], 'heights': [], 'lmfdb_label': '398544.bf3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.34130884603717554711184693453', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.3652353841487021884473877381310212354', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[89, 0, 1], [260, 0, 1]], 'xcoord_integral_points': [-348, 89, 260]}
• lmfdb_label 398544.bf3 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 16441641
    {'degree': 4, 'field': [1, 0, 21, 0, 1], 'lmfdb_label': '398544.bf3', 'torsion': [2, 4]}
  • id: 16441640
    {'degree': 4, 'field': [81, 0, -20, 0, 1], 'lmfdb_label': '398544.bf3', 'torsion': [2, 4]}
  • id: 16441642
    {'degree': 4, 'field': [441, 0, -4, 0, 1], 'lmfdb_label': '398544.bf3', 'torsion': [2, 4]}
  • id: 16441643
    {'degree': 8, 'field': [-6255408, 0, 192052, 0, -8664, 0, 0, 0, 1], 'lmfdb_label': '398544.bf3', 'torsion': [2, 6]}
  • id: 16441645
    {'degree': 16, 'field': [-7789383, 27163080, -14782608, -17655600, 14108992, 3128760, -4578336, -215520, 754518, 600, -69616, 720, 3600, -24, -96, 0, 1], 'lmfdb_label': '398544.bf3', 'torsion': [2, 8]}
  • id: 16441646
    {'degree': 16, 'field': [1972741, 12396706, 32453950, -9279590, 12133976, -464324, 413832, 6718, 13673, -38452, 3744, -874, 524, 2, 34, -4, 1], 'lmfdb_label': '398544.bf3', 'torsion': [2, 8]}
  • id: 16441644
    {'degree': 16, 'field': [146434201, 0, -15727804, 0, -4766946, 0, 245080, 0, 73027, 0, -440, 0, -426, 0, -4, 0, 1], 'lmfdb_label': '398544.bf3', 'torsion': [4, 4]}
  • id: 16441647
    {'degree': 16, 'field': [7517560356, -11953298352, 10359432328, -6058218272, 2985362104, -1102286328, 350969540, -85862200, 17182373, -2419440, 200600, 9728, -3646, 312, 28, -8, 1], 'lmfdb_label': '398544.bf3', 'torsion': [2, 8]}
• 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: 9858892
    {'conductor': 398544, 'conductor_valuation': 4, 'discriminant_valuation': 14, 'j_denominator_valuation': 2, 'kodaira_symbol': -10, 'lmfdb_label': '398544.bf3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 9858893
    {'conductor': 398544, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '398544.bf3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 9858894
    {'conductor': 398544, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '398544.bf3', 'prime': 19, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 9858895
    {'conductor': 398544, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '398544.bf3', 'prime': 23, 'reduction_type': 1, '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: 4136131
    {'adelic_gens': [[3493, 4, 3492, 5], [1749, 1292, 2394, 2585], [1, 4, 0, 1], [1, 0, 4, 1], [3041, 2394, 0, 1], [2943, 0, 0, 3495], [227, 2204, 912, 2013]], 'adelic_image': '3496.48.0.?', 'conductor': 398544, 'lmfdb_label': '398544.bf3', 'prime': 0}
  • id: 1355679
    {'conductor': 398544, 'elladic_image': '8.12.0.3', 'lmfdb_label': '398544.bf3', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 398544.bf does not appear in ec_padic