Elliptic curve data - 304704.bj1

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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': '304704bj', 'Clabel': '304704bj3', 'Cnumber': 3, 'abc_quality': 1.0646600114779046, 'absD': 8538121601502225629184, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 552, 'ainvs': [0, 0, 0, -75268236, 251303058160], 'analytic_rank': 1, 'bad_primes': [2, 3, 23], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 304704, 'degree': 25952256, 'elladic_images': ['8.12.0.9'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.2117882765157375052268482225', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 35, 'isogeny_degrees': [1, 2, 4], 'jinv': [1666957239793, 301806], 'lmfdb_iso': '304704.bj', 'lmfdb_label': '304704.bj1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -247, 1391], 'min_quad_twist_disc': 552, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.p.1', '24.24.0-8.p.1.2', '184.24.0.?', '276.12.0.?', '552.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.7714663025266066909651706494', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 4761], [3, 8, 33856], [23, 288, 576]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.055014253377189850000001005947', 'prec': 107}, 'szpiro_ratio': 5.228700950883607, '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, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, -8, 0], 'aplist': [0, 0, -2, 0, 0, 2, 2, -8, 0, -2, -8, 2, -10, 8, -8, -2, -4, 2, 8, 0, -6, -8, 16, 18, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 304704, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '304704.bj', 'trace_hash': 1601158005579068436}
• 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': '0.0016228416636537283504012958593', 'prec': 110}, 'conductor': 304704, 'gens': [[1173, 405743, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '4.7714663025266066909651706494', 'prec': 100}], 'lmfdb_label': '304704.bj1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.12664405326218982877556800182', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.8342226604473883563887300209808556098', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[5060, 0, 1]], 'xcoord_integral_points': [1173, 5060]}
• lmfdb_label 304704.bj1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 12875501
    {'degree': 2, 'field': [-46, 0, 1], 'lmfdb_label': '304704.bj1', 'torsion': [2, 2]}
  • id: 12875502
    {'degree': 2, 'field': [-17, -1, 1], 'lmfdb_label': '304704.bj1', 'torsion': [4]}
  • id: 12875503
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '304704.bj1', 'torsion': [4]}
  • id: 12875504
    {'degree': 4, 'field': [100, 0, -26, 0, 1], 'lmfdb_label': '304704.bj1', 'torsion': [2, 4]}
  • id: 12875508
    {'degree': 8, 'field': [-514188, 0, 68310, 0, -2484, 0, 0, 0, 1], 'lmfdb_label': '304704.bj1', 'torsion': [6]}
  • id: 12875506
    {'degree': 8, 'field': [4, 0, -800, 0, 306, 0, -32, 0, 1], 'lmfdb_label': '304704.bj1', 'torsion': [8]}
  • id: 12875507
    {'degree': 8, 'field': [3364, 0, -2548, 0, 693, 0, 56, 0, 1], 'lmfdb_label': '304704.bj1', 'torsion': [8]}
  • id: 12875505
    {'degree': 8, 'field': [21904, 0, 14112, 0, -152, 0, 24, 0, 1], 'lmfdb_label': '304704.bj1', 'torsion': [2, 4]}
  • id: 12875514
    {'degree': 16, 'field': [-4163319, 7673940, -6314760, 5922720, -5839020, -1915596, 3579120, -66600, -172374, -22668, -22760, 3720, 2208, -124, -72, 0, 1], 'lmfdb_label': '304704.bj1', 'torsion': [12]}
  • id: 12875511
    {'degree': 16, 'field': [14641, 0, -64372, 0, 105800, 0, -83064, 0, 34271, 0, -7704, 0, 920, 0, -52, 0, 1], 'lmfdb_label': '304704.bj1', 'torsion': [2, 8]}
  • id: 12875513
    {'degree': 16, 'field': [104976, 0, -8438904, 0, 2430324, 0, -351864, 0, -4212, 0, 3276, 0, -324, 0, 0, 0, 1], 'lmfdb_label': '304704.bj1', 'torsion': [12]}
  • id: 12875509
    {'degree': 16, 'field': [1874161, 0, 0, 0, 3215740, 0, 0, 0, -38154, 0, 0, 0, 220, 0, 0, 0, 1], 'lmfdb_label': '304704.bj1', 'torsion': [4, 4]}
  • id: 12875510
    {'degree': 16, 'field': [37015056, 0, -9612720, 0, 908476, 0, -266364, 0, 43077, 0, 28, 0, -117, 0, -12, 0, 1], 'lmfdb_label': '304704.bj1', 'torsion': [2, 8]}
  • id: 12875512
    {'degree': 16, 'field': [38340864, 0, -209347840, 0, 124979776, 0, -32354400, 0, 3720752, 0, -223280, 0, 7185, 0, -106, 0, 1], 'lmfdb_label': '304704.bj1', '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: 7545272
    {'conductor': 304704, 'conductor_valuation': 6, 'discriminant_valuation': 19, 'j_denominator_valuation': 1, 'kodaira_symbol': -13, 'lmfdb_label': '304704.bj1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 7545273
    {'conductor': 304704, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '304704.bj1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 7545274
    {'conductor': 304704, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '304704.bj1', 'prime': 23, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

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

  
  
  • id: 3578761
    {'adelic_gens': [[344, 429, 111, 266], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [7, 6, 546, 547], [164, 183, 345, 362], [256, 537, 465, 328], [367, 0, 0, 551], [545, 8, 544, 9]], 'adelic_image': '552.48.0.?', 'conductor': 304704, 'lmfdb_label': '304704.bj1', 'prime': 0}
  • id: 1072166
    {'conductor': 304704, 'elladic_image': '8.12.0.9', 'lmfdb_label': '304704.bj1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 304704.bj does not appear in ec_padic