Elliptic curve data - 248004.b1

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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': '248004b', 'Clabel': '248004b1', 'Cnumber': 1, 'abc_quality': 0.7810665563237756, 'absD': 136734436256980029696, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 996, 'ainvs': [0, 0, 0, -764679, 618673534], 'analytic_rank': 0, 'bad_primes': [2, 3, 83], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 248004, 'degree': 7934976, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.5509871635314147313850098147', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 3], 'jinv': [-810448, 2241], 'lmfdb_iso': '248004.b', 'lmfdb_label': '248004.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -12, 36], 'min_quad_twist_disc': 249, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '12.8.0-3.a.1.3', '249.8.0.?', '996.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 62001], [3, 2, 27556], [83, 3528, 36]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.66983740507423594899517032971', 'prec': 107}, 'szpiro_ratio': 4.348156493202755, '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, 0, 0, -3, 0, 2, 0, 0, 0, 3, 0, 4, 0, 0, 0, 0, 0, 7, 0], 'aplist': [0, 0, -3, 2, 3, 4, 0, 7, 3, 6, 8, 11, 0, 4, -12, -3, 9, -1, 13, 6, 10, -8, 0, 3, -8], 'class_deg': 3, 'class_size': 2, 'conductor': 248004, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '248004.b', 'trace_hash': 598051263792874562}
• 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': '0.0060847214684195603759877151730', 'prec': 110}, 'conductor': 248004, 'gens': [], 'heights': [], 'lmfdb_label': '248004.b1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.16252502527417838227231334832', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.9006006065802811745355203597188145299', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 248004.b1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 10677859
    {'degree': 2, 'field': [-62, -1, 1], 'lmfdb_label': '248004.b1', 'torsion': [3]}
  • id: 10677860
    {'degree': 3, 'field': [-6, 0, -1, 1], 'lmfdb_label': '248004.b1', 'torsion': [2]}
  • id: 10677863
    {'degree': 6, 'field': [48, 72, -77, 26, -4, -2, 1], 'lmfdb_label': '248004.b1', 'torsion': [6]}
  • id: 10677862
    {'degree': 6, 'field': [332, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '248004.b1', 'torsion': [3]}
  • id: 10677861
    {'degree': 6, 'field': [996, 0, 1, 0, -2, 0, 1], 'lmfdb_label': '248004.b1', 'torsion': [2, 2]}
  • id: 10677864
    {'degree': 12, 'field': [1296, -432, -1728, -3096, -252, 0, 864, 24, 36, -84, 0, -2, 1], 'lmfdb_label': '248004.b1', 'torsion': [4]}
  • id: 10677866
    {'degree': 12, 'field': [2304, 0, 12576, 0, 1801, 0, -324, 0, -34, 0, 12, 0, 1], 'lmfdb_label': '248004.b1', 'torsion': [2, 6]}
  • id: 10677865
    {'degree': 12, 'field': [110889, -1998, -4959, 13230, -4890, -2118, 805, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '248004.b1', 'torsion': [3, 3]}
  • id: 10677868
    {'degree': 18, 'field': [53770896, -17489760, 30982416, -34043456, 9680640, -10441104, 4466584, 1238016, -872940, 279040, 13236, -6324, 1897, -366, 195, -56, 15, -6, 1], 'lmfdb_label': '248004.b1', 'torsion': [6]}
  • id: 10677867
    {'degree': 18, 'field': [1746457875, -1360642860, 365665428, -167250024, -206365509, -1947294, 60644001, 16834068, 4899519, -681150, -1949760, -117252, 207358, -16332, -6087, 766, 15, -6, 1], 'lmfdb_label': '248004.b1', 'torsion': [9]}
• 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: 6146749
    {'conductor': 248004, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '248004.b1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
  • id: 6146750
    {'conductor': 248004, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '248004.b1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 6146751
    {'conductor': 248004, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '248004.b1', 'prime': 83, '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: 3238393
    {'adelic_gens': [[499, 6, 501, 19], [4, 3, 9, 7], [414, 575, 329, 894], [991, 6, 990, 7], [911, 990, 741, 977], [1, 6, 0, 1], [3, 4, 8, 11], [1, 0, 6, 1]], 'adelic_image': '996.16.0.?', 'conductor': 248004, 'lmfdb_label': '248004.b1', 'prime': 0}
  • id: 895512
    {'conductor': 248004, 'elladic_image': '3.4.0.1', 'lmfdb_label': '248004.b1', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 248004.b does not appear in ec_padic