Elliptic curve data - 259920.bw1

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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': '259920bw', 'Clabel': '259920bw2', 'Cnumber': 2, 'abc_quality': 0.9720873477579399, 'absD': 1756052201424584079360000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 228, 'ainvs': [0, 0, 0, -34960323, 47595574978], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 19], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 259920, 'degree': 28016640, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.3520242117915832522778435801', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 48, 'isogeny_degrees': [1, 2], 'jinv': [4904335099, 1822500], 'lmfdb_iso': '259920.bw', 'lmfdb_label': '259920.bw1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -673, -4072], 'min_quad_twist_disc': -228, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '12.6.0.g.1', '76.6.0.?', '228.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '9.9149741616683642214065989717', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.098758347477247247843781733735', 'prec': 110}, 'szpiro_ratio': 5.1108530562720205, '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, -1, 0, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, 2, 0, 0, 0], 'aplist': [0, 0, -1, 0, 2, -4, 2, 0, -6, -2, -4, 8, 6, 8, -6, -6, -4, -6, -8, 0, -14, -8, -6, 6, 0], 'class_deg': 2, 'class_size': 2, 'conductor': 259920, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '259920.bw', 'trace_hash': 1627307217129167480}
• 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': '0.0012259387234583281266350731878', 'prec': 110}, 'conductor': 259920, 'gens': [[549047, 353587842, 7]], 'heights': [{'__RealLiteral__': 0, 'data': '9.9149741616683642214065989717', 'prec': 100}], 'lmfdb_label': '259920.bw1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.076577707881976884744441697673', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.0741279600767091995684318287514395455', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[5054, 0, 1]], 'xcoord_integral_points': [5054]}
• lmfdb_label 259920.bw1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11144837
    {'degree': 2, 'field': [-19, 0, 1], 'lmfdb_label': '259920.bw1', 'torsion': [2, 2]}
  • id: 11144838
    {'degree': 4, 'field': [76, 0, -19, 0, 1], 'lmfdb_label': '259920.bw1', 'torsion': [4]}
  • id: 11144841
    {'degree': 8, 'field': [-243675, 0, 0, 0, 1710, 0, -76, 0, 1], 'lmfdb_label': '259920.bw1', 'torsion': [6]}
  • id: 11144839
    {'degree': 8, 'field': [1, 0, -15, 0, 44, 0, -15, 0, 1], 'lmfdb_label': '259920.bw1', 'torsion': [2, 4]}
  • id: 11144840
    {'degree': 8, 'field': [294, -252, 376, 58, 71, 52, 14, -2, 1], 'lmfdb_label': '259920.bw1', 'torsion': [2, 4]}
  • id: 11144843
    {'degree': 16, 'field': [419904, 0, -1618704, 0, 245916, 0, -126171, 0, 33390, 0, -6579, 0, 789, 0, -46, 0, 1], 'lmfdb_label': '259920.bw1', 'torsion': [2, 6]}
  • id: 11144842
    {'degree': 16, 'field': [18284176, 0, -9023640, 0, 1091152, 0, -46710, 0, 9873, 0, 2820, 0, -398, 0, -30, 0, 1], 'lmfdb_label': '259920.bw1', 'torsion': [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: 6443140
    {'conductor': 259920, 'conductor_valuation': 4, 'discriminant_valuation': 14, 'j_denominator_valuation': 2, 'kodaira_symbol': -10, 'lmfdb_label': '259920.bw1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 6443141
    {'conductor': 259920, 'conductor_valuation': 2, 'discriminant_valuation': 12, 'j_denominator_valuation': 6, 'kodaira_symbol': -10, 'lmfdb_label': '259920.bw1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 6443142
    {'conductor': 259920, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '259920.bw1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6443143
    {'conductor': 259920, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '259920.bw1', 'prime': 19, '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: 3310767
    {'adelic_gens': [[172, 61, 57, 172], [160, 1, 131, 0], [225, 4, 224, 5], [1, 4, 0, 1], [1, 0, 4, 1], [77, 4, 154, 9], [3, 4, 8, 11], [1, 2, 2, 5]], 'adelic_image': '228.12.0.?', 'conductor': 259920, 'lmfdb_label': '259920.bw1', 'prime': 0}
  • id: 933441
    {'conductor': 259920, 'elladic_image': '2.3.0.1', 'lmfdb_label': '259920.bw1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 259920.bw does not appear in ec_padic