Elliptic curve data - 267696.ep2

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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': '267696ep', 'Clabel': '267696ep1', 'Cnumber': 1, 'abc_quality': 0.9963908492093383, 'absD': 20720474678573102923776, 'adelic_genus': 1, 'adelic_index': 48, 'adelic_level': 1560, 'ainvs': [0, 0, 0, 6813573, 1049783722], 'analytic_rank': 1, 'bad_primes': [2, 3, 11, 13], 'class_deg': 5, 'class_size': 2, 'cm': 0, 'conductor': 267696, 'degree': 14515200, 'elladic_images': ['5.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.9714644608976976098244191692', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 119, 'isogeny_degrees': [1, 5], 'jinv': [2427173723519, 1437646496], 'lmfdb_iso': '267696.ep', 'lmfdb_label': '267696.ep2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, 280, 393], 'min_quad_twist_disc': 156, 'modell_images': ['5B.4.1'], 'modm_images': ['5.12.0.a.1', '104.2.0.?', '120.24.0.?', '520.24.1.?', '780.24.0.?', '1560.48.1.?'], 'nonmax_primes': [5], 'nonmax_rad': 5, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '16.003290291249999628553860627', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.44653645727292908668282070850', 'prec': 103}, 'szpiro_ratio': 4.706251629695537, '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, 1, 0, 3, 0, 0, 0, -1, 0, 0, 0, 0, 0, -3, 0, 0, 0], 'aplist': [0, 0, 1, 3, -1, 0, -3, 0, 4, 0, -8, 7, -8, 1, 7, 6, -10, -8, 8, -7, 16, -10, -4, 0, -8], 'class_deg': 5, 'class_size': 2, 'conductor': 267696, 'isogeny_matrix': [[1, 5], [5, 1]], 'lmfdb_iso': '267696.ep', 'trace_hash': 1556244395005588670}
• 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': '0.0026243319205304805565844728535', 'prec': 110}, 'conductor': 267696, 'gens': [[-42809793, 1120177641154, 541]], 'heights': [{'__RealLiteral__': 0, 'data': '16.003290291249999628553860627', 'prec': 100}], 'lmfdb_label': '267696.ep2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.073918331899874343948025000183', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '9.4634921859092338251337013354949947899', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 267696.ep2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11450272
    {'degree': 2, 'field': [-39, 0, 1], 'lmfdb_label': '267696.ep2', 'torsion': [5]}
  • id: 11450273
    {'degree': 3, 'field': [-2, -1, 0, 1], 'lmfdb_label': '267696.ep2', 'torsion': [2]}
  • id: 11450275
    {'degree': 6, 'field': [-92, -84, 46, 32, -8, -2, 1], 'lmfdb_label': '267696.ep2', 'torsion': [10]}
  • id: 11450274
    {'degree': 6, 'field': [26, 0, 29, 0, 8, 0, 1], 'lmfdb_label': '267696.ep2', 'torsion': [2, 2]}
  • id: 11450276
    {'degree': 8, 'field': [-8112, 0, 6201, 0, -1365, 0, -13, 0, 1], 'lmfdb_label': '267696.ep2', 'torsion': [3]}
  • id: 11450277
    {'degree': 12, 'field': [-61952, -87040, -44344, 69294, -24270, 3252, 1756, -1894, 238, 148, -32, -5, 1], 'lmfdb_label': '267696.ep2', 'torsion': [4]}
  • id: 11450278
    {'degree': 12, 'field': [4, 0, 104, 0, 28, 0, 100, 0, 49, 0, 12, 0, 1], 'lmfdb_label': '267696.ep2', 'torsion': [2, 10]}
  • id: 11450279
    {'degree': 16, 'field': [3031528308, -778387608, 811375780, -65407316, 32731798, -4079902, 8052245, -5621974, 1236248, 154106, -72421, 23086, -4151, 112, 4, -8, 1], 'lmfdb_label': '267696.ep2', 'torsion': [15]}
  • id: 11450280
    {'degree': 20, 'field': [20914250298379649641, -2737607831035513394, 3018962401969082114, -311136714406415054, 185213656773619859, -15333760674880482, 6396759578390816, -428873581582566, 138297712925696, -7484793550566, 1961815112099, -84410328658, 18538545193, -614985818, 115480178, -2793308, 454643, -7188, 1023, -8, 1], 'lmfdb_label': '267696.ep2', 'torsion': [5]}
• 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: 6635724
    {'conductor': 267696, 'conductor_valuation': 4, 'discriminant_valuation': 17, 'j_denominator_valuation': 5, 'kodaira_symbol': -13, 'lmfdb_label': '267696.ep2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 6635725
    {'conductor': 267696, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '267696.ep2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 6635726
    {'conductor': 267696, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '267696.ep2', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6635727
    {'conductor': 267696, 'conductor_valuation': 2, 'discriminant_valuation': 11, 'j_denominator_valuation': 5, 'kodaira_symbol': -9, 'lmfdb_label': '267696.ep2', 'prime': 13, '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: 3357621
    {'adelic_gens': [[1039, 0, 0, 1559], [6, 13, 1505, 1441], [1169, 510, 645, 989], [479, 510, 315, 989], [1, 0, 10, 1], [1, 10, 0, 1], [1551, 10, 1550, 11], [391, 270, 0, 1327], [781, 1050, 1305, 571]], 'adelic_image': '1560.48.1.?', 'conductor': 267696, 'lmfdb_label': '267696.ep2', 'prime': 0}
  • id: 958079
    {'conductor': 267696, 'elladic_image': '5.12.0.1', 'lmfdb_label': '267696.ep2', 'modell_image': '5B.4.1', 'prime': 5}
• lmfdb_iso 267696.ep does not appear in ec_padic