Elliptic curve data - 277725.ba2

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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': '277725ba', 'Clabel': '277725ba2', 'Cnumber': 2, 'abc_quality': 0.9046443494099247, 'absD': 35681819228943767578125, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 420, 'ainvs': [1, 0, 0, -14951138, 24034696017], 'analytic_rank': 1, 'bad_primes': [3, 5, 7, 23], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 277725, 'degree': 20275200, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.0686797043609191303916511236', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 26, 'isogeny_degrees': [1, 2], 'jinv': [-1278348920477, 123409881], 'lmfdb_iso': '277725.ba', 'lmfdb_label': '277725.ba2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -1130, -16275], 'min_quad_twist_disc': -115, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '20.6.0.a.1', '84.6.0.?', '420.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '7.6429835806950154596888662775', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 2645], [3, 4, 92575], [5, 14, 11109], [7, 8, 39675], [23, 288, 525]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.29385416207076900403770520777', 'prec': 103}, 'szpiro_ratio': 4.892842329568261, '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, -1, 1, -1, 0, -1, 1, 3, 1, 0, 2, -1, 2, -1, 0, -1, -4, -1, -2, 0], 'aplist': [-1, 1, 0, 1, 2, 2, -4, -2, 0, 6, 2, 8, -6, 4, 0, 6, 4, -14, -8, 10, 14, 8, -8, -6, -6], 'class_deg': 2, 'class_size': 2, 'conductor': 277725, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '277725.ba', 'trace_hash': 2215108250385130485}
• 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': '0.0021606214102683273667596557252', 'prec': 110}, 'conductor': 277725, 'gens': [[1413493, 1677884573, 3]], 'heights': [{'__RealLiteral__': 0, 'data': '7.6429835806950154596888662775', 'prec': 100}], 'lmfdb_label': '277725.ba2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.11318327730193711798770077287', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.9204634402236497798049431964714111993', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-18017, 18017, 2]], 'xcoord_integral_points': []}
• lmfdb_label 277725.ba2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11838443
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '277725.ba2', 'torsion': [2, 2]}
  • id: 11838444
    {'degree': 4, 'field': [-6254, -856, -99, -1, 1], 'lmfdb_label': '277725.ba2', 'torsion': [4]}
  • id: 11838447
    {'degree': 8, 'field': [-391659, -175296, 177582, -4573, 2290, -7, 7, -4, 1], 'lmfdb_label': '277725.ba2', 'torsion': [6]}
  • id: 11838445
    {'degree': 8, 'field': [17956, 0, -5292, 0, 649, 0, 12, 0, 1], 'lmfdb_label': '277725.ba2', 'torsion': [2, 4]}
  • id: 11838446
    {'degree': 8, 'field': [689661, -1033956, 567148, -127730, 12821, -1550, 212, -2, 1], 'lmfdb_label': '277725.ba2', 'torsion': [2, 4]}
  • id: 11838448
    {'degree': 16, 'field': [456976, 0, 122356, 0, -1169945, 0, 1244719, 0, -1221521, 0, -53606, 0, 2905, 0, 31, 0, 1], 'lmfdb_label': '277725.ba2', 'torsion': [8]}
  • id: 11838449
    {'degree': 16, 'field': [5613755625, 0, -1722262500, 0, 258066000, 0, -16460125, 0, 143000, 0, 32525, 0, -1595, 0, 10, 0, 1], 'lmfdb_label': '277725.ba2', '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: 6880642
    {'conductor': 277725, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '277725.ba2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 6880643
    {'conductor': 277725, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '277725.ba2', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 6880644
    {'conductor': 277725, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '277725.ba2', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 6880645
    {'conductor': 277725, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '277725.ba2', '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: 3417327
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [316, 109, 105, 316], [1, 2, 2, 5], [281, 4, 142, 9], [1, 4, 0, 1], [417, 4, 416, 5], [88, 1, 83, 0], [241, 4, 62, 9]], 'adelic_image': '420.12.0.?', 'conductor': 277725, 'lmfdb_label': '277725.ba2', 'prime': 0}
  • id: 989579
    {'conductor': 277725, 'elladic_image': '2.3.0.1', 'lmfdb_label': '277725.ba2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 277725.ba does not appear in ec_padic