Elliptic curve data - 138720.bp4

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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': '138720f', 'Clabel': '138720f3', 'Cnumber': 3, 'abc_quality': 1.1738269518331081, 'absD': 164194480728691200, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 408, 'ainvs': [0, 1, 0, 6840, 19496700], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 138720, 'degree': 1966080, 'elladic_images': ['8.12.0.16'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.9822471122457719490017320566', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 2, 'iso_nlabel': 41, 'isogeny_degrees': [1, 2, 4], 'jinv': [2863288, 13286025], 'lmfdb_iso': '138720.bp', 'lmfdb_label': '138720.bp4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 24, 3960], 'min_quad_twist_disc': 17, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.d.1', '24.24.0.n.1', '68.12.0-4.c.1.1', '136.24.0.?', '408.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 289], [3, 4, 46240], [5, 6, 27744], [17, 146, 480]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.045780054797704926814040656569', 'prec': 107}, 'szpiro_ratio': 3.9774980424715385, '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, 1, 0, 1, 0, 4, 0, 1, 0, -4, 0, 6, 0, 1, 0, 0, 0, 4, 0], 'aplist': [0, 1, 1, 4, -4, 6, 0, 4, 0, -10, 4, 10, -2, -4, 8, 2, 12, 10, 12, 0, -10, 4, 4, -6, 14], 'class_deg': 4, 'class_size': 4, 'conductor': 138720, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '138720.bp', 'trace_hash': 129360535881581108}
• 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': '0.018977632607297042692353085518', 'prec': 107}, 'conductor': 138720, 'gens': [], 'heights': [], 'lmfdb_label': '138720.bp4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.25392926329874472459124978004', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.0943023191698733901899947210106153312', 'prec': 130}, 'tamagawa_product': 96, 'torsion_generators': [[-261, 0, 1]], 'xcoord_integral_points': [-261]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '5': [3, 0], '17': 'a'}, 'iwp0': 5, 'lmfdb_label': '138720.bp4'}
• ec_torsion_growth •

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

  
  
  • id: 6271200
    {'degree': 2, 'field': [-34, 0, 1], 'lmfdb_label': '138720.bp4', 'torsion': [4]}
  • id: 6271199
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '138720.bp4', 'torsion': [2, 2]}
  • id: 6271201
    {'degree': 2, 'field': [17, 0, 1], 'lmfdb_label': '138720.bp4', 'torsion': [4]}
  • id: 6271202
    {'degree': 4, 'field': [81, 0, -16, 0, 1], 'lmfdb_label': '138720.bp4', 'torsion': [2, 4]}
  • id: 6271206
    {'degree': 8, 'field': [-250563, 0, 78608, 0, 1734, 0, 0, 0, 1], 'lmfdb_label': '138720.bp4', 'torsion': [6]}
  • id: 6271204
    {'degree': 8, 'field': [225, 0, 2112, 0, 124, 0, -32, 0, 1], 'lmfdb_label': '138720.bp4', 'torsion': [8]}
  • id: 6271203
    {'degree': 8, 'field': [5206, -2344, 2540, -376, 149, 44, -10, -4, 1], 'lmfdb_label': '138720.bp4', 'torsion': [2, 4]}
  • id: 6271205
    {'degree': 8, 'field': [7425, 3600, 2940, 0, 169, -60, 34, 0, 1], 'lmfdb_label': '138720.bp4', 'torsion': [8]}
  • id: 6271212
    {'degree': 16, 'field': [42984, 125712, 352152, 555288, 499800, 392424, 246256, 84144, 48109, 3904, 5848, -464, 610, -32, 40, 0, 1], 'lmfdb_label': '138720.bp4', 'torsion': [12]}
  • id: 6271208
    {'degree': 16, 'field': [50625, 0, -475200, 0, 4432644, 0, -276288, 0, 82735, 0, 8192, 0, 900, 0, 32, 0, 1], 'lmfdb_label': '138720.bp4', 'torsion': [2, 8]}
  • id: 6271207
    {'degree': 16, 'field': [734706, 19992, 1171556, -2279752, 981986, -68384, 384184, -179336, -104253, 78264, 4464, -9704, 586, 448, -44, -8, 1], 'lmfdb_label': '138720.bp4', 'torsion': [4, 4]}
  • id: 6271209
    {'degree': 16, 'field': [1126521, -5084100, 7433316, -4849452, 2815632, -510744, 252712, -97580, 59937, -26848, 8828, -2292, 746, -196, 48, -8, 1], 'lmfdb_label': '138720.bp4', 'torsion': [2, 8]}
  • id: 6271211
    {'degree': 16, 'field': [19580625, 0, -25834500, 0, 12492300, 0, -3009604, 0, 403802, 0, -34804, 0, 1996, 0, -68, 0, 1], 'lmfdb_label': '138720.bp4', 'torsion': [12]}
  • id: 6271210
    {'degree': 16, 'field': [1557486225, 0, 2145557700, 0, 129535020, 0, -4679308, 0, 119162, 0, 20228, 0, 844, 0, 4, 0, 1], 'lmfdb_label': '138720.bp4', '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: 3423682
    {'conductor': 138720, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '138720.bp4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 3423683
    {'conductor': 138720, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '138720.bp4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
  • id: 3423684
    {'conductor': 138720, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '138720.bp4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 3423685
    {'conductor': 138720, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '138720.bp4', 'prime': 17, '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: 2565491
    {'adelic_gens': [[137, 272, 68, 273], [120, 17, 187, 222], [1, 0, 8, 1], [167, 0, 0, 407], [288, 391, 119, 84], [7, 6, 402, 403], [401, 8, 400, 9], [1, 8, 0, 1], [1, 4, 4, 17]], 'adelic_image': '408.48.0.?', 'conductor': 138720, 'lmfdb_label': '138720.bp4', 'prime': 0}
  • id: 536393
    {'conductor': 138720, 'elladic_image': '8.12.0.16', 'lmfdb_label': '138720.bp4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 138720.bp does not appear in ec_padic