Elliptic curve data - 138384.cm3

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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': '138384r', 'Clabel': '138384r2', 'Cnumber': 2, 'abc_quality': 1.0250423431234554, 'absD': 10186875966168907776, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 744, 'ainvs': [0, 0, 0, -2862819, -1858064670], 'analytic_rank': 0, 'bad_primes': [2, 3, 31], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 138384, 'degree': 2949120, 'elladic_images': ['8.12.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.5047956513375660963330013665', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 64, 'isogeny_degrees': [1, 2], 'jinv': [979146657, 3844], 'lmfdb_iso': '138384.cm', 'lmfdb_label': '138384.cm3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -21, 41], 'min_quad_twist_disc': -372, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '8.12.0.a.1', '12.12.0-2.a.1.1', '24.24.0-8.a.1.3', '124.12.0.?', '248.24.0.?', '372.24.0.?', '744.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 8649], [3, 6, 15376], [31, 512, 144]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.45465127579900718174643553569', 'prec': 107}, 'szpiro_ratio': 4.748822710952112, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -6, 0, -4, 0], 'aplist': [0, 0, 2, 0, 0, -2, -6, -4, -8, 2, 0, -10, 6, 8, -8, -6, -12, 6, 12, 8, -10, -8, -8, -6, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 138384, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '138384.cm', 'trace_hash': 864057967259463316}
• 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': '0.0066736302437990729535259031558', 'prec': 110}, 'conductor': 138384, 'gens': [], 'heights': [], 'lmfdb_label': '138384.cm3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.11609235897996164456070543359', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.46436943591984657824282173437942448067', 'prec': 133}, 'tamagawa_product': 64, 'torsion_generators': [[-930, 0, 1], [1953, 0, 1]], 'xcoord_integral_points': [-1023, -930, 1953]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '31': 'a'}, 'iwp0': 3, 'lmfdb_label': '138384.cm3'}
• ec_torsion_growth •

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

  
  
  • id: 6255944
    {'degree': 4, 'field': [64, -8, -7, -1, 1], 'lmfdb_label': '138384.cm3', 'torsion': [2, 4]}
  • id: 6255943
    {'degree': 4, 'field': [961, 0, -124, 0, 1], 'lmfdb_label': '138384.cm3', 'torsion': [2, 4]}
  • id: 6255945
    {'degree': 4, 'field': [2209, 0, 92, 0, 1], 'lmfdb_label': '138384.cm3', 'torsion': [2, 4]}
  • id: 6255946
    {'degree': 8, 'field': [-56907, -39294, -21042, -7164, -1644, -294, -12, 0, 1], 'lmfdb_label': '138384.cm3', 'torsion': [2, 6]}
  • id: 6255949
    {'degree': 16, 'field': [64, -64, -4488, 760, 321433, -188988, 133985, -68284, 30762, -11212, 4625, -1308, 410, -108, 25, -4, 1], 'lmfdb_label': '138384.cm3', 'torsion': [2, 8]}
  • id: 6255948
    {'degree': 16, 'field': [256, 0, -2048, 0, -7488, 0, -1792, 0, 8132, 0, -448, 0, -468, 0, -32, 0, 1], 'lmfdb_label': '138384.cm3', 'torsion': [2, 8]}
  • id: 6255950
    {'degree': 16, 'field': [15499969, 0, 8308992, 0, 2656856, 0, 539552, 0, 77106, 0, 7424, 0, 600, 0, 32, 0, 1], 'lmfdb_label': '138384.cm3', 'torsion': [2, 8]}
  • id: 6255947
    {'degree': 16, 'field': [16777216, 0, 0, 0, -397312, 0, 0, 0, 5313, 0, 0, 0, -97, 0, 0, 0, 1], 'lmfdb_label': '138384.cm3', 'torsion': [4, 4]}
• 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: 3414713
    {'conductor': 138384, 'conductor_valuation': 4, 'discriminant_valuation': 14, 'j_denominator_valuation': 2, 'kodaira_symbol': -10, 'lmfdb_label': '138384.cm3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 3414714
    {'conductor': 138384, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '138384.cm3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 3414715
    {'conductor': 138384, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '138384.cm3', 'prime': 31, '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: 2563211
    {'adelic_gens': [[1, 0, 4, 1], [1, 4, 0, 1], [185, 492, 0, 743], [373, 498, 0, 1], [431, 492, 366, 239], [741, 4, 740, 5], [247, 0, 0, 743]], 'adelic_image': '744.48.0.?', 'conductor': 138384, 'lmfdb_label': '138384.cm3', 'prime': 0}
  • id: 535150
    {'conductor': 138384, 'elladic_image': '8.12.0.3', 'lmfdb_label': '138384.cm3', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 138384.cm does not appear in ec_padic