Elliptic curve data - 56144.k2

Formats: - HTML - YAML - JSON - 2025-10-14T03:56:36.597830

• 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': '56144h', 'Clabel': '56144h1', 'Cnumber': 1, 'abc_quality': 0.9723140120881086, 'absD': 632406016, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 2552, 'ainvs': [0, 0, 0, -11, 1210], 'analytic_rank': 0, 'bad_primes': [2, 11, 29], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 56144, 'degree': 19008, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.36768679499140196825503422707', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2], 'jinv': [-27, 116], 'lmfdb_iso': '56144.k', 'lmfdb_label': '56144.k2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -1, -19], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '88.6.0.?', '232.6.0.?', '638.6.0.?', '2552.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 319], [11, 42, 464], [29, 30, 1936]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.92493420376813597717768378888', 'prec': 107}, 'szpiro_ratio': 2.5348134949901704, '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, -2, 0, 4, 0, -3, 0, 0, 0, 6, 0, 0, 0, 2, 0, 4, 0], 'aplist': [0, 0, -2, 4, 0, 6, 2, 4, 0, -1, 6, -8, -2, 4, -2, 2, -4, 10, -4, -12, 6, -8, -2, -6, 18], 'class_deg': 2, 'class_size': 2, 'conductor': 56144, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '56144.k', 'trace_hash': 1529720696308456443}
• 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': '0.47932635399671725606830347461', 'prec': 103}, 'conductor': 56144, 'gens': [], 'heights': [], 'lmfdb_label': '56144.k2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.3014386099219943696641762036', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.6028772198439887393283524073017171641', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-11, 0, 1]], 'xcoord_integral_points': [-11]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '11': 'a', '29': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '56144.k2'}
• ec_torsion_growth •

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

  
  
  • id: 2709802
    {'degree': 2, 'field': [80, -1, 1], 'lmfdb_label': '56144.k2', 'torsion': [2, 2]}
  • id: 2709803
    {'degree': 4, 'field': [-319, 0, 66, 0, 1], 'lmfdb_label': '56144.k2', 'torsion': [4]}
  • id: 2709806
    {'degree': 8, 'field': [-1455123, 79794, -4866, 12540, 1128, -330, -48, 0, 1], 'lmfdb_label': '56144.k2', 'torsion': [6]}
  • id: 2709805
    {'degree': 8, 'field': [293764, 0, -53444, 0, 3197, 0, -68, 0, 1], 'lmfdb_label': '56144.k2', 'torsion': [2, 4]}
  • id: 2709804
    {'degree': 8, 'field': [295936, 0, 26172, 0, 712, 0, 27, 0, 1], 'lmfdb_label': '56144.k2', 'torsion': [2, 4]}
  • id: 2709808
    {'degree': 16, 'field': [2108304, 0, 13176900, 0, 37039068, 0, 12314412, 0, 1561989, 0, 85668, 0, 1650, 0, 0, 0, 1], 'lmfdb_label': '56144.k2', 'torsion': [2, 6]}
  • id: 2709807
    {'degree': 16, 'field': [49252324, 0, 0, 0, -9418156, 0, -2779128, 0, -434027, 0, 4356, 0, 3014, 0, 132, 0, 1], 'lmfdb_label': '56144.k2', '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: 1349972
    {'conductor': 56144, 'conductor_valuation': 4, 'discriminant_valuation': 14, 'j_denominator_valuation': 2, 'kodaira_symbol': -10, 'lmfdb_label': '56144.k2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1349973
    {'conductor': 56144, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '56144.k2', 'prime': 11, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1349974
    {'conductor': 56144, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '56144.k2', 'prime': 29, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 2037106
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [932, 1, 2319, 0], [1, 2, 2, 5], [2549, 4, 2548, 5], [1, 4, 0, 1], [961, 1596, 2232, 319], [178, 1, 2463, 0], [1277, 4, 2, 9]], 'adelic_image': '2552.12.0.?', 'conductor': 56144, 'lmfdb_label': '56144.k2', 'prime': 0}
  • id: 238919
    {'conductor': 56144, 'elladic_image': '2.3.0.1', 'lmfdb_label': '56144.k2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 56144.k does not appear in ec_padic