Elliptic curve data - 18496.k4

Formats: - HTML - YAML - JSON - 2024-04-29T02:42:35.137891

• 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': '18496j', 'Clabel': '18496j4', 'Cnumber': 4, 'abc_quality': 1.1807067659885138, 'absD': 528480705039302656, 'adelic_genus': 53, 'adelic_index': 1536, 'adelic_level': 1088, 'ainvs': [0, 0, 0, -12716, 34980560], 'analytic_rank': 0, 'bad_primes': [2, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 18496, 'degree': 147456, 'elladic_images': ['16.96.0.181'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0796913219266825232931824869', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2, 4], 'jinv': [-35937, 83521], 'lmfdb_iso': '18496.k', 'lmfdb_label': '18496.k4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -1, -14], 'min_quad_twist_disc': -136, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0.d.1', '8.48.0-8.t.1.3', '16.96.0-16.m.2.4', '68.24.0-4.d.1.2', '136.96.1.?', '272.384.9.?', '544.768.21.?', '1088.1536.53.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 4, 'sha_primes': [2], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.37663612094134348095743300422', 'prec': 107}, 'szpiro_ratio': 4.912186255021881, '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, 2, 0, 0, 0, 0, 0, -4, 0], 'aplist': [0, 0, -2, 4, 0, 2, 0, -4, 4, 6, 4, -2, 6, 4, 0, -6, -12, -10, 4, -4, 6, 12, -4, 10, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 18496, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '18496.k', 'trace_hash': 994613068893359885}
• 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': '0.015617196316654287357027338747', 'prec': 107}, 'conductor': 18496, 'gens': [], 'heights': [], 'lmfdb_label': '18496.k4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.23544518696141637360823606891', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.8835614956913309888658885513025073612', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-340, 0, 1]], 'xcoord_integral_points': [-340]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '17': 'a'}, 'iwp0': 3, 'lmfdb_label': '18496.k4'}
• ec_torsion_growth •

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

  
  
  • id: 948811
    {'degree': 2, 'field': [-34, 0, 1], 'lmfdb_label': '18496.k4', 'torsion': [4]}
  • id: 948810
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '18496.k4', 'torsion': [2, 2]}
  • id: 948812
    {'degree': 2, 'field': [34, 0, 1], 'lmfdb_label': '18496.k4', 'torsion': [4]}
  • id: 948813
    {'degree': 4, 'field': [289, 0, 0, 0, 1], 'lmfdb_label': '18496.k4', 'torsion': [2, 4]}
  • id: 948817
    {'degree': 8, 'field': [-13872, 0, 4488, 0, -408, 0, 0, 0, 1], 'lmfdb_label': '18496.k4', 'torsion': [6]}
  • id: 948815
    {'degree': 8, 'field': [4, 0, -14, 0, 21, 0, -10, 0, 1], 'lmfdb_label': '18496.k4', 'torsion': [8]}
  • id: 948816
    {'degree': 8, 'field': [4, 0, 14, 0, 21, 0, 10, 0, 1], 'lmfdb_label': '18496.k4', 'torsion': [8]}
  • id: 948814
    {'degree': 8, 'field': [256, 0, 0, 0, 49, 0, 0, 0, 1], 'lmfdb_label': '18496.k4', 'torsion': [4, 4]}
  • id: 948818
    {'degree': 16, 'field': [1, 0, 0, 0, 17, 0, 0, 0, -32, 0, 0, 0, 17, 0, 0, 0, 1], 'lmfdb_label': '18496.k4', 'torsion': [4, 8]}
  • id: 948819
    {'degree': 16, 'field': [751689, 0, 0, 0, 137853, 0, 0, 0, 8670, 0, 0, 0, 204, 0, 0, 0, 1], 'lmfdb_label': '18496.k4', 'torsion': [2, 6]}
  • id: 948820
    {'degree': 16, 'field': [24275329, 0, -14587958, 0, 8112517, 0, -2208272, 0, 336766, 0, -32282, 0, 1960, 0, -68, 0, 1], 'lmfdb_label': '18496.k4', 'torsion': [12]}
  • id: 948821
    {'degree': 16, 'field': [46548721, -29631280, 38664416, -19914786, 14856740, -6687038, 3665065, -1416432, 600118, -186498, 60811, -14140, 3479, -546, 98, -8, 1], 'lmfdb_label': '18496.k4', 'torsion': [12]}
• 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: 417118
    {'conductor': 18496, 'conductor_valuation': 6, 'discriminant_valuation': 18, 'j_denominator_valuation': 0, 'kodaira_symbol': -12, 'lmfdb_label': '18496.k4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 417119
    {'conductor': 18496, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '18496.k4', '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: 1787686
    {'adelic_gens': [[1, 64, 0, 1], [9, 124, 756, 745], [914, 225, 349, 590], [1025, 64, 1024, 65], [897, 610, 114, 809], [575, 1076, 0, 1087], [1, 0, 64, 1], [57, 16, 176, 393]], 'adelic_image': '1088.1536.53.?', 'conductor': 18496, 'lmfdb_label': '18496.k4', 'prime': 0}
  • id: 86737
    {'conductor': 18496, 'elladic_image': '16.96.0.181', 'lmfdb_label': '18496.k4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 18496.k does not appear in ec_padic