Elliptic curve data - 160113.i1

Formats: - HTML - YAML - JSON - 2024-05-25T02:40:02.443129

• 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': '160113f', 'Clabel': '160113f1', 'Cnumber': 1, 'abc_quality': 0.8651174046959357, 'absD': 3790105753059, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 38, 'ainvs': [0, 1, 1, -6554, 222509], 'analytic_rank': 1, 'bad_primes': [3, 19, 53], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 160113, 'degree': 585728, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1485975474974882727431483339', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 8, 'isogeny_degrees': [1], 'jinv': [-1404928, 171], 'lmfdb_iso': '160113.i', 'lmfdb_label': '160113.i1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 1, -2, 2], 'min_quad_twist_disc': 53, 'modell_images': [], 'modm_images': ['38.2.0.a.1'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '6.5855125743901817448594383736', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.83654840927857264432908623561', 'prec': 107}, 'szpiro_ratio': 3.1850214616770147, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, 2, 1, 2, 3, 2, -5, 0, 1, 6, 1, 2, 2, -10, 3, -4, -1, 2, 1, 6], 'aplist': [2, 1, 3, -5, 1, 2, -1, 1, 4, -2, 6, 0, 0, -1, -9, 0, -8, 1, -8, 12, 11, -16, -12, -6, -10], 'class_deg': 1, 'class_size': 1, 'conductor': 160113, 'isogeny_matrix': [[1]], 'lmfdb_iso': '160113.i', 'trace_hash': 1395401899766288936}
• 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': '0.10054045501719304715719137691', 'prec': 103}, 'conductor': 160113, 'gens': [[30169, 7728029, 32]], 'heights': [{'__RealLiteral__': 0, 'data': '6.5855125743901817448594383736', 'prec': 100}], 'lmfdb_label': '160113.i1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.76310723407521888851982988428', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '20.101809142441863057023890897978639881', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 160113.i1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7163751
    {'degree': 3, 'field': [-2, -2, 0, 1], 'lmfdb_label': '160113.i1', 'torsion': [2]}
  • id: 7163752
    {'degree': 6, 'field': [1, -3, 4, -3, 4, -3, 1], 'lmfdb_label': '160113.i1', 'torsion': [2, 2]}
  • id: 7163753
    {'degree': 8, 'field': [-2803477, -1806397, 179525, 75159, -2757, -870, -17, -2, 1], 'lmfdb_label': '160113.i1', 'torsion': [3]}
  • id: 7163754
    {'degree': 12, 'field': [-2276827361, 933905556, -1099994968, 603461394, -97611831, -1276216, 1317600, -122968, 6841, -92, -8, -2, 1], 'lmfdb_label': '160113.i1', 'torsion': [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: 3961607
    {'conductor': 160113, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '160113.i1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 3961608
    {'conductor': 160113, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '160113.i1', 'prime': 19, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 3961609
    {'conductor': 160113, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '160113.i1', 'prime': 53, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
• ec_galrep •

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

  
  {'adelic_gens': [[37, 2, 36, 3], [1, 2, 0, 1], [1, 0, 2, 1], [21, 2, 21, 3], [1, 1, 37, 0]], 'adelic_image': '38.2.0.?', 'conductor': 160113, 'lmfdb_label': '160113.i1', 'prime': 0}
• lmfdb_iso 160113.i does not appear in ec_padic