Elliptic curve data - 416160.r1

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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': '416160r', 'Clabel': '416160r1', 'Cnumber': 1, 'abc_quality': 0.8489816898373131, 'absD': 478619028187200000, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 680, 'ainvs': [0, 0, 0, 165597, -20860598], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 17], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 416160, 'degree': 4147200, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0795997114886612660881919949', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 17, 'isogeny_degrees': [1], 'jinv': [55742968, 53125], 'lmfdb_iso': '416160.r', 'lmfdb_label': '416160.r1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 64, 136], 'min_quad_twist_disc': -51, 'modell_images': [], 'modm_images': ['680.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '12.521534783068036528350956022', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 13005], [3, 6, 46240], [5, 6, 83232], [17, 162, 1440]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.40617349029346060179712202359', 'prec': 107}, 'szpiro_ratio': 3.6839156530811525, '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, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 3, 0], 'aplist': [0, 0, -1, -2, 0, 5, 0, 3, -2, -3, 7, 8, -2, 10, -3, 1, 1, -11, 14, 13, 7, -16, 0, 9, 5], 'class_deg': 1, 'class_size': 1, 'conductor': 416160, 'isogeny_matrix': [[1]], 'lmfdb_iso': '416160.r', 'trace_hash': 1185194642221208293}
• 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': '0.015620057975194539561217762148', 'prec': 107}, 'conductor': 416160, 'gens': [[5881014, 18041140588, 115]], 'heights': [{'__RealLiteral__': 0, 'data': '12.521534783068036528350956022', 'prec': 100}], 'lmfdb_label': '416160.r1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.16126959921109573593930816947', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.0773715838927073630636138037806006154', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 416160.r1 does not appear in ec_iwasawa
• lmfdb_label 416160.r1 does not appear in ec_torsion_growth
• 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: 10282502
    {'conductor': 416160, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '416160.r1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 10282503
    {'conductor': 416160, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '416160.r1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 10282504
    {'conductor': 416160, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '416160.r1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 10282505
    {'conductor': 416160, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '416160.r1', '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

  
  {'adelic_gens': [[1, 1, 679, 0], [241, 2, 241, 3], [341, 2, 341, 3], [511, 2, 511, 3], [1, 0, 2, 1], [1, 2, 0, 1], [137, 2, 137, 3], [679, 2, 678, 3]], 'adelic_image': '680.2.0.?', 'conductor': 416160, 'lmfdb_label': '416160.r1', 'prime': 0}
• lmfdb_iso 416160.r does not appear in ec_padic