Elliptic curve data - 16704.bb1

Formats: - HTML - YAML - JSON - 2026-04-28T09:14:45.794820

• 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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '16704bp', 'Clabel': '16704bp2', 'Cnumber': 2, 'abc_quality': 0.8661276626980977, 'absD': 2976251904, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 696, 'ainvs': [0, 0, 0, -396, -1520], 'analytic_rank': 0, 'bad_primes': [2, 3, 29], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 16704, 'degree': 7168, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.51402257008139115832381032379', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 27, 'isogeny_degrees': [1, 2], 'jinv': [1940598, 841], 'lmfdb_iso': '16704.bb', 'lmfdb_label': '16704.bb1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -891, -5130], 'min_quad_twist_disc': 24, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '24.6.0.a.1', '232.6.0.?', '348.6.0.?', '696.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 3], [3, 6, 1856], [29, 30, 576]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.74258900787889211953274649084', 'prec': 107}, 'szpiro_ratio': 3.0398662047514, '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, 0, 0, 0, 0, -2, 0, 0, 0, 6, 0, 0, 0], 'aplist': [0, 0, -2, 4, 0, -2, 6, 0, 4, -1, -6, -4, 6, 4, 0, 2, 2, 0, 12, 0, 14, -10, -6, -6, 2], 'class_deg': 2, 'class_size': 2, 'conductor': 16704, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '16704.bb', 'trace_hash': 1421445682107293621}
• 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': '0.35770554172963034767212868875', 'prec': 103}, 'conductor': 16704, 'gens': [], 'heights': [], 'lmfdb_label': '16704.bb1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.1132893793980671562874189955', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.2265787587961343125748379910323204053', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-4, 0, 1]], 'xcoord_integral_points': [-4]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '29': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '16704.bb1'}
• ec_torsion_growth •

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

  
  
  • id: 855164
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '16704.bb1', 'torsion': [2, 2]}
  • id: 855165
    {'degree': 4, 'field': [96, 0, 6, 0, 1], 'lmfdb_label': '16704.bb1', 'torsion': [4]}
  • id: 855168
    {'degree': 8, 'field': [-12, 0, 0, 0, 12, 0, 2, 0, 1], 'lmfdb_label': '16704.bb1', 'torsion': [6]}
  • id: 855166
    {'degree': 8, 'field': [16, 0, -32, 0, 18, 0, -8, 0, 1], 'lmfdb_label': '16704.bb1', 'torsion': [2, 4]}
  • id: 855167
    {'degree': 8, 'field': [784, 0, -248, 0, 33, 0, 16, 0, 1], 'lmfdb_label': '16704.bb1', 'torsion': [2, 4]}
  • id: 855170
    {'degree': 16, 'field': [81, 0, -810, 0, 540, 0, -2598, 0, 510, 0, 354, 0, 148, 0, 22, 0, 1], 'lmfdb_label': '16704.bb1', 'torsion': [2, 6]}
  • id: 855169
    {'degree': 16, 'field': [9278116, 0, 9482272, 0, 3774788, 0, 734416, 0, 77197, 0, 6128, 0, 554, 0, 32, 0, 1], 'lmfdb_label': '16704.bb1', '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: 371293
    {'conductor': 16704, 'conductor_valuation': 6, 'discriminant_valuation': 17, 'j_denominator_valuation': 0, 'kodaira_symbol': -11, 'lmfdb_label': '16704.bb1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 371294
    {'conductor': 16704, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '16704.bb1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 371295
    {'conductor': 16704, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '16704.bb1', 'prime': 29, 'reduction_type': -1, '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

  
  
  • id: 1775138
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [2, 1, 347, 0], [1, 2, 2, 5], [1, 4, 0, 1], [553, 4, 410, 9], [236, 1, 463, 0], [693, 4, 692, 5], [436, 265, 609, 88]], 'adelic_image': '696.12.0.?', 'conductor': 16704, 'lmfdb_label': '16704.bb1', 'prime': 0}
  • id: 78291
    {'conductor': 16704, 'elladic_image': '2.3.0.1', 'lmfdb_label': '16704.bb1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 16704.bb does not appear in ec_padic