Elliptic curve data - 7872.bd1

Formats: - HTML - YAML - JSON - 2025-10-13T20:45:56.993954

• 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': '7872bi', 'Clabel': '7872bi3', 'Cnumber': 3, 'abc_quality': 0.9826480023940802, 'absD': 141033996288, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 328, 'ainvs': [0, 1, 0, -28097, 1803327], 'analytic_rank': 0, 'bad_primes': [2, 3, 41], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 7872, 'degree': 18432, 'elladic_images': ['8.24.0.53'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.2028629220127594200612902607', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 29, 'isogeny_degrees': [1, 2, 4], 'jinv': [9357915116017, 538002], 'lmfdb_iso': '7872.bd', 'lmfdb_label': '7872.bd1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -439, -3577], 'min_quad_twist_disc': -8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '8.24.0-8.m.1.1', '328.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 41], [3, 4, 2624], [41, 42, 192]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.16314215117284145593544207851', 'prec': 103}, 'szpiro_ratio': 4.720050671434397, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
• 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, 1, 0, 2, 0, -4, 0, 1, 0, -4, 0, -2, 0, 2, 0, 2, 0, -4, 0], 'aplist': [0, 1, 2, -4, -4, -2, 2, -4, 0, 6, 8, 2, 1, 4, -12, 6, -4, 10, 12, 12, -6, -12, 12, 2, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 7872, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '7872.bd', 'trace_hash': 770188801515918096}
• 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': '0.090200000711501232328206021004', 'prec': 107}, 'conductor': 7872, 'gens': [], 'heights': [], 'lmfdb_label': '7872.bd1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.97843449483270301413603174388', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.9568689896654060282720634877511284901', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[79, 288, 1]], 'xcoord_integral_points': [79, 97]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [7, 0], '41': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '7872.bd1'}
• ec_torsion_growth •

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

  
  
  • id: 411688
    {'degree': 2, 'field': [-82, 0, 1], 'lmfdb_label': '7872.bd1', 'torsion': [2, 4]}
  • id: 411689
    {'degree': 4, 'field': [82, 0, 16, 0, 1], 'lmfdb_label': '7872.bd1', 'torsion': [8]}
  • id: 411693
    {'degree': 8, 'field': [-768, 0, 800, 0, -96, 0, 0, 0, 1], 'lmfdb_label': '7872.bd1', 'torsion': [12]}
  • id: 411692
    {'degree': 8, 'field': [18, 828, -247, -642, 249, 88, -37, -2, 1], 'lmfdb_label': '7872.bd1', 'torsion': [2, 8]}
  • id: 411691
    {'degree': 8, 'field': [6561, 0, -1324, 0, 120, 0, -12, 0, 1], 'lmfdb_label': '7872.bd1', 'torsion': [2, 8]}
  • id: 411690
    {'degree': 8, 'field': [6889, 0, -980, 0, 170, 0, 4, 0, 1], 'lmfdb_label': '7872.bd1', 'torsion': [4, 4]}
  • id: 411695
    {'degree': 16, 'field': [2178576, 0, -3400704, 0, 5223744, 0, -1648768, 0, 77432, 0, -19432, 0, -383, 0, -68, 0, 1], 'lmfdb_label': '7872.bd1', 'torsion': [2, 12]}
  • id: 411694
    {'degree': 16, 'field': [45212176, 0, 35287552, 0, 14470048, 0, 3496480, 0, 500938, 0, 42640, 0, 2152, 0, 64, 0, 1], 'lmfdb_label': '7872.bd1', 'torsion': [16]}
• 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: 162788
    {'conductor': 7872, 'conductor_valuation': 6, 'discriminant_valuation': 19, 'j_denominator_valuation': 1, 'kodaira_symbol': -13, 'lmfdb_label': '7872.bd1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 162789
    {'conductor': 7872, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '7872.bd1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
  • id: 162790
    {'conductor': 7872, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '7872.bd1', 'prime': 41, '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: 1715910
    {'adelic_gens': [[40, 197, 119, 90], [37, 40, 182, 35], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [321, 8, 320, 9], [7, 6, 322, 323], [188, 1, 15, 6]], 'adelic_image': '328.48.0.?', 'conductor': 7872, 'lmfdb_label': '7872.bd1', 'prime': 0}
  • id: 38457
    {'conductor': 7872, 'elladic_image': '8.24.0.53', 'lmfdb_label': '7872.bd1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 7872.bd does not appear in ec_padic