Elliptic curve data - 10230.bf4

Formats: - HTML - YAML - JSON - 2026-07-14T09:15:18.299166

• 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': '10230bg', 'Clabel': '10230bg2', 'Cnumber': 2, 'abc_quality': 0.9920428670213398, 'absD': 6242069790000000000, 'adelic_genus': 5, 'adelic_index': 288, 'adelic_level': 20460, 'ainvs': [1, 0, 0, -430355, 162005025], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 11, 31], 'class_deg': 10, 'class_size': 4, 'cm': 0, 'conductor': 10230, 'degree': 352000, 'elladic_images': ['2.3.0.1', '5.24.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.3064283841242792694955993759', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 31, 'isogeny_degrees': [1, 2, 5, 10], 'jinv': [-8814635019030000319921, 6242069790000000000], 'lmfdb_iso': '10230.bf', 'lmfdb_label': '10230.bf4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -430355, 162005025], 'min_quad_twist_disc': 1, 'modell_images': ['2B', '5B.1.1'], 'modm_images': ['2.3.0.a.1', '5.24.0-5.a.1.2', '10.72.0-10.a.2.1', '22.6.0.a.1', '110.144.1.?', '1860.144.1.?', '20460.288.5.?'], 'nonmax_primes': [2, 5], 'nonmax_rad': 10, 'num_bad_primes': 5, 'num_int_pts': 8, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 11], [3, 4, 3410], [5, 6, 341], [11, 12, 930], [31, 32, 330]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.3064283841242792694955993759', 'prec': 100}, 'szpiro_ratio': 5.559343667940444, 'torsion': 10, 'torsion_primes': [2, 5], 'torsion_structure': [10]}
• 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, 1, 1, 1, 1, 1, -2, 1, 1, 1, 1, 1, -6, -2, 1, 1, 8, 1, 0, 1], 'aplist': [1, 1, 1, -2, 1, -6, 8, 0, 4, -10, 1, -2, 12, 4, 8, -6, 0, 12, 8, -8, 14, 10, -6, -10, -2], 'class_deg': 10, 'class_size': 4, 'conductor': 10230, 'isogeny_matrix': [[1, 2, 5, 10], [2, 1, 10, 5], [5, 10, 1, 2], [10, 5, 2, 1]], 'lmfdb_iso': '10230.bf', 'trace_hash': 1628854454134330619}
• 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': '0.0099234288396642852227382012294', 'prec': 110}, 'conductor': 10230, 'gens': [], 'heights': [], 'lmfdb_label': '10230.bf4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.21959672270351880509753037922', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.3919344540703761019506075843869595470', 'prec': 130}, 'tamagawa_product': 2000, 'torsion_generators': [[250, 8245, 1]], 'xcoord_integral_points': [-290, 250, 610, 2110]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 1], '3': [1, 0], '5': [3, 0], '11': [1, 0], '31': [1, 0]}, 'iwp0': 7, 'lmfdb_label': '10230.bf4'}
• ec_torsion_growth •

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

  
  
  • id: 530557
    {'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '10230.bf4', 'torsion': [2, 10]}
  • id: 530558
    {'degree': 4, 'field': [-704, 0, 37, 0, 1], 'lmfdb_label': '10230.bf4', 'torsion': [20]}
  • id: 530561
    {'degree': 8, 'field': [-522504, 62964, -60498, -4933, 2470, -7, 7, -4, 1], 'lmfdb_label': '10230.bf4', 'torsion': [30]}
  • id: 530560
    {'degree': 8, 'field': [19881, 0, -10875, 0, 1768, 0, -35, 0, 1], 'lmfdb_label': '10230.bf4', 'torsion': [2, 20]}
  • id: 530559
    {'degree': 8, 'field': [21195, -1746, 1005, 282, -266, -14, 5, -2, 1], 'lmfdb_label': '10230.bf4', 'torsion': [2, 20]}
  • id: 530563
    {'degree': 16, 'field': [96947540496, 0, 132325574427, 0, 449765298, 0, -160949731, 0, 9026195, 0, -154351, 0, 5143, 0, 22, 0, 1], 'lmfdb_label': '10230.bf4', 'torsion': [2, 30]}
  • id: 530562
    {'degree': 16, 'field': [9701954121616, 0, 12966350231800, 0, 1067676936841, 0, -80158609610, 0, -2138367149, 0, -1176860, 0, 146971, 0, -650, 0, 1], 'lmfdb_label': '10230.bf4', 'torsion': [40]}
  • id: 530564
    {'degree': 20, 'field': [83187416791999521, 56643660588982068, 38770416012451311, 25869987173551392, 17260187735273464, 528893778033104, 200252674281309, 3218597507933, 979264106671, 118406078927, -5305585729, 812118539, -160840567, -437709, -530163, -48686, 7423, -314, 137, -1, 1], 'lmfdb_label': '10230.bf4', 'torsion': [5, 10]}
• 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: 217105
    {'conductor': 10230, 'conductor_valuation': 1, 'discriminant_valuation': 10, 'j_denominator_valuation': 10, 'kodaira_symbol': 14, 'lmfdb_label': '10230.bf4', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 10}
  • id: 217106
    {'conductor': 10230, 'conductor_valuation': 1, 'discriminant_valuation': 10, 'j_denominator_valuation': 10, 'kodaira_symbol': 14, 'lmfdb_label': '10230.bf4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 10}
  • id: 217107
    {'conductor': 10230, 'conductor_valuation': 1, 'discriminant_valuation': 10, 'j_denominator_valuation': 10, 'kodaira_symbol': 14, 'lmfdb_label': '10230.bf4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 10}
  • id: 217108
    {'conductor': 10230, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '10230.bf4', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 217109
    {'conductor': 10230, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '10230.bf4', 'prime': 31, '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: 1731648
    {'adelic_gens': [[9241, 6, 0, 1], [20441, 20, 20440, 21], [6821, 6, 0, 1], [1, 10, 10, 101], [11166, 13, 5495, 20276], [10231, 6, 0, 1], [1, 0, 20, 1], [16371, 14, 20440, 20367], [11, 16, 20220, 20111], [1, 20, 0, 1]], 'adelic_image': '20460.288.5.?', 'conductor': 10230, 'lmfdb_label': '10230.bf4', 'prime': 0}
  • id: 49305
    {'conductor': 10230, 'elladic_image': '2.3.0.1', 'lmfdb_label': '10230.bf4', 'modell_image': '2B', 'prime': 2}
  • id: 49306
    {'conductor': 10230, 'elladic_image': '5.24.0.1', 'lmfdb_label': '10230.bf4', 'modell_image': '5B.1.1', 'prime': 5}
• lmfdb_iso 10230.bf does not appear in ec_padic