Elliptic curve data - 9408.r3

Formats: - HTML - YAML - JSON - 2026-04-20T23:59:41.876022

• 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': '9408bw', 'Clabel': '9408bw2', 'Cnumber': 2, 'abc_quality': 0.9724335123602292, 'absD': 9836344885248, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 168, 'ainvs': [0, -1, 0, -5553, -49167], 'analytic_rank': 1, 'bad_primes': [2, 3, 7], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 9408, 'degree': 18432, 'elladic_images': ['2.3.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1850314829249003651534387524', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 17, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [9826000, 5103], 'lmfdb_iso': '9408.r', 'lmfdb_label': '9408.r3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -28, -28], 'min_quad_twist_disc': 56, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '12.24.0.j.1', '24.48.0-12.j.1.6', '28.6.0.a.1', '84.48.1.?', '168.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 7, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.4905848473752282772419172512', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 49], [3, 4, 3136], [7, 32, 192]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.59659530225602581505267509436', 'prec': 107}, 'szpiro_ratio': 4.09648822547565, '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, -1, 0, 0, 0, 0, 0, 1, 0, -6, 0, 2, 0, 0, 0, 0, 0, 4, 0], 'aplist': [0, -1, 0, 0, -6, 2, 0, 4, 6, -6, 8, -2, -12, -4, 12, 6, 0, -10, 8, -6, 10, 4, 12, -12, 10], 'class_deg': 6, 'class_size': 4, 'conductor': 9408, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '9408.r', 'trace_hash': 1969321038316156394}
• 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': '0.093474840369995931323055431297', 'prec': 107}, 'conductor': 9408, 'gens': [[89, 392, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.4905848473752282772419172512', 'prec': 100}], 'lmfdb_label': '9408.r3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.58538687077762961336036680463', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.4902751977341420611814332080058069577', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-9, 0, 1]], 'xcoord_integral_points': [-63, -9, 89, 352]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [7, 0], '5': [5, 1, 0], '7': 'a', '11': [1, 0], '13': [1, 0], '17': [1, 1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '9408.r3'}
• ec_torsion_growth •

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

  
  
  • id: 489879
    {'degree': 2, 'field': [-14, 0, 1], 'lmfdb_label': '9408.r3', 'torsion': [6]}
  • id: 489878
    {'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '9408.r3', 'torsion': [2, 2]}
  • id: 489881
    {'degree': 4, 'field': [9, 0, -8, 0, 1], 'lmfdb_label': '9408.r3', 'torsion': [2, 6]}
  • id: 489880
    {'degree': 4, 'field': [28, 0, -10, 0, 1], 'lmfdb_label': '9408.r3', 'torsion': [4]}
  • id: 489882
    {'degree': 6, 'field': [168, 0, 28, 0, 14, 0, 1], 'lmfdb_label': '9408.r3', 'torsion': [6]}
  • id: 489884
    {'degree': 8, 'field': [9, 0, 12, 0, 19, 0, -4, 0, 1], 'lmfdb_label': '9408.r3', 'torsion': [2, 4]}
  • id: 489883
    {'degree': 8, 'field': [81, 0, -144, 0, 75, 0, -16, 0, 1], 'lmfdb_label': '9408.r3', 'torsion': [2, 4]}
  • id: 489885
    {'degree': 8, 'field': [441, 0, -168, 0, 67, 0, -10, 0, 1], 'lmfdb_label': '9408.r3', 'torsion': [12]}
  • id: 489887
    {'degree': 12, 'field': [729, 0, 816, 0, -173, 0, 64, 0, 123, 0, 16, 0, 1], 'lmfdb_label': '9408.r3', 'torsion': [2, 6]}
  • id: 489886
    {'degree': 12, 'field': [15876, 0, 10584, 0, 5292, 0, 924, 0, 112, 0, 14, 0, 1], 'lmfdb_label': '9408.r3', 'torsion': [3, 6]}
  • id: 489889
    {'degree': 16, 'field': [1, 0, 4, 0, -32, 0, -292, 0, 782, 0, -292, 0, -32, 0, 4, 0, 1], 'lmfdb_label': '9408.r3', 'torsion': [2, 12]}
  • id: 489890
    {'degree': 16, 'field': [81, 0, 180, 0, 130, 0, 384, 0, 651, 0, 320, 0, 114, 0, 12, 0, 1], 'lmfdb_label': '9408.r3', 'torsion': [2, 12]}
  • id: 489888
    {'degree': 16, 'field': [5149, -28112, 63888, -77512, 51090, -14064, -3008, 4364, -2331, 1072, -212, 36, 0, -8, 12, -4, 1], 'lmfdb_label': '9408.r3', 'torsion': [8]}
  • id: 489891
    {'degree': 18, 'field': [-1210104, 0, 47712672, 0, -139236048, 0, 23371432, 0, 802032, 0, -182280, 0, -9478, 0, 420, 0, 42, 0, 1], 'lmfdb_label': '9408.r3', 'torsion': [18]}
• 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: 197980
    {'conductor': 9408, 'conductor_valuation': 6, 'discriminant_valuation': 14, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '9408.r3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 197981
    {'conductor': 9408, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '9408.r3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 197982
    {'conductor': 9408, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '9408.r3', 'prime': 7, '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

  
  
  • id: 1726281
    {'adelic_gens': [[157, 12, 156, 13], [157, 166, 134, 93], [110, 165, 123, 92], [65, 2, 60, 1], [83, 0, 0, 167], [95, 156, 96, 155], [1, 6, 6, 37], [78, 61, 77, 50], [1, 0, 12, 1], [11, 2, 118, 159], [1, 12, 0, 1]], 'adelic_image': '168.96.1.?', 'conductor': 9408, 'lmfdb_label': '9408.r3', 'prime': 0}
  • id: 45737
    {'conductor': 9408, 'elladic_image': '2.3.0.1', 'lmfdb_label': '9408.r3', 'modell_image': '2B', 'prime': 2}
  • id: 45738
    {'conductor': 9408, 'elladic_image': '3.4.0.1', 'lmfdb_label': '9408.r3', 'modell_image': '3B', 'prime': 3}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 394436
    {'lmfdb_iso': '9408.r', 'p': 11, 'prec': 20, 'unit': 17817725240916561203, 'val': 1}
  • id: 394442
    {'lmfdb_iso': '9408.r', 'p': 13, 'prec': 20, 'unit': 409150650429766043265, 'val': 1}
  • id: 394444
    {'lmfdb_iso': '9408.r', 'p': 19, 'prec': 20, 'unit': 1490747496163344951122733, 'val': 1}
  • id: 394447
    {'lmfdb_iso': '9408.r', 'p': 23, 'prec': 20, 'unit': 57188023728450023011135667, 'val': 1}
  • id: 394441
    {'lmfdb_iso': '9408.r', 'p': 29, 'prec': 20, 'unit': 6012614373460615110548308299, 'val': 1}
  • id: 394452
    {'lmfdb_iso': '9408.r', 'p': 31, 'prec': 20, 'unit': 9951182539154843542226543310, 'val': 1}
  • id: 394437
    {'lmfdb_iso': '9408.r', 'p': 37, 'prec': 20, 'unit': 47754222975515714878280554249, 'val': 1}
  • id: 394439
    {'lmfdb_iso': '9408.r', 'p': 41, 'prec': 20, 'unit': 4346789287318803444073440191015, 'val': 1}
  • id: 394440
    {'lmfdb_iso': '9408.r', 'p': 43, 'prec': 20, 'unit': 7458355080620788608900400439270, 'val': 1}
  • id: 394443
    {'lmfdb_iso': '9408.r', 'p': 47, 'prec': 20, 'unit': 2223599091647762460780398629277, 'val': 1}
  • id: 394445
    {'lmfdb_iso': '9408.r', 'p': 53, 'prec': 20, 'unit': 47646583545078895040428877286764, 'val': 1}
  • id: 394450
    {'lmfdb_iso': '9408.r', 'p': 61, 'prec': 20, 'unit': 550033232693125579164061356007605, 'val': 1}
  • id: 394435
    {'lmfdb_iso': '9408.r', 'p': 67, 'prec': 20, 'unit': 27120154874231370992726061596567997, 'val': 1}
  • id: 394438
    {'lmfdb_iso': '9408.r', 'p': 71, 'prec': 20, 'unit': 72577312166352033653370868080670519, 'val': 1}
  • id: 394446
    {'lmfdb_iso': '9408.r', 'p': 73, 'prec': 20, 'unit': 199556787638081005942846231266667207, 'val': 1}
  • id: 394449
    {'lmfdb_iso': '9408.r', 'p': 79, 'prec': 20, 'unit': 1112866159587624694236987025016947430, 'val': 1}
  • id: 394451
    {'lmfdb_iso': '9408.r', 'p': 83, 'prec': 20, 'unit': 359720261939558021086274625624940097, 'val': 1}
  • id: 394448
    {'lmfdb_iso': '9408.r', 'p': 89, 'prec': 20, 'unit': 4095097264568049485636551590795418781, 'val': 1}
  • id: 394434
    {'lmfdb_iso': '9408.r', 'p': 97, 'prec': 20, 'unit': 159508868271710253943443409468822386, 'val': 1}