Elliptic curve data - 322.a2

Formats: - HTML - YAML - JSON - 2026-08-15T06:38:48.106235

• 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': '322a', 'Clabel': '322a1', 'Cnumber': 1, 'abc_quality': 0.9340477219886528, 'absD': 725788, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1288, 'ainvs': [1, -1, 0, -8, 44], 'analytic_rank': 1, 'bad_primes': [2, 7, 23], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 322, 'degree': 48, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.19356734017816964909222675451', 'prec': 97}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [-60698457, 725788], 'lmfdb_iso': '322.a', 'lmfdb_label': '322.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -8, 44], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '14.6.0.b.1', '184.6.0.?', '1288.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 11, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.16689364344617958654816546643', 'prec': 97}, 'semistable': True, 'serre_invariants': [[2, 4, 7], [3, 2, 46], [7, 8, 46], [23, 24, 14]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.19356734017816964909222675451', 'prec': 97}, 'szpiro_ratio': 3.6361258462150583, '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, -1, 0, 1, -2, 0, 1, -1, -3, 2, -4, 0, 4, -1, 0, 1, -8, 3, -2, -2], 'aplist': [-1, 0, -2, 1, -4, 4, -8, -2, 1, 2, -6, -10, 6, -8, 6, 2, 0, 10, 8, -12, 6, 0, 2, 12, 12], 'class_deg': 2, 'class_size': 2, 'conductor': 322, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '322.a', 'trace_hash': 154601339104624152}
• 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': '1.4727548290619120152911746561', 'prec': 97}, 'conductor': 322, 'gens': [[-2, 8, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.16689364344617958654816546643', 'prec': 97}], 'lmfdb_label': '322.a2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '2.4232379290346946561411067819', 'prec': 97}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 97}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2132690207407248855216632714698938663', 'prec': 127}, 'tamagawa_product': 12, 'torsion_generators': [[-4, 2, 1]], 'xcoord_integral_points': [-4, -2, 4, 5, 19, 334]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': [1, 1, 0], '5': [7, 0], '7': [2, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [2, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '322.a2'}
• ec_torsion_growth •

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

  
  
  • id: 13563
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '322.a2', 'torsion': [2, 2]}
  • id: 13564
    {'degree': 4, 'field': [-37, 6, -5, -2, 1], 'lmfdb_label': '322.a2', 'torsion': [4]}
  • id: 13567
    {'degree': 8, 'field': [-2, 5, -2, -7, 7, -7, 7, -4, 1], 'lmfdb_label': '322.a2', 'torsion': [6]}
  • id: 13565
    {'degree': 8, 'field': [18, 30, 139, 4, 46, 6, 10, -2, 1], 'lmfdb_label': '322.a2', 'torsion': [2, 4]}
  • id: 13566
    {'degree': 8, 'field': [441, 0, 1414, 0, -33, 0, -6, 0, 1], 'lmfdb_label': '322.a2', 'torsion': [2, 4]}
  • id: 13569
    {'degree': 16, 'field': [784, 0, -721, 0, -1130, 0, 749, 0, 679, 0, 269, 0, 91, 0, 14, 0, 1], 'lmfdb_label': '322.a2', 'torsion': [2, 6]}
  • id: 13568
    {'degree': 16, 'field': [99067, 992696, -1837452, 1575608, -480860, -436848, 278984, -152568, 85657, -31024, 5228, 928, -458, 112, 4, -8, 1], 'lmfdb_label': '322.a2', '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: 3005
    {'conductor': 322, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '322.a2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 3006
    {'conductor': 322, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '322.a2', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 3007
    {'conductor': 322, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '322.a2', 'prime': 23, '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: 1667108
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [281, 4, 562, 9], [809, 484, 160, 1127], [1, 4, 0, 1], [370, 1, 1103, 0], [1285, 4, 1284, 5], [645, 4, 2, 9]], 'adelic_image': '1288.12.0.?', 'conductor': 322, 'lmfdb_label': '322.a2', 'prime': 0}
  • id: 1313
    {'conductor': 322, 'elladic_image': '2.3.0.1', 'lmfdb_label': '322.a2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 3585
    {'lmfdb_iso': '322.a', 'p': 5, 'prec': 20, 'unit': 145491818883, 'val': 3}
  • id: 3584
    {'lmfdb_iso': '322.a', 'p': 11, 'prec': 20, 'unit': 3972823670187767040, 'val': 1}
  • id: 3590
    {'lmfdb_iso': '322.a', 'p': 13, 'prec': 20, 'unit': 1167231172354324257070, 'val': 1}
  • id: 3592
    {'lmfdb_iso': '322.a', 'p': 17, 'prec': 20, 'unit': 65523044532775433244459, 'val': 1}
  • id: 3593
    {'lmfdb_iso': '322.a', 'p': 19, 'prec': 20, 'unit': 1893123015146434995599162, 'val': 1}
  • id: 3589
    {'lmfdb_iso': '322.a', 'p': 29, 'prec': 20, 'unit': 420728996967440222183503686, 'val': 1}
  • id: 3598
    {'lmfdb_iso': '322.a', 'p': 31, 'prec': 20, 'unit': 15740670253119561385822504755, 'val': 1}
  • id: 3600
    {'lmfdb_iso': '322.a', 'p': 37, 'prec': 20, 'unit': 524748958211017818742448178924, 'val': 1}
  • id: 3587
    {'lmfdb_iso': '322.a', 'p': 41, 'prec': 20, 'unit': 1828507981729072865119423929078, 'val': 1}
  • id: 3588
    {'lmfdb_iso': '322.a', 'p': 43, 'prec': 20, 'unit': 9596568048195465355461265913044, 'val': 1}
  • id: 3591
    {'lmfdb_iso': '322.a', 'p': 47, 'prec': 20, 'unit': 49720347691316272264401828003866, 'val': 1}
  • id: 3594
    {'lmfdb_iso': '322.a', 'p': 53, 'prec': 20, 'unit': 318007075123618704824897252104808, 'val': 1}
  • id: 3599
    {'lmfdb_iso': '322.a', 'p': 61, 'prec': 20, 'unit': 3079908921767594568593892538805904, 'val': 1}
  • id: 3583
    {'lmfdb_iso': '322.a', 'p': 67, 'prec': 20, 'unit': 49431430233529790474769032787097389, 'val': 1}
  • id: 3586
    {'lmfdb_iso': '322.a', 'p': 71, 'prec': 20, 'unit': 68956970985757467337820087328671215, 'val': 1}
  • id: 3595
    {'lmfdb_iso': '322.a', 'p': 73, 'prec': 20, 'unit': 153620233947342782725395892820772245, 'val': 1}
  • id: 3596
    {'lmfdb_iso': '322.a', 'p': 83, 'prec': 20, 'unit': 2798775113266116615408405302438527237, 'val': 1}
  • id: 3597
    {'lmfdb_iso': '322.a', 'p': 89, 'prec': 20, 'unit': 7668661910796623839636749147751954447, 'val': 1}
  • id: 3582
    {'lmfdb_iso': '322.a', 'p': 97, 'prec': 20, 'unit': 50617014562702771529863971302929784393, 'val': 1}