Elliptic curve data - 297.a1

Formats: - HTML - YAML - JSON - 2026-07-02T22:47:49.894318

• 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': '297a', 'Clabel': '297a1', 'Cnumber': 1, 'abc_quality': 0.9461121308337243, 'absD': 2381643, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 6, 'ainvs': [0, 0, 1, -81, 290], 'analytic_rank': 1, 'bad_primes': [3, 11], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 297, 'degree': 72, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.0085490294016567848462213244558', 'prec': 113}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1], 'jinv': [-2985984, 121], 'lmfdb_iso': '297.a', 'lmfdb_label': '297.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 1, -81, 290], 'min_quad_twist_disc': 1, 'modell_images': [], 'modm_images': ['6.2.0.a.1'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 2, 'num_int_pts': 10, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.057892977299888693563918701268', 'prec': 107}, 'semistable': False, 'serre_invariants': [[2, 2, 27], [3, 2, 11], [11, 12, 27]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.83250824590273905339265525215', 'prec': 107}, 'szpiro_ratio': 4.3670180072771645, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
• 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, -2, 0, 2, -2, 0, 1, 0, 0, 4, 1, 0, -5, -2, 0, -4, -2, 0, 3, -4], 'aplist': [-2, 0, -2, 1, 1, -5, -2, 3, -4, -6, -8, -9, 4, 0, -10, 6, 14, 9, 5, -12, 7, 11, -12, -6, -7], 'class_deg': 1, 'class_size': 1, 'conductor': 297, 'isogeny_matrix': [[1]], 'lmfdb_iso': '297.a', 'trace_hash': 663346784261467663}
• 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': '1.0172450672686989269002014182', 'prec': 100}, 'conductor': 297, 'gens': [[15, 49, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.057892977299888693563918701268', 'prec': 107}], 'lmfdb_label': '297.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '2.5629322348818417625175123977', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.89025466617100477491981456156394126739', 'prec': 133}, 'tamagawa_product': 6, 'torsion_generators': [], 'xcoord_integral_points': [-3, 1, 4, 6, 15]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [1, 6, 0], '3': 'a', '5': [3, 0], '7': [1, 0], '11': [2, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '297.a1'}
• ec_torsion_growth •

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

  
  
  • id: 12490
    {'degree': 3, 'field': [-2, 0, 0, 1], 'lmfdb_label': '297.a1', 'torsion': [2]}
  • id: 12491
    {'degree': 6, 'field': [1, -3, 0, 5, 0, -3, 1], 'lmfdb_label': '297.a1', 'torsion': [2, 2]}
  • id: 12492
    {'degree': 8, 'field': [-1, 1, 2, -7, 7, -7, 7, -4, 1], 'lmfdb_label': '297.a1', 'torsion': [3]}
  • id: 12493
    {'degree': 12, 'field': [-113, -150, 192, 268, -153, -120, -48, 48, 39, -2, -12, 0, 1], 'lmfdb_label': '297.a1', 'torsion': [4]}
• 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: 2723
    {'conductor': 297, 'conductor_valuation': 3, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '297.a1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
  • id: 2724
    {'conductor': 297, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '297.a1', 'prime': 11, '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

  
  {'adelic_gens': [[5, 2, 5, 3], [1, 1, 5, 0], [1, 2, 0, 1], [5, 2, 4, 3], [1, 0, 2, 1]], 'adelic_image': '6.2.0.?', 'conductor': 297, 'lmfdb_label': '297.a1', 'prime': 0}
• ec_padic •

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

  
  
  • id: 3081
    {'lmfdb_iso': '297.a', 'p': 5, 'prec': 20, 'unit': 1296965861974, 'val': 2}
  • id: 3082
    {'lmfdb_iso': '297.a', 'p': 7, 'prec': 20, 'unit': 32097103421425332, 'val': -1}
  • id: 3087
    {'lmfdb_iso': '297.a', 'p': 13, 'prec': 20, 'unit': 1036353375338710385136, 'val': 1}
  • id: 3089
    {'lmfdb_iso': '297.a', 'p': 17, 'prec': 20, 'unit': 148203363025376688970656, 'val': 1}
  • id: 3090
    {'lmfdb_iso': '297.a', 'p': 19, 'prec': 20, 'unit': 1925097368670045814386066, 'val': 1}
  • id: 3094
    {'lmfdb_iso': '297.a', 'p': 23, 'prec': 20, 'unit': 70826498722766335405987139, 'val': 1}
  • id: 3086
    {'lmfdb_iso': '297.a', 'p': 29, 'prec': 20, 'unit': 342823987669562592067634016, 'val': 1}
  • id: 3083
    {'lmfdb_iso': '297.a', 'p': 31, 'prec': 20, 'unit': 17244546777082067359844290162, 'val': 1}
  • id: 3098
    {'lmfdb_iso': '297.a', 'p': 37, 'prec': 20, 'unit': 410901376000131638208036287966, 'val': 1}
  • id: 3084
    {'lmfdb_iso': '297.a', 'p': 41, 'prec': 20, 'unit': 283064674292975178763798635293, 'val': 1}
  • id: 3096
    {'lmfdb_iso': '297.a', 'p': 47, 'prec': 20, 'unit': 53615335123362644424594171613233, 'val': 1}
  • id: 3091
    {'lmfdb_iso': '297.a', 'p': 53, 'prec': 20, 'unit': 429823791328719557127869586441652, 'val': 1}
  • id: 3092
    {'lmfdb_iso': '297.a', 'p': 59, 'prec': 20, 'unit': 1935347768531842431395387860847264, 'val': 1}
  • id: 3097
    {'lmfdb_iso': '297.a', 'p': 61, 'prec': 20, 'unit': 2478648377297391546255636179032557, 'val': 1}
  • id: 3080
    {'lmfdb_iso': '297.a', 'p': 67, 'prec': 20, 'unit': 936851645318979953009771421857568, 'val': 1}
  • id: 3085
    {'lmfdb_iso': '297.a', 'p': 71, 'prec': 20, 'unit': 98707287394196993473579584331400932, 'val': 1}
  • id: 3093
    {'lmfdb_iso': '297.a', 'p': 73, 'prec': 20, 'unit': 222550429957939387890068480123200524, 'val': 1}
  • id: 3088
    {'lmfdb_iso': '297.a', 'p': 79, 'prec': 20, 'unit': 233333703335926562674125344987282876, 'val': 1}
  • id: 3079
    {'lmfdb_iso': '297.a', 'p': 83, 'prec': 20, 'unit': 2703650243797981253777648758376430667, 'val': 1}
  • id: 3095
    {'lmfdb_iso': '297.a', 'p': 89, 'prec': 20, 'unit': 9534499635233471231616375868280652234, 'val': 1}
  • id: 3078
    {'lmfdb_iso': '297.a', 'p': 97, 'prec': 20, 'unit': 40900126435375016221816686119720967086, 'val': 1}