Elliptic curve data - 67270.f2

Formats: - HTML - YAML - JSON - 2024-05-21T19:57:49.682939

• 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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '67270v', 'Clabel': '67270v1', 'Cnumber': 1, 'abc_quality': 0.995523658071532, 'absD': 2156988946302400, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1736, 'ainvs': [1, 0, 1, -2423, 2234778], 'analytic_rank': 0, 'bad_primes': [2, 5, 7, 31], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 67270, 'degree': 368640, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6212833055753055051746771933', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 5, 'isogeny_degrees': [1, 2], 'jinv': [-1771561, 2430400], 'lmfdb_iso': '67270.f', 'lmfdb_label': '67270.f2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -2, -76], 'min_quad_twist_disc': -31, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '56.6.0.d.1', '62.6.0.b.1', '1736.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.095710296667267617789904968973', 'prec': 110}, 'szpiro_ratio': 3.846781637321979, '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, -2, 1, 1, 2, 1, -1, 1, -1, 0, -2, -2, -1, -2, 1, -4, -1, 4, 1], 'aplist': [-1, -2, 1, 1, 0, -2, -4, 4, -2, 4, 0, 8, 10, 8, 8, -4, 4, -6, 12, 0, 8, 14, 6, 4, 10], 'class_deg': 2, 'class_size': 2, 'conductor': 67270, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '67270.f', 'trace_hash': 1275963730379920793}
• 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': '0.039063505494773087654681118793', 'prec': 107}, 'conductor': 67270, 'gens': [], 'heights': [], 'lmfdb_label': '67270.f2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.37324211450456754520940285229', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4929684580182701808376114091707632934', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-137, 68, 1]], 'xcoord_integral_points': [-137]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [17, 0], '5': [1, 0], '7': [1, 0], '31': 'a'}, 'iwp0': 3, 'lmfdb_label': '67270.f2'}
• ec_torsion_growth •

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

  
  
  • id: 3204693
    {'degree': 2, 'field': [8, -1, 1], 'lmfdb_label': '67270.f2', 'torsion': [2, 2]}
  • id: 3204694
    {'degree': 4, 'field': [25, -10, -3, -2, 1], 'lmfdb_label': '67270.f2', 'torsion': [4]}
  • id: 3204697
    {'degree': 8, 'field': [-8304, 4989, -4698, -583, 295, -7, 7, -4, 1], 'lmfdb_label': '67270.f2', 'torsion': [6]}
  • id: 3204696
    {'degree': 8, 'field': [9040, -5960, 789, -750, 636, 64, 36, -2, 1], 'lmfdb_label': '67270.f2', 'torsion': [2, 4]}
  • id: 3204695
    {'degree': 8, 'field': [12569, -1544, 4082, 204, 55, 44, 18, -4, 1], 'lmfdb_label': '67270.f2', 'torsion': [2, 4]}
  • id: 3204698
    {'degree': 16, 'field': [-164664400, -363825280, 458014608, 19405568, -54081220, -10468528, 3054860, 2851744, 398705, 41272, 63856, 29792, 4290, -392, -124, 0, 1], 'lmfdb_label': '67270.f2', 'torsion': [8]}
  • id: 3204699
    {'degree': 16, 'field': [345744, 0, 559335, 0, 468832, 0, -92610, 0, 8205, 0, 715, 0, 18, 0, 0, 0, 1], 'lmfdb_label': '67270.f2', 'torsion': [2, 6]}
• 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: 1627146
    {'conductor': 67270, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '67270.f2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1627147
    {'conductor': 67270, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '67270.f2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1627148
    {'conductor': 67270, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '67270.f2', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1627149
    {'conductor': 67270, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '67270.f2', 'prime': 31, '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: 2109282
    {'adelic_gens': [[1122, 1, 1175, 0], [1, 2, 2, 5], [1, 4, 0, 1], [869, 4, 2, 9], [1089, 652, 216, 1519], [1, 0, 4, 1], [745, 4, 1490, 9], [3, 4, 8, 11], [1733, 4, 1732, 5]], 'adelic_image': '1736.12.0.?', 'conductor': 67270, 'lmfdb_label': '67270.f2', 'prime': 0}
  • id: 281275
    {'conductor': 67270, 'elladic_image': '2.3.0.1', 'lmfdb_label': '67270.f2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 67270.f does not appear in ec_padic