Elliptic curve data - 258.f2

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• 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': '258f', 'Clabel': '258f1', 'Cnumber': 1, 'abc_quality': 0.9966384920336764, 'absD': 1540767744, 'adelic_genus': 2, 'adelic_index': 96, 'adelic_level': 3612, 'ainvs': [1, 0, 0, 159, 1737], 'analytic_rank': 0, 'bad_primes': [2, 3, 43], 'class_deg': 7, 'class_size': 2, 'cm': 0, 'conductor': 258, 'degree': 168, 'elladic_images': ['7.48.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.44596692313088271889563763905', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 5, 'isogeny_degrees': [1, 7], 'jinv': [444369620591, 1540767744], 'lmfdb_iso': '258.f', 'lmfdb_label': '258.f2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 159, 1737], 'min_quad_twist_disc': 1, 'modell_images': ['7B.1.1'], 'modm_images': ['7.48.0-7.a.1.2', '516.2.0.?', '3612.96.2.?'], 'nonmax_primes': [7], 'nonmax_rad': 7, 'num_bad_primes': 3, 'num_int_pts': 6, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'serre_invariants': [[2, 4, 129], [3, 4, 86], [7, 2, 43], [43, 44, 6]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.44596692313088271889563763905', 'prec': 103}, 'szpiro_ratio': 5.11937126571374, 'torsion': 7, 'torsion_primes': [7], 'torsion_structure': [7]}
• 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, 1, 1, 1, -1, 5, 1, -7, 1, -1, 1, 4, 1, -1, -1], 'aplist': [1, 1, -1, 1, 5, -7, 4, -1, -4, -5, -10, 10, 0, 1, -1, 12, 4, -8, -2, -12, 4, 10, -7, 6, -7], 'class_deg': 7, 'class_size': 2, 'conductor': 258, 'isogeny_matrix': [[1, 7], [7, 1]], 'lmfdb_iso': '258.f', 'trace_hash': 300724365588704024}
• 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': '0.40986237504252563796301475426', 'prec': 103}, 'conductor': 258, 'gens': [], 'heights': [], 'lmfdb_label': '258.f2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.0680841433839959066322578555', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.1361682867679918132645157110453621860', 'prec': 130}, 'tamagawa_product': 98, 'torsion_generators': [[6, 51, 1]], 'xcoord_integral_points': [-6, 6, 42]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [2, 0], '3': [3, 0], '5': [0, 0], '7': [6, 0], '43': [1, 0]}, 'iwp0': 11, 'lmfdb_label': '258.f2'}
• ec_torsion_growth •

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

  
  
  • id: 11170
    {'degree': 3, 'field': [-9, 1, -1, 1], 'lmfdb_label': '258.f2', 'torsion': [14]}
  • id: 11171
    {'degree': 6, 'field': [144, 72, 114, 18, 7, -2, 1], 'lmfdb_label': '258.f2', 'torsion': [2, 14]}
  • id: 11172
    {'degree': 8, 'field': [-108, 0, -36, 71, -32, -7, 7, -4, 1], 'lmfdb_label': '258.f2', 'torsion': [21]}
  • id: 11173
    {'degree': 12, 'field': [24, 324, 114, -51, 143, 59, -101, 80, -40, 25, -1, -1, 1], 'lmfdb_label': '258.f2', 'torsion': [28]}
• 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: 2375
    {'conductor': 258, 'conductor_valuation': 1, 'discriminant_valuation': 14, 'j_denominator_valuation': 14, 'kodaira_symbol': 18, 'lmfdb_label': '258.f2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 14}
  • id: 2376
    {'conductor': 258, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '258.f2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 7}
  • id: 2377
    {'conductor': 258, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '258.f2', 'prime': 43, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1666862
    {'adelic_gens': [[1, 14, 0, 1], [3599, 14, 3598, 15], [1807, 14, 0, 1291], [2948, 7, 581, 3606], [1, 0, 14, 1], [8, 5, 91, 57], [2416, 7, 2401, 3606], [8, 7, 1799, 3606]], 'adelic_image': '3612.96.2.?', 'conductor': 258, 'lmfdb_label': '258.f2', 'prime': 0}
  • id: 1089
    {'conductor': 258, 'elladic_image': '7.48.0.1', 'lmfdb_label': '258.f2', 'modell_image': '7B.1.1', 'prime': 7}
• lmfdb_iso 258.f does not appear in ec_padic