Elliptic curve data - 208725.a1

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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
  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': '208725j', 'Clabel': '208725j1', 'Cnumber': 1, 'abc_quality': 0.9358734837944656, 'absD': 522136464029296875, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 230, 'ainvs': [0, -1, 1, -303508, -73046832], 'analytic_rank': 1, 'bad_primes': [3, 5, 11, 23], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 208725, 'degree': 6451200, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1264524658156212075454941529', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1], 'jinv': [-111701610496, 18862875], 'lmfdb_iso': '208725.a', 'lmfdb_label': '208725.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, -100, 406], 'min_quad_twist_disc': -55, 'modell_images': [], 'modm_images': ['230.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 4, 'num_int_pts': 4, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.7461616148408899678043000453', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.12278587319938574821414269730', 'prec': 103}, 'szpiro_ratio': 4.060744432487037, '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, -1, 2, 0, 2, -5, 0, 1, 0, 0, -2, -6, 10, 0, -4, 1, -2, -2, 0], 'aplist': [-2, -1, 0, -5, 0, -6, 1, -2, 1, 1, -5, 7, 7, -8, 12, -9, 3, -12, 1, 5, -2, 8, 3, 8, -14], 'class_deg': 1, 'class_size': 1, 'conductor': 208725, 'isogeny_matrix': [[1]], 'lmfdb_iso': '208725.a', 'trace_hash': 85522269808147632}
• 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': '0.014222857411766098166222094315', 'prec': 107}, 'conductor': 208725, 'gens': [[2512, 122512, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.7461616148408899678043000453', 'prec': 100}], 'lmfdb_label': '208725.a1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.10077047520695014357292574034', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4076922857252154269698244771102508819', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [], 'xcoord_integral_points': [753, 2512]}
• lmfdb_label 208725.a1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 9128640
    {'degree': 3, 'field': [-3, 5, -1, 1], 'lmfdb_label': '208725.a1', 'torsion': [2]}
  • id: 9128641
    {'degree': 6, 'field': [151, -23, 28, -11, 8, -3, 1], 'lmfdb_label': '208725.a1', 'torsion': [2, 2]}
  • id: 9128642
    {'degree': 8, 'field': [-4329775, 2627270, -883504, 63560, 4373, -283, 1, -2, 1], 'lmfdb_label': '208725.a1', 'torsion': [3]}
  • id: 9128643
    {'degree': 12, 'field': [-8939565, 3875490, -52998, 415972, -278919, 86844, -51352, -1548, -1211, -294, 2, -4, 1], 'lmfdb_label': '208725.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: 5172396
    {'conductor': 208725, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '208725.a1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5172397
    {'conductor': 208725, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '208725.a1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5172398
    {'conductor': 208725, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '208725.a1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 5172399
    {'conductor': 208725, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '208725.a1', 'prime': 23, '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

  
  {'adelic_gens': [[1, 2, 0, 1], [229, 2, 228, 3], [51, 2, 51, 3], [1, 0, 2, 1], [1, 1, 229, 0], [47, 2, 47, 3]], 'adelic_image': '230.2.0.?', 'conductor': 208725, 'lmfdb_label': '208725.a1', 'prime': 0}
• lmfdb_iso 208725.a does not appear in ec_padic