Elliptic curve data - 257600.k1

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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': '257600k', 'Clabel': '257600k2', 'Cnumber': 2, 'abc_quality': 0.8465629105408569, 'absD': 1327155200000000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1288, 'ainvs': [0, 1, 0, -112033, -14363937], 'analytic_rank': 1, 'bad_primes': [2, 5, 7, 23], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 257600, 'degree': 1769472, 'elladic_images': ['8.6.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7266857940765990965478554794', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2], 'jinv': [75933869762, 648025], 'lmfdb_iso': '257600.k', 'lmfdb_label': '257600.k1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -1120, 14700], 'min_quad_twist_disc': -40, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.b.1', '644.6.0.?', '1288.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 5, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.2122967848044718859759485448', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.059991667933706945760269692612', 'prec': 110}, 'szpiro_ratio': 3.731651732008454, '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, 0, -2, 0, 0, 0, -1, 0, 1, 0, -2, 0, -4, 0, 0, 0, -2, 0, 8, 0], 'aplist': [0, -2, 0, -1, -2, -4, -2, 8, 1, -6, 0, 8, -10, -10, -8, 12, 6, -10, -10, 0, 10, 4, 16, 6, 10], 'class_deg': 2, 'class_size': 2, 'conductor': 257600, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '257600.k', 'trace_hash': 1332867843849403748}
• 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': '0.031638783399879475351273621847', 'prec': 107}, 'conductor': 257600, 'gens': [[-182, 175, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.2122967848044718859759485448', 'prec': 100}], 'lmfdb_label': '257600.k1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.26108765007081725921248827634', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.3547640754985653131098772755490770304', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-207, 0, 1]], 'xcoord_integral_points': [-207, -182, 437]}
• lmfdb_label 257600.k1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 11054216
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '257600.k1', 'torsion': [2, 2]}
  • id: 11054217
    {'degree': 4, 'field': [830, -110, 19, -1, 1], 'lmfdb_label': '257600.k1', 'torsion': [4]}
  • id: 11054220
    {'degree': 8, 'field': [-1428300, 0, -126960, 0, -920, 0, 70, 0, 1], 'lmfdb_label': '257600.k1', 'torsion': [6]}
  • id: 11054219
    {'degree': 8, 'field': [237169, 0, -10380, 0, -1004, 0, 20, 0, 1], 'lmfdb_label': '257600.k1', 'torsion': [2, 4]}
  • id: 11054218
    {'degree': 8, 'field': [735296, -181696, 61944, -6592, 2183, -246, 31, -2, 1], 'lmfdb_label': '257600.k1', 'torsion': [2, 4]}
  • id: 11054222
    {'degree': 16, 'field': [1487567761, 0, -85535196, 0, -61204988, 0, -49452388, 0, 10110390, 0, -602452, 0, 16132, 0, -204, 0, 1], 'lmfdb_label': '257600.k1', 'torsion': [2, 6]}
  • id: 11054221
    {'degree': 16, 'field': [4420506250000, 0, -1594493950000, 0, 178878005100, 0, -5229319760, 0, 31871454, 0, 481880, 0, -1781, 0, -70, 0, 1], 'lmfdb_label': '257600.k1', '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: 6385915
    {'conductor': 257600, 'conductor_valuation': 6, 'discriminant_valuation': 17, 'j_denominator_valuation': 0, 'kodaira_symbol': -11, 'lmfdb_label': '257600.k1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 6385916
    {'conductor': 257600, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '257600.k1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6385917
    {'conductor': 257600, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '257600.k1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 6385918
    {'conductor': 257600, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '257600.k1', '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: 3297166
    {'adelic_gens': [[1, 2, 2, 5], [2, 1, 643, 0], [1, 4, 0, 1], [1285, 4, 1284, 5], [1129, 162, 160, 1127], [281, 4, 562, 9], [1, 0, 4, 1], [185, 4, 370, 9], [3, 4, 8, 11]], 'adelic_image': '1288.12.0.?', 'conductor': 257600, 'lmfdb_label': '257600.k1', 'prime': 0}
  • id: 926116
    {'conductor': 257600, 'elladic_image': '8.6.0.6', 'lmfdb_label': '257600.k1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 257600.k does not appear in ec_padic