Elliptic curve data - 284592.kr1

Formats: - HTML - YAML - JSON - 2024-06-01T14:17:39.234603

• 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': '284592kr', 'Clabel': '284592kr1', 'Cnumber': 1, 'abc_quality': 1.047898410460437, 'absD': 183455470809748844784, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 462, 'ainvs': [0, 1, 0, 508996, 636667359], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 11], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 284592, 'degree': 7741440, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.5690463121331577474967837963', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 277, 'isogeny_degrees': [1], 'jinv': [5820759945472, 73222472421], 'lmfdb_iso': '284592.kr', 'lmfdb_label': '284592.kr1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, 10388, 1859141], 'min_quad_twist_disc': 28, 'modell_images': [], 'modm_images': ['462.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.59594981754108755431054071448', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.76556835921926002245621082293', 'prec': 103}, 'szpiro_ratio': 4.305035290656025, '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, 0, 1, 0, 3, 0, 0, 0, 1, 0, 0, 0, 3, 0, 3, 0, -4, 0, 1, 0], 'aplist': [0, 1, 3, 0, 0, 3, -4, 1, -4, -3, -2, -3, 0, -4, 3, -10, 3, 2, -9, 16, 5, 6, 16, 6, -4], 'class_deg': 1, 'class_size': 1, 'conductor': 284592, 'isogeny_matrix': [[1]], 'lmfdb_iso': '284592.kr', 'trace_hash': 2224948543140215866}
• 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': '0.0058688731907064341745544538199', 'prec': 110}, 'conductor': 284592, 'gens': [[4285, 392931, 2]], 'heights': [{'__RealLiteral__': 0, 'data': '0.59594981754108755431054071448', 'prec': 103}], 'lmfdb_label': '284592.kr1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.13295615495369585237194531417', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '13.311512975984094044736930743766449831', 'prec': 130}, 'tamagawa_product': 168, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 284592.kr1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 12105659
    {'degree': 3, 'field': [3, 0, -1, 1], 'lmfdb_label': '284592.kr1', 'torsion': [2]}
  • id: 12105660
    {'degree': 6, 'field': [81, 27, 42, 15, 4, -2, 1], 'lmfdb_label': '284592.kr1', 'torsion': [2, 2]}
  • id: 12105661
    {'degree': 8, 'field': [-444675, 0, 6776, 0, -2310, 0, 0, 0, 1], 'lmfdb_label': '284592.kr1', 'torsion': [3]}
  • id: 12105662
    {'degree': 12, 'field': [-348273, 331236, -276120, 116418, 35654, -50404, 12076, 3038, -2143, 430, -28, -4, 1], 'lmfdb_label': '284592.kr1', '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: 7051486
    {'conductor': 284592, 'conductor_valuation': 4, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '284592.kr1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 7051487
    {'conductor': 284592, 'conductor_valuation': 1, 'discriminant_valuation': 21, 'j_denominator_valuation': 21, 'kodaira_symbol': 25, 'lmfdb_label': '284592.kr1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 21}
  • id: 7051488
    {'conductor': 284592, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '284592.kr1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 7051489
    {'conductor': 284592, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '284592.kr1', 'prime': 11, '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

  
  {'adelic_gens': [[155, 2, 155, 3], [211, 2, 211, 3], [199, 2, 199, 3], [1, 1, 461, 0], [1, 2, 0, 1], [1, 0, 2, 1], [461, 2, 460, 3]], 'adelic_image': '462.2.0.?', 'conductor': 284592, 'lmfdb_label': '284592.kr1', 'prime': 0}
• lmfdb_iso 284592.kr does not appear in ec_padic