Elliptic curve data - 503857.a1

Formats: - HTML - YAML - JSON - 2024-05-15T14:16:48.780037

• 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[]

  
  {'abc_quality': 0.8067412910948464, 'absD': 503857, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 2015428, 'ainvs': [1, -1, 0, 4, -35], 'analytic_rank': 0, 'bad_primes': [503857], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 503857, 'degree': 40512, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.22632948406757047013599170192', 'prec': 107}, 'faltings_index': 1, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1], 'jinv': [6128487, 503857], 'lmfdb_iso': '503857.a', 'lmfdb_label': '503857.a1', 'lmfdb_number': 1, 'min_quad_twist_ainvs': [1, -1, 0, 4, -35], 'min_quad_twist_disc': 1, 'modell_images': [], 'modm_images': ['2015428.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 1, 'num_int_pts': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 4, 'sha_primes': [2], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.22632948406757047013599170192', 'prec': 107}, 'szpiro_ratio': 1.5672223230209064, '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, 1, 0, -1, 2, 0, 4, -3, -3, 2, 0, 0, 1, 4, 0, -1, -4, -3, 4, -2], 'aplist': [1, 0, 2, 4, 0, 1, -4, 4, 8, 4, 4, 7, -6, -1, 6, -6, 5, 1, 10, 0, -2, 11, 7, -12, -16], 'class_deg': 1, 'class_size': 1, 'conductor': 503857, 'isogeny_matrix': [[1]], 'lmfdb_iso': '503857.a', 'trace_hash': 396726484305524675}
• 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': '1.5724878266054880457786577203', 'prec': 100}, 'conductor': 503857, 'gens': [], 'heights': [], 'lmfdb_label': '503857.a1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.3985333685688253916634426411', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.5941334742753015666537705643830976058', 'prec': 130}, 'tamagawa_product': 1, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 503857.a1 does not appear in ec_iwasawa
• lmfdb_label 503857.a1 does not appear in ec_torsion_growth
• 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

  
  {'conductor': 503857, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '503857.a1', 'prime': 503857, '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': [[1007715, 2, 1007715, 3], [2015427, 2, 2015426, 3], [1, 0, 2, 1], [1, 2, 0, 1], [1, 1, 2015427, 0], [17, 2, 17, 3]], 'adelic_image': '2015428.2.0.?', 'conductor': 503857, 'lmfdb_label': '503857.a1', 'prime': 0}
• lmfdb_iso 503857.a does not appear in ec_padic