Elliptic curve data - 161700.x1

Formats: - HTML - YAML - JSON - 2024-05-05T14:36:15.894846

• 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': '161700ee', 'Clabel': '161700ee1', 'Cnumber': 1, 'abc_quality': 0.9495393403923615, 'absD': 11745320853420000000, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 2310, 'ainvs': [0, -1, 0, -7033133, -7178671863], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 161700, 'degree': 4976640, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.6363149186463320491186964175', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 23, 'isogeny_degrees': [1], 'jinv': [-81756451446784, 24958395], 'lmfdb_iso': '161700.x', 'lmfdb_label': '161700.x1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -5741, 169401], 'min_quad_twist_disc': -35, 'modell_images': [], 'modm_images': ['2310.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '6.2738637330487070073199708041', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.39654276752832833632081896486', 'prec': 103}, 'szpiro_ratio': 4.9120414085354644, '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, 0, 0, 0, 0, 1, 0, -1, 0, 2, 0, 0, 0, -7, 0, -3, 0], 'aplist': [0, -1, 0, 0, -1, 2, -7, -3, -3, -5, 0, -2, 0, -1, 8, 9, 9, -5, 2, -12, 0, -14, 9, -5, 7], 'class_deg': 1, 'class_size': 1, 'conductor': 161700, 'isogeny_matrix': [[1]], 'lmfdb_iso': '161700.x', 'trace_hash': 521741273114202677}
• 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': '0.0051301014852636704100822192165', 'prec': 110}, 'conductor': 161700, 'gens': [[302368, 165729025, 3]], 'heights': [{'__RealLiteral__': 0, 'data': '6.2738637330487070073199708041', 'prec': 100}], 'lmfdb_label': '161700.x1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.046352631327563845805850899733', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.6529614818780824543472588686086208443', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 161700.x1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7226601
    {'degree': 3, 'field': [-26, 18, 0, 1], 'lmfdb_label': '161700.x1', 'torsion': [2]}
  • id: 7226602
    {'degree': 6, 'field': [2055, 2190, 1099, 64, -3, -2, 1], 'lmfdb_label': '161700.x1', 'torsion': [2, 2]}
  • id: 7226603
    {'degree': 8, 'field': [209484, -32400, -33642, -1407, 3360, -147, -35, -4, 1], 'lmfdb_label': '161700.x1', 'torsion': [3]}
  • id: 7226604
    {'degree': 12, 'field': [8164013, -41035786, 43379768, -19991970, 4534435, -298436, -59328, -7636, 4535, 150, -104, -2, 1], 'lmfdb_label': '161700.x1', '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: 4001059
    {'conductor': 161700, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '161700.x1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 4001060
    {'conductor': 161700, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '161700.x1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 4001061
    {'conductor': 161700, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '161700.x1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 4001062
    {'conductor': 161700, 'conductor_valuation': 2, 'discriminant_valuation': 11, 'j_denominator_valuation': 5, 'kodaira_symbol': -9, 'lmfdb_label': '161700.x1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 4001063
    {'conductor': 161700, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '161700.x1', 'prime': 11, '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': [[1541, 2, 1541, 3], [211, 2, 211, 3], [661, 2, 661, 3], [1387, 2, 1387, 3], [1, 0, 2, 1], [1, 2, 0, 1], [2309, 2, 2308, 3], [1, 1, 2309, 0]], 'adelic_image': '2310.2.0.?', 'conductor': 161700, 'lmfdb_label': '161700.x1', 'prime': 0}
• lmfdb_iso 161700.x does not appear in ec_padic