Elliptic curve data - 205350.i2

Formats: - HTML - YAML - JSON - 2024-05-20T10:33:18.474094

• 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': '205350dy', 'Clabel': '205350dy1', 'Cnumber': 1, 'abc_quality': 1.0697736458506328, 'absD': 70646436105541200, 'adelic_genus': 1, 'adelic_index': 48, 'adelic_level': 740, 'ainvs': [1, 1, 0, 101130, -3168540], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 37], 'class_deg': 5, 'class_size': 2, 'cm': 0, 'conductor': 205350, 'degree': 2419200, 'elladic_images': ['5.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.9221722767342454316599203738', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 8, 'isogeny_degrees': [1, 5], 'jinv': [90325805449595, 55788550416], 'lmfdb_iso': '205350.i', 'lmfdb_label': '205350.i2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 101130, -3168540], 'min_quad_twist_disc': 1, 'modell_images': ['5B'], 'modm_images': ['5.6.0.a.1', '20.12.0.p.1', '148.2.0.?', '185.24.0.?', '740.48.1.?'], 'nonmax_primes': [5], 'nonmax_rad': 5, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.75120314650083925813443656717', 'prec': 103}, 'szpiro_ratio': 3.775694495593082, '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, -1, 1, 0, 1, -2, -1, 1, 0, -2, -1, 6, 2, 0, 1, 8, -1, -1, 0], 'aplist': [-1, -1, 0, -2, -2, 6, 8, -1, 1, 6, 0, 0, 3, 1, -12, 9, 9, 0, 2, 12, 1, -1, 4, 6, -2], 'class_deg': 5, 'class_size': 2, 'conductor': 205350, 'isogeny_matrix': [[1, 5], [5, 1]], 'lmfdb_iso': '205350.i', 'trace_hash': 911954862884362571}
• 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': '0.021400423798793317197586246124', 'prec': 107}, 'conductor': 205350, 'gens': [], 'heights': [], 'lmfdb_label': '205350.i2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.20004985698980406230309936740', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.6003988559184324984247949392241863941', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [], 'xcoord_integral_points': []}
• lmfdb_label 205350.i2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 8988610
    {'degree': 3, 'field': [-20, 10, 0, 1], 'lmfdb_label': '205350.i2', 'torsion': [2]}
  • id: 8988611
    {'degree': 4, 'field': [49, -7, 5, -1, 1], 'lmfdb_label': '205350.i2', 'torsion': [5]}
  • id: 8988612
    {'degree': 6, 'field': [37, 0, 7, 0, 19, 0, 1], 'lmfdb_label': '205350.i2', 'torsion': [2, 2]}
  • id: 8988613
    {'degree': 8, 'field': [-8854544, -1776962, 321493, 93906, -2805, -1314, -17, -2, 1], 'lmfdb_label': '205350.i2', 'torsion': [3]}
  • id: 8988615
    {'degree': 12, 'field': [11963, 6452, 10857, -13415, 6018, -6185, 2254, -803, 476, -61, 37, -3, 1], 'lmfdb_label': '205350.i2', 'torsion': [10]}
  • id: 8988614
    {'degree': 12, 'field': [465504, 1938734, 1750993, -273410, 302025, -5106, -32661, 9278, 2275, -110, -7, -2, 1], 'lmfdb_label': '205350.i2', 'torsion': [4]}
  • id: 8988616
    {'degree': 20, 'field': [-1024, 0, 0, 0, 0, 1355712, 0, 0, 0, 0, 13697284, 0, 0, 0, 0, -20862, 0, 0, 0, 0, 1], 'lmfdb_label': '205350.i2', 'torsion': [5]}
• 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: 5086681
    {'conductor': 205350, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '205350.i2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5086682
    {'conductor': 205350, 'conductor_valuation': 1, 'discriminant_valuation': 20, 'j_denominator_valuation': 20, 'kodaira_symbol': 24, 'lmfdb_label': '205350.i2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5086683
    {'conductor': 205350, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '205350.i2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 5086684
    {'conductor': 205350, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '205350.i2', 'prime': 37, '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

  
  
  • id: 2978707
    {'adelic_gens': [[731, 10, 730, 11], [1, 0, 10, 1], [1, 10, 0, 1], [371, 10, 375, 51], [6, 13, 685, 621], [43, 10, 135, 657], [371, 10, 0, 667]], 'adelic_image': '740.48.1.?', 'conductor': 205350, 'lmfdb_label': '205350.i2', 'prime': 0}
  • id: 759404
    {'conductor': 205350, 'elladic_image': '5.6.0.1', 'lmfdb_label': '205350.i2', 'modell_image': '5B', 'prime': 5}
• lmfdb_iso 205350.i does not appear in ec_padic