Elliptic curve data - 231200.by1

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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
  serre_invariants	integer[]
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '231200by', 'Clabel': '231200by1', 'Cnumber': 1, 'abc_quality': 0.8489816898373131, 'absD': 10258466825000000000, 'adelic_genus': 0, 'adelic_index': 2, 'adelic_level': 680, 'ainvs': [0, 1, 0, 459992, -96423512], 'analytic_rank': 1, 'bad_primes': [2, 5, 17], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 231200, 'degree': 3317760, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.3350125233716566076909490431', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 50, 'isogeny_degrees': [1], 'jinv': [55742968, 53125], 'lmfdb_iso': '231200.by', 'lmfdb_label': '231200.by1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 64, 136], 'min_quad_twist_disc': -340, 'modell_images': [], 'modm_images': ['680.2.0.?'], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.4290514916557950003641713417', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 7225], [5, 14, 9248], [17, 162, 800]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.40617349029346060179712202354', 'prec': 107}, 'szpiro_ratio': 4.10738694853261, '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, -2, 0, -2, 0, 0, 0, -5, 0, 0, 0, 0, 0, -3, 0], 'aplist': [0, 1, 0, -2, 0, -5, 0, -3, 2, 3, -7, -8, 2, 10, 3, 1, 1, -11, 14, 13, -7, 16, 0, -9, -5], 'class_deg': 1, 'class_size': 1, 'conductor': 231200, 'isogeny_matrix': [[1]], 'lmfdb_iso': '231200.by', 'trace_hash': 1546983378193097700}
• 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': '0.0093720347851167237367306572891', 'prec': 110}, 'conductor': 231200, 'gens': [[5043, 361250, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.4290514916557950003641713417', 'prec': 100}], 'lmfdb_label': '231200.by1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.12491889439882371232940564025', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.7124970360522163567443421167379564303', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [], 'xcoord_integral_points': [5043]}
• lmfdb_label 231200.by1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 10017558
    {'degree': 3, 'field': [10, -6, -1, 1], 'lmfdb_label': '231200.by1', 'torsion': [2]}
  • id: 10017559
    {'degree': 6, 'field': [270, -360, 171, -20, 2, 0, 1], 'lmfdb_label': '231200.by1', 'torsion': [2, 2]}
  • id: 10017560
    {'degree': 8, 'field': [-4876875, 0, -306000, 0, -7650, 0, 0, 0, 1], 'lmfdb_label': '231200.by1', 'torsion': [3]}
  • id: 10017561
    {'degree': 12, 'field': [-52064, 8620, 15124, -5060, -2300, 1396, 300, -436, 20, 75, -11, -5, 1], 'lmfdb_label': '231200.by1', '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: 5731300
    {'conductor': 231200, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '231200.by1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 5731301
    {'conductor': 231200, 'conductor_valuation': 2, 'discriminant_valuation': 11, 'j_denominator_valuation': 5, 'kodaira_symbol': -9, 'lmfdb_label': '231200.by1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 5731302
    {'conductor': 231200, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '231200.by1', 'prime': 17, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
• 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': [[1, 1, 679, 0], [241, 2, 241, 3], [341, 2, 341, 3], [511, 2, 511, 3], [1, 0, 2, 1], [1, 2, 0, 1], [137, 2, 137, 3], [679, 2, 678, 3]], 'adelic_image': '680.2.0.?', 'conductor': 231200, 'lmfdb_label': '231200.by1', 'prime': 0}
• lmfdb_iso 231200.by does not appear in ec_padic