Elliptic curve data - 167310.z1

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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': '167310fr', 'Clabel': '167310fr2', 'Cnumber': 2, 'abc_quality': 1.1429957712248329, 'absD': 16768131334570044000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1560, 'ainvs': [1, -1, 0, -140591385, 641667358541], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 11, 13], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 167310, 'degree': 19169280, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.1579093519344202272612882407', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 25, 'isogeny_degrees': [1, 2], 'jinv': [1073361235887380439, 58564000], 'lmfdb_iso': '167310.z', 'lmfdb_label': '167310.z1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -7487115, -7883458075], 'min_quad_twist_disc': -39, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '40.6.0.e.1', '156.6.0.?', '1560.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 195], [3, 6, 3718], [5, 6, 16731], [11, 12, 15210], [13, 62, 990]], 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.95954426167124025237236135029', 'prec': 103}, 'szpiro_ratio': 5.645156737295421, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
• 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, -1, 0, 2, -1, 0, 1, -1, 0, 0, -2, 0, 1, -2, 0, -2, -1], 'aplist': [-1, 0, -1, 2, -1, 0, -2, -2, 2, -6, 8, 4, 6, 0, 8, 12, 4, 2, -8, -8, -10, -8, 0, -10, -10], 'class_deg': 2, 'class_size': 2, 'conductor': 167310, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '167310.z', 'trace_hash': 1104501179944263154}
• 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': '0.0018074853594222878319645067787', 'prec': 110}, 'conductor': 167310, 'gens': [], 'heights': [], 'lmfdb_label': '167310.z1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.16490161191727352061721924057', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.3192128953381881649377539245809601810', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[27379, -27379, 2]], 'xcoord_integral_points': []}
• lmfdb_label 167310.z1 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7459991
    {'degree': 2, 'field': [-390, 0, 1], 'lmfdb_label': '167310.z1', 'torsion': [2, 2]}
  • id: 7459992
    {'degree': 4, 'field': [1560, 0, -78, 0, 1], 'lmfdb_label': '167310.z1', 'torsion': [4]}
  • id: 7459993
    {'degree': 8, 'field': [8836, 0, 9208, 0, 1344, 0, -68, 0, 1], 'lmfdb_label': '167310.z1', 'torsion': [2, 4]}
  • id: 7459995
    {'degree': 8, 'field': [10752, -1584, -1728, -1440, -168, -132, 12, -3, 1], 'lmfdb_label': '167310.z1', 'torsion': [6]}
  • id: 7459994
    {'degree': 8, 'field': [1345600, 0, -281600, 0, 3960, 0, -80, 0, 1], 'lmfdb_label': '167310.z1', 'torsion': [2, 4]}
  • id: 7459997
    {'degree': 16, 'field': [-1556629871456, 336514482624, 186447915844, 19482409464, 9372281332, -4798214304, -206092088, -2779536, 17147620, 5476752, -865544, -151320, 19720, 1584, -227, -6, 1], 'lmfdb_label': '167310.z1', 'torsion': [2, 6]}
  • id: 7459996
    {'degree': 16, 'field': [34821540328, 1521962464, 22883617890, 3512406712, 4193438496, 1263687576, 389724885, 25907822, -5821101, -2889720, -118158, 28272, 12032, -88, -141, -6, 1], 'lmfdb_label': '167310.z1', 'torsion': [8]}
• 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: 4144164
    {'conductor': 167310, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '167310.z1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 4144165
    {'conductor': 167310, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '167310.z1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4144166
    {'conductor': 167310, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '167310.z1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 4144167
    {'conductor': 167310, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '167310.z1', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 4144168
    {'conductor': 167310, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '167310.z1', 'prime': 13, '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: 2745343
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [524, 1, 1039, 0], [1, 4, 0, 1], [2, 1, 779, 0], [314, 1, 623, 0], [196, 1369, 585, 976], [1204, 1, 479, 0], [1557, 4, 1556, 5]], 'adelic_image': '1560.12.0.?', 'conductor': 167310, 'lmfdb_label': '167310.z1', 'prime': 0}
  • id: 634272
    {'conductor': 167310, 'elladic_image': '2.3.0.1', 'lmfdb_label': '167310.z1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 167310.z does not appear in ec_padic