Elliptic curve data - 1728.n2

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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': '1728a', 'Clabel': '1728a3', 'Cnumber': 3, 'abc_quality': 1.23864473399791, 'absD': 15552, 'ainvs': [0, 0, 0, -120, 506], 'analytic_rank': 1, 'bad_primes': [2, 3], 'class_deg': 27, 'class_size': 4, 'cm': -27, 'conductor': 1728, 'degree': 144, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.15058462164698299173481920743', 'prec': 107}, 'faltings_index': 2, 'faltings_ratio': 3, 'iso_nlabel': 13, 'isogeny_degrees': [1, 3, 9, 27], 'jinv': [-12288000, 1], 'lmfdb_iso': '1728.n', 'lmfdb_label': '1728.n2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 1, -30, 63], 'min_quad_twist_disc': 8, 'modell_images': [], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 2, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.25152563439374242147402372615', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 27], [3, 8, 32]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.95491333220533468452478745021', 'prec': 107}, 'szpiro_ratio': 3.4845331618928492, '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, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 7, 0], 'aplist': [0, 0, 0, -1, 0, -5, 0, 7, 0, 0, -4, -11, 0, -8, 0, 0, 0, 1, -5, 0, -7, 17, 0, 0, -19], 'class_deg': 27, 'class_size': 4, 'conductor': 1728, 'isogeny_matrix': [[1, 27, 3, 9], [27, 1, 9, 3], [3, 9, 1, 3], [9, 3, 3, 1]], 'lmfdb_iso': '1728.n', 'trace_hash': 1835559835706002148}
• 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': '1.3514380440104491068077171701', 'prec': 100}, 'conductor': 1728, 'gens': [[7, 3, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.25152563439374242147402372615', 'prec': 103}], 'lmfdb_label': '1728.n2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '3.7476067207013083074870676651', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.8278574736479477248342302820456660197', 'prec': 130}, 'tamagawa_product': 3, 'torsion_generators': [], 'xcoord_integral_points': [-1, 7]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 1, 0], '7': [1, 0], '11': [1, 1, 0], '13': [1, 0], '17': [1, 1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '1728.n2'}
• ec_torsion_growth •

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

  
  
  • id: 87715
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '1728.n2', 'torsion': [3]}
  • id: 87716
    {'degree': 3, 'field': [-2, 0, 0, 1], 'lmfdb_label': '1728.n2', 'torsion': [2]}
  • id: 87719
    {'degree': 6, 'field': [-8, 0, 36, 0, -12, 0, 1], 'lmfdb_label': '1728.n2', 'torsion': [9]}
  • id: 87720
    {'degree': 6, 'field': [-2, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '1728.n2', 'torsion': [6]}
  • id: 87717
    {'degree': 6, 'field': [1, -3, 0, 5, 0, -3, 1], 'lmfdb_label': '1728.n2', 'torsion': [2, 2]}
  • id: 87718
    {'degree': 6, 'field': [24, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '1728.n2', 'torsion': [3]}
  • id: 87721
    {'degree': 12, 'field': [-3, 0, 0, 0, 3, 0, 0, 0, -9, 0, 0, 0, 1], 'lmfdb_label': '1728.n2', 'torsion': [4]}
  • id: 87725
    {'degree': 12, 'field': [4, 0, 24, 0, 60, 0, 44, 0, 0, 0, -6, 0, 1], 'lmfdb_label': '1728.n2', 'torsion': [2, 6]}
  • id: 87722
    {'degree': 12, 'field': [121, 396, 564, 432, 6, -72, 62, -72, 24, 0, 6, 0, 1], 'lmfdb_label': '1728.n2', 'torsion': [3, 3]}
  • id: 87723
    {'degree': 12, 'field': [576, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '1728.n2', 'torsion': [9]}
  • id: 87724
    {'degree': 12, 'field': [1344, 0, -2016, 0, 336, 0, 480, 0, 72, 0, 6, 0, 1], 'lmfdb_label': '1728.n2', 'torsion': [7]}
  • id: 87726
    {'degree': 18, 'field': [-512, 0, 20736, 0, -69120, 0, 88704, 0, -57024, 0, 20592, 0, -4368, 0, 540, 0, -36, 0, 1], 'lmfdb_label': '1728.n2', 'torsion': [27]}
  • id: 87728
    {'degree': 18, 'field': [-8, 0, 96, 0, -432, 0, 996, 0, -1320, 0, 1044, 0, -492, 0, 132, 0, -18, 0, 1], 'lmfdb_label': '1728.n2', 'torsion': [18]}
  • id: 87727
    {'degree': 18, 'field': [216, 0, 0, 0, 0, 0, 108, 0, 0, 0, 0, 0, 90, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '1728.n2', 'torsion': [6]}
• 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: 27659
    {'conductor': 1728, 'conductor_valuation': 6, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '1728.n2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 27660
    {'conductor': 1728, 'conductor_valuation': 3, 'discriminant_valuation': 5, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '1728.n2', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 3}
• lmfdb_label 1728.n2 does not appear in ec_galrep
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 47928
    {'lmfdb_iso': '1728.n', 'p': 7, 'prec': 20, 'unit': 6481371048043327, 'val': 1}
  • id: 47931
    {'lmfdb_iso': '1728.n', 'p': 13, 'prec': 20, 'unit': 148593012187274634561, 'val': 1}
  • id: 47933
    {'lmfdb_iso': '1728.n', 'p': 19, 'prec': 20, 'unit': 1667846122796531864854685, 'val': 1}
  • id: 47935
    {'lmfdb_iso': '1728.n', 'p': 31, 'prec': 20, 'unit': 8292476593643646495202773934, 'val': 1}
  • id: 47927
    {'lmfdb_iso': '1728.n', 'p': 37, 'prec': 20, 'unit': 405303380629351886747038479515, 'val': 1}
  • id: 47930
    {'lmfdb_iso': '1728.n', 'p': 43, 'prec': 20, 'unit': 3798786422252466304101048230454, 'val': 1}
  • id: 47934
    {'lmfdb_iso': '1728.n', 'p': 61, 'prec': 20, 'unit': 432660639859578572640311593059899303, 'val': 0}
  • id: 47926
    {'lmfdb_iso': '1728.n', 'p': 67, 'prec': 20, 'unit': 36815274499852505928378945771578360, 'val': 1}
  • id: 47929
    {'lmfdb_iso': '1728.n', 'p': 73, 'prec': 20, 'unit': 93871678719891744537878106674827312, 'val': 1}
  • id: 47932
    {'lmfdb_iso': '1728.n', 'p': 79, 'prec': 20, 'unit': 463425154609143287127947956784495343, 'val': 1}
  • id: 47925
    {'lmfdb_iso': '1728.n', 'p': 97, 'prec': 20, 'unit': 31456032389650936847794628804389097655, 'val': 1}