Elliptic curve data - 1728.y2

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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': '1728j', 'Clabel': '1728j3', 'Cnumber': 3, 'abc_quality': 1.0496550478531228, 'absD': 32614907904, 'adelic_genus': 3, 'adelic_index': 144, 'adelic_level': 72, 'ainvs': [0, 0, 0, -876, 13232], 'analytic_rank': 0, 'bad_primes': [2, 3], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 1728, 'degree': 1152, 'elladic_images': ['9.36.0.4'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.72451634274000679710197849719', 'prec': 103}, 'faltings_index': 2, 'faltings_ratio': 3, 'iso_nlabel': 24, 'isogeny_degrees': [1, 3, 9], 'jinv': [-1167051, 512], 'lmfdb_iso': '1728.y', 'lmfdb_label': '1728.y2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -123, -667], 'min_quad_twist_disc': -24, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '6.8.0-3.a.1.2', '9.36.0.d.1', '18.72.0-9.d.1.2', '24.16.0-24.d.1.1', '72.144.3.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 27], [3, 8, 32]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.77295954837829020510522186705', 'prec': 107}, 'szpiro_ratio': 4.360181548457515, '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, 3, 0, -1, 0, 0, 0, -3, 0, 4, 0, 0, 0, 0, 0, -2, 0], 'aplist': [0, 0, 3, -1, -3, 4, 0, -2, 6, 6, 5, -2, 6, 10, -6, 9, 12, -8, -14, 0, -7, 8, -3, 18, -1], 'class_deg': 9, 'class_size': 3, 'conductor': 1728, 'isogeny_matrix': [[1, 9, 3], [9, 1, 3], [3, 3, 1]], 'lmfdb_iso': '1728.y', 'trace_hash': 1730641451199619672}
• 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': '0.23479730111822426412933519504', 'prec': 103}, 'conductor': 1728, 'gens': [], 'heights': [], 'lmfdb_label': '1728.y2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.0930334821267245052555983495', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.1860669642534490105111966989412796740', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [0, 0], '7': [0, 0], '11': [0, 0], '13': [0, 0], '17': [0, 0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '1728.y2'}
• ec_torsion_growth •

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

  
  
  • id: 87839
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '1728.y2', 'torsion': [9]}
  • id: 87840
    {'degree': 3, 'field': [-2, 3, 0, 1], 'lmfdb_label': '1728.y2', 'torsion': [2]}
  • id: 87843
    {'degree': 6, 'field': [-1, 0, 0, -2, 0, 0, 1], 'lmfdb_label': '1728.y2', 'torsion': [18]}
  • id: 87841
    {'degree': 6, 'field': [6, 0, -3, 0, 0, 0, 1], 'lmfdb_label': '1728.y2', 'torsion': [2, 2]}
  • id: 87842
    {'degree': 6, 'field': [24, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '1728.y2', 'torsion': [3]}
  • id: 87844
    {'degree': 12, 'field': [-8, 48, -102, 70, 45, -72, -24, 90, -57, 4, 12, -6, 1], 'lmfdb_label': '1728.y2', 'torsion': [4]}
  • id: 87846
    {'degree': 12, 'field': [4, 0, -12, 0, 21, 0, -22, 0, 3, 0, 6, 0, 1], 'lmfdb_label': '1728.y2', 'torsion': [2, 18]}
  • id: 87845
    {'degree': 12, 'field': [121, 396, 564, 432, 6, -72, 62, -72, 24, 0, 6, 0, 1], 'lmfdb_label': '1728.y2', 'torsion': [3, 9]}
  • id: 87847
    {'degree': 18, 'field': [-128, 0, 0, 0, -576, 0, 2916, 0, -648, 0, 0, 0, -108, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '1728.y2', 'torsion': [27]}
  • id: 87848
    {'degree': 18, 'field': [4096, 0, 0, 1536, 0, 0, 936, 0, 0, -88, 0, 0, 105, 0, 0, -18, 0, 0, 1], 'lmfdb_label': '1728.y2', 'torsion': [2, 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: 27689
    {'conductor': 1728, 'conductor_valuation': 6, 'discriminant_valuation': 27, 'j_denominator_valuation': 9, 'kodaira_symbol': -21, 'lmfdb_label': '1728.y2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 27690
    {'conductor': 1728, 'conductor_valuation': 3, 'discriminant_valuation': 5, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '1728.y2', 'prime': 3, 'reduction_type': 0, '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

  
  
  • id: 1675374
    {'adelic_gens': [[10, 9, 9, 1], [55, 18, 0, 1], [1, 18, 10, 37], [35, 54, 27, 53], [65, 54, 63, 19], [1, 18, 0, 1], [55, 18, 54, 19], [1, 0, 18, 1]], 'adelic_image': '72.144.3.?', 'conductor': 1728, 'lmfdb_label': '1728.y2', 'prime': 0}
  • id: 8505
    {'conductor': 1728, 'elladic_image': '9.36.0.4', 'lmfdb_label': '1728.y2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 1728.y does not appear in ec_padic