Elliptic curve data - 1728.k1

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

  
  {'Ciso': '1728y', 'Clabel': '1728y1', 'Cnumber': 1, 'abc_quality': 1.2262943855309167, 'absD': 644972544, 'adelic_genus': 3, 'adelic_index': 36, 'adelic_level': 72, 'ainvs': [0, 0, 0, -108, 1296], 'analytic_rank': 1, 'bad_primes': [2, 3], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 1728, 'degree': 576, 'elladic_images': ['9.9.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.37510416419092823696485610454', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 10, 'isogeny_degrees': [1], 'jinv': [-216, 1], 'lmfdb_iso': '1728.k', 'lmfdb_label': '1728.k1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -3, 6], 'min_quad_twist_disc': 24, 'modell_images': ['3Nn'], 'modm_images': ['3.3.0.a.1', '9.9.0.a.1', '12.6.0.d.1', '24.12.1.bi.1', '36.18.0.a.1', '72.36.3.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 2, 'num_int_pts': 8, 'optimality': 1, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.17072412902146954095677645967', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.3152890280100856683531179750', 'prec': 103}, 'szpiro_ratio': 3.7368568478295674, '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, -1, 0, 3, 0, 0, 0, -3, 0, 0, 0, 0, 0, -4, 0, -6, 0], 'aplist': [0, 0, -1, 3, -3, 0, -4, -6, -6, -2, 9, 2, 10, -6, -6, 13, -12, -8, -6, -12, 9, 0, -3, -14, -9], 'class_deg': 1, 'class_size': 1, 'conductor': 1728, 'isogeny_matrix': [[1]], 'lmfdb_iso': '1728.k', 'trace_hash': 837586824734176122}
• 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': '0.47226815563125025449224051205', 'prec': 103}, 'conductor': 1728, 'gens': [[18, 72, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.17072412902146954095677645967', 'prec': 103}], 'lmfdb_label': '1728.k1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.4076132756683367784845193590', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.8837626058504140031043896467435431725', 'prec': 130}, 'tamagawa_product': 12, 'torsion_generators': [], 'xcoord_integral_points': [-14, 0, 18, 928]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [3, 0], '7': [1, 0], '11': [1, 0], '13': [1, 1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [3, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '1728.k1'}
• ec_torsion_growth •

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

  
  
  • id: 88009
    {'degree': 3, 'field': [-2, 3, 0, 1], 'lmfdb_label': '1728.k1', 'torsion': [2]}
  • id: 88010
    {'degree': 6, 'field': [6, 0, -3, 0, 0, 0, 1], 'lmfdb_label': '1728.k1', 'torsion': [2, 2]}
  • id: 88011
    {'degree': 8, 'field': [-3, 0, 0, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '1728.k1', 'torsion': [3]}
  • id: 88012
    {'degree': 12, 'field': [-8, 48, -102, 70, 45, -72, -24, 90, -57, 4, 12, -6, 1], 'lmfdb_label': '1728.k1', 'torsion': [4]}
  • id: 88013
    {'degree': 16, 'field': [9, 0, 0, 0, -18, 0, 0, 0, 39, 0, 0, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '1728.k1', 'torsion': [3, 3]}
• 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: 27731
    {'conductor': 1728, 'conductor_valuation': 6, 'discriminant_valuation': 15, 'j_denominator_valuation': 0, 'kodaira_symbol': -9, 'lmfdb_label': '1728.k1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 27732
    {'conductor': 1728, 'conductor_valuation': 3, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '1728.k1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1675363
    {'adelic_gens': [[53, 28, 53, 17], [35, 54, 27, 53], [1, 18, 0, 1], [3, 16, 50, 51], [5, 18, 36, 29], [12, 11, 49, 51], [55, 18, 54, 19], [1, 0, 18, 1], [17, 68, 26, 31]], 'adelic_image': '72.36.3.?', 'conductor': 1728, 'lmfdb_label': '1728.k1', 'prime': 0}
  • id: 8499
    {'conductor': 1728, 'elladic_image': '9.9.0.1', 'lmfdb_label': '1728.k1', 'modell_image': '3Nn', 'prime': 3}
• ec_padic •

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

  
  
  • id: 48134
    {'lmfdb_iso': '1728.k', 'p': 5, 'prec': 20, 'unit': 1357236938946, 'val': 2}
  • id: 48135
    {'lmfdb_iso': '1728.k', 'p': 7, 'prec': 20, 'unit': 7174915785178073, 'val': 1}
  • id: 48141
    {'lmfdb_iso': '1728.k', 'p': 11, 'prec': 20, 'unit': 44091745349774764060, 'val': 1}
  • id: 48142
    {'lmfdb_iso': '1728.k', 'p': 17, 'prec': 20, 'unit': 152994090447267302564700, 'val': 1}
  • id: 48143
    {'lmfdb_iso': '1728.k', 'p': 19, 'prec': 20, 'unit': 156895792911192411211182, 'val': 1}
  • id: 48146
    {'lmfdb_iso': '1728.k', 'p': 23, 'prec': 20, 'unit': 16677095276143983697426932, 'val': 1}
  • id: 48139
    {'lmfdb_iso': '1728.k', 'p': 29, 'prec': 20, 'unit': 1086729253570669562211290171, 'val': 1}
  • id: 48136
    {'lmfdb_iso': '1728.k', 'p': 31, 'prec': 20, 'unit': 15452234737406057513967782583, 'val': 1}
  • id: 48151
    {'lmfdb_iso': '1728.k', 'p': 37, 'prec': 20, 'unit': 209873306219653824679583238716, 'val': 1}
  • id: 48137
    {'lmfdb_iso': '1728.k', 'p': 41, 'prec': 20, 'unit': 34257286365485085395177623625, 'val': 2}
  • id: 48138
    {'lmfdb_iso': '1728.k', 'p': 43, 'prec': 20, 'unit': 1393474877513558133009565733454, 'val': 1}
  • id: 48140
    {'lmfdb_iso': '1728.k', 'p': 47, 'prec': 20, 'unit': 5689681890630745010943196045577, 'val': 1}
  • id: 48144
    {'lmfdb_iso': '1728.k', 'p': 53, 'prec': 20, 'unit': 277799390088431213364398700676006, 'val': 1}
  • id: 48149
    {'lmfdb_iso': '1728.k', 'p': 59, 'prec': 20, 'unit': 741090062821427774248085965886259, 'val': 1}
  • id: 48150
    {'lmfdb_iso': '1728.k', 'p': 61, 'prec': 20, 'unit': 551582286545306590227113041659420, 'val': 1}
  • id: 48133
    {'lmfdb_iso': '1728.k', 'p': 67, 'prec': 20, 'unit': 24803392931616494289738072363680903, 'val': 1}
  • id: 48148
    {'lmfdb_iso': '1728.k', 'p': 71, 'prec': 20, 'unit': 97777490771283885844640993124543396, 'val': 1}
  • id: 48145
    {'lmfdb_iso': '1728.k', 'p': 73, 'prec': 20, 'unit': 3168086919557745512977952769393109, 'val': 2}
  • id: 48132
    {'lmfdb_iso': '1728.k', 'p': 83, 'prec': 20, 'unit': 244590855893522006735876097810745682, 'val': 1}
  • id: 48147
    {'lmfdb_iso': '1728.k', 'p': 89, 'prec': 20, 'unit': 380505288902000916316443142641179210, 'val': 1}
  • id: 48131
    {'lmfdb_iso': '1728.k', 'p': 97, 'prec': 20, 'unit': 7822413476741498466784346007363737524, 'val': 1}