Elliptic curve data - 3213.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
  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': '3213r', 'Clabel': '3213r3', 'Cnumber': 3, 'abc_quality': 1.1232788169201537, 'absD': 7205567889330222237, 'adelic_genus': 3, 'adelic_index': 144, 'adelic_level': 2142, 'ainvs': [0, 0, 1, -1103490, -427069591], 'analytic_rank': 1, 'bad_primes': [3, 7, 17], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 3213, 'degree': 44712, 'elladic_images': ['9.72.0.13'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.3782431001477024634129430366', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 9, 'iso_nlabel': 10, 'isogeny_degrees': [1, 3, 9], 'jinv': [838870874148864000, 40675641638471], 'lmfdb_iso': '3213.k', 'lmfdb_label': '3213.k1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 1, -1103490, -427069591], 'min_quad_twist_disc': 1, 'modell_images': ['3B.1.2'], 'modm_images': ['3.8.0-3.a.1.1', '9.72.0-9.e.1.1', '714.16.0.?', '2142.144.3.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '6.5268644544357489407715866923', 'prec': 100}, 'semistable': False, 'serre_invariants': [[3, 4, 1], [7, 8, 459], [17, 18, 189]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.3711818355352685796339682361', 'prec': 100}, 'szpiro_ratio': 6.607533162708135, '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, -2, 0, 0, 1, 0, 0, 0, 0, 0, -4, 0, 0, 4, -1, 0, 2, 0], 'aplist': [0, 0, 0, 1, 0, -4, -1, 2, 9, -9, 5, 2, 0, -1, -9, 0, 9, -1, 5, -9, -7, -10, 0, -9, -1], 'class_deg': 9, 'class_size': 3, 'conductor': 3213, 'isogeny_matrix': [[1, 3, 9], [3, 1, 3], [9, 3, 1]], 'lmfdb_iso': '3213.k', 'trace_hash': 1378549721123119123}
• 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': '0.0085957601741415972828077736353', 'prec': 110}, 'conductor': 3213, 'gens': [[-2783, 15781, 2]], 'heights': [{'__RealLiteral__': 0, 'data': '6.5268644544357489407715866923', 'prec': 100}], 'lmfdb_label': '3213.k1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.14774460371650815001510285655', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.8929270069959186757271819636471861058', 'prec': 130}, 'tamagawa_product': 3, 'torsion_generators': [], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [6, 1, 0], '3': 'a', '5': [1, 1, 0], '7': [2, 0], '11': [3, 1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '3213.k1'}
• ec_torsion_growth •

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

  
  
  • id: 167736
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '3213.k1', 'torsion': [3]}
  • id: 167737
    {'degree': 3, 'field': [-12, -24, 0, 1], 'lmfdb_label': '3213.k1', 'torsion': [2]}
  • id: 167738
    {'degree': 3, 'field': [-3, 0, 0, 1], 'lmfdb_label': '3213.k1', 'torsion': [3]}
  • id: 167741
    {'degree': 6, 'field': [1, 0, 0, -1, 0, 0, 1], 'lmfdb_label': '3213.k1', 'torsion': [9]}
  • id: 167742
    {'degree': 6, 'field': [3, 0, 0, -3, 0, 0, 1], 'lmfdb_label': '3213.k1', 'torsion': [9]}
  • id: 167740
    {'degree': 6, 'field': [3, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '3213.k1', 'torsion': [3, 3]}
  • id: 167739
    {'degree': 6, 'field': [121, -495, 450, 89, -42, -3, 1], 'lmfdb_label': '3213.k1', 'torsion': [2, 2]}
  • id: 167743
    {'degree': 6, 'field': [739, -309, 342, -67, 36, -3, 1], 'lmfdb_label': '3213.k1', 'torsion': [6]}
  • id: 167744
    {'degree': 9, 'field': [-343, 0, 0, -663, 0, 0, -69, 0, 0, 1], 'lmfdb_label': '3213.k1', 'torsion': [6]}
  • id: 167746
    {'degree': 12, 'field': [275625, -22050, -25011, 31458, -6618, -3522, 1057, 90, -18, -26, 21, -6, 1], 'lmfdb_label': '3213.k1', 'torsion': [2, 6]}
  • id: 167745
    {'degree': 12, 'field': [26764297, 28886550, 8584884, -1019606, -794901, 29316, 50208, -4668, -2829, 334, 12, -6, 1], 'lmfdb_label': '3213.k1', 'torsion': [4]}
  • id: 167751
    {'degree': 18, 'field': [-47899031, 140336712, -123518844, -62333790, 145621350, -49161816, -19666089, 17084988, -814860, -1432768, -3240, 43416, 29091, 360, -1944, -162, -18, 0, 1], 'lmfdb_label': '3213.k1', 'torsion': [2, 6]}
  • id: 167747
    {'degree': 18, 'field': [1, 0, 0, 6, 0, 0, 33, 0, 0, 20, 0, 0, 15, 0, 0, -3, 0, 0, 1], 'lmfdb_label': '3213.k1', 'torsion': [3, 9]}
  • id: 167749
    {'degree': 18, 'field': [4096, -24576, 147456, -780288, 2365440, -3796992, 3326208, -1531392, 1022976, -146176, 29568, 16128, -12048, -768, 1152, -12, -24, 0, 1], 'lmfdb_label': '3213.k1', 'torsion': [18]}
  • id: 167748
    {'degree': 18, 'field': [62500, -391500, 2222856, -1838088, 2387340, -2765934, 2476539, -1672803, 945333, -335192, 70173, -5319, -4878, 3051, -621, -18, 45, -9, 1], 'lmfdb_label': '3213.k1', 'torsion': [3, 6]}
  • id: 167750
    {'degree': 18, 'field': [117649, 0, 0, 227409, 0, 0, 415902, 0, 0, 46433, 0, 0, 5424, 0, 0, -69, 0, 0, 1], 'lmfdb_label': '3213.k1', 'torsion': [18]}
• 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: 58163
    {'conductor': 3213, 'conductor_valuation': 3, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '3213.k1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 58164
    {'conductor': 3213, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '3213.k1', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 58165
    {'conductor': 3213, 'conductor_valuation': 1, 'discriminant_valuation': 9, 'j_denominator_valuation': 9, 'kodaira_symbol': 13, 'lmfdb_label': '3213.k1', 'prime': 17, 'reduction_type': -1, '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: 1684892
    {'adelic_gens': [[1234, 9, 603, 2134], [1, 18, 0, 1], [10, 9, 81, 73], [1, 0, 18, 1], [1900, 9, 1503, 2134], [2125, 18, 2124, 19], [2128, 2133, 1971, 842], [1, 18, 10, 181]], 'adelic_image': '2142.144.3.?', 'conductor': 3213, 'lmfdb_label': '3213.k1', 'prime': 0}
  • id: 16132
    {'conductor': 3213, 'elladic_image': '9.72.0.13', 'lmfdb_label': '3213.k1', 'modell_image': '3B.1.2', 'prime': 3}
• ec_padic •

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

  
  
  • id: 105947
    {'lmfdb_iso': '3213.k', 'p': 13, 'prec': 20, 'unit': 318907337919621688182, 'val': 1}
  • id: 105950
    {'lmfdb_iso': '3213.k', 'p': 19, 'prec': 20, 'unit': 1831624980228930104585243, 'val': 1}
  • id: 105951
    {'lmfdb_iso': '3213.k', 'p': 23, 'prec': 20, 'unit': 3489484895136323704155195, 'val': 1}
  • id: 105946
    {'lmfdb_iso': '3213.k', 'p': 29, 'prec': 20, 'unit': 1486604773847515240630500062, 'val': 1}
  • id: 105955
    {'lmfdb_iso': '3213.k', 'p': 31, 'prec': 20, 'unit': 17401681549437111610499295498, 'val': 1}
  • id: 105942
    {'lmfdb_iso': '3213.k', 'p': 37, 'prec': 20, 'unit': 40050962947705343072401145478, 'val': 1}
  • id: 105945
    {'lmfdb_iso': '3213.k', 'p': 43, 'prec': 20, 'unit': 2134449763849530660546802766467, 'val': 1}
  • id: 105953
    {'lmfdb_iso': '3213.k', 'p': 47, 'prec': 20, 'unit': 23685560970510129153024725437899, 'val': 1}
  • id: 105949
    {'lmfdb_iso': '3213.k', 'p': 59, 'prec': 20, 'unit': 4395844219842387098874699511487919, 'val': 1}
  • id: 105954
    {'lmfdb_iso': '3213.k', 'p': 61, 'prec': 20, 'unit': 2875984544897747958488145338384618, 'val': 1}
  • id: 105941
    {'lmfdb_iso': '3213.k', 'p': 67, 'prec': 20, 'unit': 23460737250310861398311540446724558, 'val': 1}
  • id: 105943
    {'lmfdb_iso': '3213.k', 'p': 71, 'prec': 20, 'unit': 118839627973800331017702051544659887, 'val': 1}
  • id: 105944
    {'lmfdb_iso': '3213.k', 'p': 73, 'prec': 20, 'unit': 104494016901982166847876937472964100, 'val': 1}
  • id: 105948
    {'lmfdb_iso': '3213.k', 'p': 79, 'prec': 20, 'unit': 538299485913926879090526570108345236, 'val': 1}
  • id: 105952
    {'lmfdb_iso': '3213.k', 'p': 89, 'prec': 20, 'unit': 402839039504508373526335755255257164, 'val': 1}
  • id: 105940
    {'lmfdb_iso': '3213.k', 'p': 97, 'prec': 20, 'unit': 41983384804679282002354936800131179500, 'val': 1}