Elliptic curve data - 13680.n4

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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': '13680g', 'Clabel': '13680g1', 'Cnumber': 1, 'abc_quality': 0.9309316752705356, 'absD': 114004810800, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 456, 'ainvs': [0, 0, 0, -858, 18907], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 13680, 'degree': 8192, 'elladic_images': ['4.12.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.81261023155419766300799641202', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 13, 'isogeny_degrees': [1, 2, 4], 'jinv': [-5988775936, 9774075], 'lmfdb_iso': '13680.n', 'lmfdb_label': '13680.n4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -95, 732], 'min_quad_twist_disc': 12, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '6.6.0.a.1', '12.24.0-12.g.1.1', '152.24.0.?', '456.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.032255027033494380837963086406', 'prec': 107}, 'szpiro_ratio': 3.487904360232061, '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, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 6, 0, -1, 0], 'aplist': [0, 0, -1, 0, 0, -2, 6, -1, 4, 6, 0, -2, 2, 4, -4, 6, 12, -2, -4, 0, -6, -8, -8, -14, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 13680, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '13680.n', 'trace_hash': 55272156958375124}
• 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': '0.19686826822919333259958930913', 'prec': 103}, 'conductor': 13680, 'gens': [], 'heights': [], 'lmfdb_label': '13680.n4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.94309703626488556551718014328', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.8861940725297711310343602865686079776', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-37, 0, 1]], 'xcoord_integral_points': [-37]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [0, 0], '19': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '13680.n4'}
• ec_torsion_growth •

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

  
  
  • id: 704613
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '13680.n4', 'torsion': [4]}
  • id: 704612
    {'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '13680.n4', 'torsion': [2, 2]}
  • id: 704614
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '13680.n4', 'torsion': [4]}
  • id: 704615
    {'degree': 4, 'field': [1, 0, -1, 0, 1], 'lmfdb_label': '13680.n4', 'torsion': [2, 4]}
  • id: 704616
    {'degree': 4, 'field': [75, 0, -15, 0, 1], 'lmfdb_label': '13680.n4', 'torsion': [2, 4]}
  • id: 704618
    {'degree': 8, 'field': [6, 12, 4, -22, -13, 26, -4, -4, 1], 'lmfdb_label': '13680.n4', 'torsion': [8]}
  • id: 704619
    {'degree': 8, 'field': [256, 0, 1252, 0, -27, 0, 7, 0, 1], 'lmfdb_label': '13680.n4', 'torsion': [8]}
  • id: 704617
    {'degree': 8, 'field': [361, 266, 98, -46, -2, -2, 2, -2, 1], 'lmfdb_label': '13680.n4', 'torsion': [4, 4]}
  • id: 704620
    {'degree': 8, 'field': [538, -1028, 1966, 1112, -88, 110, 46, -2, 1], 'lmfdb_label': '13680.n4', 'torsion': [6]}
  • id: 704624
    {'degree': 16, 'field': [9, 0, 3624, 0, 1459246, 0, 7248, 0, 39, 0, 2416, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '13680.n4', 'torsion': [2, 6]}
  • id: 704622
    {'degree': 16, 'field': [25, -110, 334, -560, 725, -626, 678, -770, 392, -268, 216, -82, 65, -28, 16, -4, 1], 'lmfdb_label': '13680.n4', 'torsion': [2, 8]}
  • id: 704625
    {'degree': 16, 'field': [5776, 23104, 0, -49248, 10944, -17328, -5504, 16288, 18504, -1632, -7848, 96, -28, -28, 24, -8, 1], 'lmfdb_label': '13680.n4', 'torsion': [12]}
  • id: 704623
    {'degree': 16, 'field': [27075, -45600, 70500, -48900, 5790, 4440, 9120, -23460, 22996, -14224, 6460, -2116, 694, -136, 40, -4, 1], 'lmfdb_label': '13680.n4', 'torsion': [2, 8]}
  • id: 704621
    {'degree': 16, 'field': [38416, 0, 20188, 0, 21781, 0, -10967, 0, 1714, 0, -947, 0, 226, 0, 13, 0, 1], 'lmfdb_label': '13680.n4', 'torsion': [2, 8]}
  • id: 704626
    {'degree': 16, 'field': [5827396, -12852136, 14172488, -14078712, 6551996, 369664, 256720, -183696, 80224, -11292, -3320, 1112, -64, -84, 32, -8, 1], 'lmfdb_label': '13680.n4', 'torsion': [12]}
• 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: 299264
    {'conductor': 13680, 'conductor_valuation': 4, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '13680.n4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 299265
    {'conductor': 13680, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '13680.n4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 299266
    {'conductor': 13680, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '13680.n4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 299267
    {'conductor': 13680, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '13680.n4', 'prime': 19, 'reduction_type': -1, '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: 1755033
    {'adelic_gens': [[97, 8, 388, 33], [148, 455, 281, 450], [449, 8, 448, 9], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [7, 6, 450, 451], [167, 168, 386, 161], [403, 402, 298, 67]], 'adelic_image': '456.48.0.?', 'conductor': 13680, 'lmfdb_label': '13680.n4', 'prime': 0}
  • id: 65000
    {'conductor': 13680, 'elladic_image': '4.12.0.8', 'lmfdb_label': '13680.n4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 13680.n does not appear in ec_padic