Elliptic curve data - 78144.n1

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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': '78144bt', 'Clabel': '78144bt2', 'Cnumber': 2, 'abc_quality': 0.9762393073325316, 'absD': 9665410056192, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 1628, 'ainvs': [0, -1, 0, -5329, -5327], 'analytic_rank': 0, 'bad_primes': [2, 3, 11, 37], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 78144, 'degree': 147456, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1811491936276388748067375609', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 13, 'isogeny_degrees': [1, 2], 'jinv': [1021697727568, 589929813], 'lmfdb_iso': '78144.n', 'lmfdb_label': '78144.n1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -1332, 1332], 'min_quad_twist_disc': -8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '44.6.0.c.1', '74.6.0.?', '1628.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 37], [3, 4, 2368], [11, 12, 7104], [37, 38, 2112]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.37247748297436934715330008587', 'prec': 103}, 'szpiro_ratio': 3.315775272411024, '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, -1, 0, -2, 0, 4, 0, 1, 0, -1, 0, -4, 0, 2, 0, 4, 0, 2, 0], 'aplist': [0, -1, -2, 4, -1, -4, 4, 2, -4, -4, 0, -1, -2, 6, 8, -2, -4, 4, -4, -16, 10, 2, -4, -6, -10], 'class_deg': 2, 'class_size': 2, 'conductor': 78144, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '78144.n', 'trace_hash': 1603371648631790729}
• 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': '0.094203458159090221302706017140', 'prec': 107}, 'conductor': 78144, 'gens': [], 'heights': [], 'lmfdb_label': '78144.n1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.61002008269237752755926817846', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2200401653847550551185363569260372238', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-1, 0, 1]], 'xcoord_integral_points': [-1]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '11': [0, 0], '37': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '78144.n1'}
• ec_torsion_growth •

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

  
  
  • id: 3688999
    {'degree': 2, 'field': [-9, -1, 1], 'lmfdb_label': '78144.n1', 'torsion': [2, 2]}
  • id: 3689000
    {'degree': 4, 'field': [148, 0, -14, 0, 1], 'lmfdb_label': '78144.n1', 'torsion': [4]}
  • id: 3689003
    {'degree': 8, 'field': [-5808, 0, 64, 0, 264, 0, 0, 0, 1], 'lmfdb_label': '78144.n1', 'torsion': [6]}
  • id: 3689002
    {'degree': 8, 'field': [9, 0, 1596, 0, -833, 0, 14, 0, 1], 'lmfdb_label': '78144.n1', 'torsion': [2, 4]}
  • id: 3689001
    {'degree': 8, 'field': [2304, 0, 1472, 0, 468, 0, -6, 0, 1], 'lmfdb_label': '78144.n1', 'torsion': [2, 4]}
  • id: 3689005
    {'degree': 16, 'field': [9801, 0, -5996532, 0, -24735332, 0, 3509808, 0, 758358, 0, 16748, 0, -1416, 0, -24, 0, 1], 'lmfdb_label': '78144.n1', 'torsion': [2, 6]}
  • id: 3689004
    {'degree': 16, 'field': [15015625, 0, 1285150, 0, 230721, 0, -388504, 0, 106174, 0, -14398, 0, 1128, 0, -50, 0, 1], 'lmfdb_label': '78144.n1', 'torsion': [8]}
• 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: 1901628
    {'conductor': 78144, 'conductor_valuation': 6, 'discriminant_valuation': 14, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '78144.n1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1901629
    {'conductor': 78144, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '78144.n1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1901630
    {'conductor': 78144, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '78144.n1', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1901631
    {'conductor': 78144, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '78144.n1', 'prime': 37, '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: 2180002
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1410, 1, 923, 0], [1333, 4, 1038, 9], [1, 4, 0, 1], [409, 1222, 1220, 407], [1625, 4, 1624, 5]], 'adelic_image': '1628.12.0.?', 'conductor': 78144, 'lmfdb_label': '78144.n1', 'prime': 0}
  • id: 322182
    {'conductor': 78144, 'elladic_image': '2.3.0.1', 'lmfdb_label': '78144.n1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 78144.n does not appear in ec_padic