Elliptic curve data - 157146.j2

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '157146b', 'Clabel': '157146b1', 'Cnumber': 1, 'abc_quality': 0.9621878694896706, 'absD': 212807477317047681024, 'adelic_genus': 2, 'adelic_index': 96, 'adelic_level': 4400088, 'ainvs': [1, 0, 0, -5245956, 4677234192], 'analytic_rank': 1, 'bad_primes': [2, 3, 11, 2381], 'class_deg': 7, 'class_size': 2, 'cm': 0, 'conductor': 157146, 'degree': 6931344, 'elladic_images': ['7.48.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.7083611010143077820381635507', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 9, 'isogeny_degrees': [1, 7], 'jinv': [-15966056003238798715810369, 212807477317047681024], 'lmfdb_iso': '157146.j', 'lmfdb_label': '157146.j2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -5245956, 4677234192], 'min_quad_twist_disc': 1, 'modell_images': ['7B.1.1'], 'modm_images': ['7.48.0-7.a.1.2', '628584.2.0.?', '4400088.96.2.?'], 'nonmax_primes': [7], 'nonmax_rad': 7, 'num_bad_primes': 4, 'num_int_pts': 12, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.9712665306053729051439693954', 'prec': 100}, 'semistable': True, 'serre_invariants': [[2, 4, 78573], [3, 4, 26191], [7, 2, 2381], [11, 12, 14286], [2381, 2382, 66]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.7083611010143077820381635507', 'prec': 100}, 'szpiro_ratio': 4.852119918856678, 'torsion': 7, 'torsion_primes': [7], 'torsion_structure': [7]}
• 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, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 0, 1, -1, 1, -3, 1, 6, -1], 'aplist': [1, 1, -1, 1, 1, 0, -3, 6, 3, 9, 4, -11, 0, 2, -8, -9, 4, -8, 5, 9, -10, -11, 14, 6, -14], 'class_deg': 7, 'class_size': 2, 'conductor': 157146, 'isogeny_matrix': [[1, 7], [7, 1]], 'lmfdb_iso': '157146.j', 'trace_hash': 2294842054631972270}
• 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': '0.0044416817486811254034091711427', 'prec': 110}, 'conductor': 157146, 'gens': [[-448, 83516, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.9712665306053729051439693954', 'prec': 100}], 'lmfdb_label': '157146.j2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.17824134798141011834441393449', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '14.864721891779750504404663478098714601', 'prec': 130}, 'tamagawa_product': 1029, 'torsion_generators': [[1224, 8892, 1]], 'xcoord_integral_points': [-888, -448, 1224, 2016, 2304, 161736]}
• lmfdb_label 157146.j2 does not appear in ec_iwasawa
• ec_torsion_growth •

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

  
  
  • id: 7039924
    {'degree': 3, 'field': [324, -32, -1, 1], 'lmfdb_label': '157146.j2', 'torsion': [14]}
  • id: 7039925
    {'degree': 6, 'field': [2514336, 0, 9409, 0, -194, 0, 1], 'lmfdb_label': '157146.j2', 'torsion': [2, 14]}
  • id: 7039926
    {'degree': 8, 'field': [-20172, 0, 5759, 0, -492, 0, 0, 0, 1], 'lmfdb_label': '157146.j2', 'torsion': [21]}
  • id: 7039927
    {'degree': 12, 'field': [2100166294416, 1523199226032, 402947938632, 30511861728, -4306915058, -693244630, 12602217, 3491248, 144343, -11690, -531, -4, 1], 'lmfdb_label': '157146.j2', 'torsion': [28]}
• 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: 3886799
    {'conductor': 157146, 'conductor_valuation': 1, 'discriminant_valuation': 21, 'j_denominator_valuation': 21, 'kodaira_symbol': 25, 'lmfdb_label': '157146.j2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 21}
  • id: 3886800
    {'conductor': 157146, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '157146.j2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 7}
  • id: 3886801
    {'conductor': 157146, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '157146.j2', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 7}
  • id: 3886802
    {'conductor': 157146, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '157146.j2', 'prime': 2381, '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: 2681236
    {'adelic_gens': [[1466704, 7, 1466689, 4400082], [8, 7, 1100015, 4400082], [1, 14, 0, 1], [3300067, 2200058, 0, 2671483], [800024, 7, 400001, 4400082], [8, 7, 2200037, 4400082], [1, 0, 14, 1], [8, 5, 91, 57], [495272, 7, 1766681, 4400082], [4400075, 14, 4400074, 15]], 'adelic_image': '4400088.96.2.?', 'conductor': 157146, 'lmfdb_label': '157146.j2', 'prime': 0}
  • id: 599942
    {'conductor': 157146, 'elladic_image': '7.48.0.1', 'lmfdb_label': '157146.j2', 'modell_image': '7B.1.1', 'prime': 7}
• lmfdb_iso 157146.j does not appear in ec_padic