Elliptic curve data - 47040.j2

Formats: - HTML - YAML - JSON - 2024-05-16T08:46:04.131506

• 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': '47040s', 'Clabel': '47040s1', 'Cnumber': 1, 'abc_quality': 0.8976805217851915, 'absD': 15805440, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 420, 'ainvs': [0, -1, 0, 19, -195], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 47040, 'degree': 12288, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.061602138970672727392756260342', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 9, 'isogeny_degrees': [1, 2], 'jinv': [2048, 45], 'lmfdb_iso': '47040.j', 'lmfdb_label': '47040.j2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, 5, -22], 'min_quad_twist_disc': 8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '60.6.0.d.1', '70.6.0.a.1', '84.6.0.?', '420.12.0.?'], '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': '-1.0024980487597766900646086934', 'prec': 103}, 'szpiro_ratio': 2.2311036325793343, '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, -1, 0, 0, 0, 1, 0, -4, 0, 6, 0, 1, 0, 6, 0, 2, 0], 'aplist': [0, -1, -1, 0, -4, 6, 6, 2, 6, -6, 2, -2, -2, 8, 0, -4, 8, 8, 8, 12, 6, -8, -4, 14, 10], 'class_deg': 2, 'class_size': 2, 'conductor': 47040, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '47040.j', 'trace_hash': 1951893918549686345}
• 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': '0.88408304544890033551553325416', 'prec': 103}, 'conductor': 47040, 'gens': [], 'heights': [], 'lmfdb_label': '47040.j2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.0705829234359773368672002898', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.1411658468719546737344005796299826264', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[5, 0, 1]], 'xcoord_integral_points': [5]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '5': [0, 0], '7': 'a'}, 'iwp0': 3, 'lmfdb_label': '47040.j2'}
• ec_torsion_growth •

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

  
  
  • id: 2292270
    {'degree': 2, 'field': [9, -1, 1], 'lmfdb_label': '47040.j2', 'torsion': [2, 2]}
  • id: 2292271
    {'degree': 4, 'field': [-140, 0, -28, 0, 1], 'lmfdb_label': '47040.j2', 'torsion': [4]}
  • id: 2292274
    {'degree': 8, 'field': [-9408, 0, -20384, 0, 336, 0, 0, 0, 1], 'lmfdb_label': '47040.j2', 'torsion': [6]}
  • id: 2292272
    {'degree': 8, 'field': [81, 0, 612, 0, 1734, 0, 68, 0, 1], 'lmfdb_label': '47040.j2', 'torsion': [2, 4]}
  • id: 2292273
    {'degree': 8, 'field': [21676, 3888, -3554, -656, 299, 32, -6, -4, 1], 'lmfdb_label': '47040.j2', 'torsion': [2, 4]}
  • id: 2292275
    {'degree': 16, 'field': [117649, 0, 336140, 0, -185906, 0, 76832, 0, -12593, 0, 2744, 0, -182, 0, -28, 0, 1], 'lmfdb_label': '47040.j2', 'torsion': [8]}
  • id: 2292276
    {'degree': 16, 'field': [448084224, 0, -464679936, 0, 167932800, 0, 4741632, 0, 294000, 0, -25088, 0, -168, 0, 0, 0, 1], 'lmfdb_label': '47040.j2', 'torsion': [2, 6]}
• 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: 1121878
    {'conductor': 47040, 'conductor_valuation': 6, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '47040.j2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1121879
    {'conductor': 47040, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '47040.j2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1121880
    {'conductor': 47040, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '47040.j2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1121881
    {'conductor': 47040, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '47040.j2', 'prime': 7, 'reduction_type': 0, '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: 1977754
    {'adelic_gens': [[281, 4, 142, 9], [1, 2, 2, 5], [124, 1, 179, 0], [1, 4, 0, 1], [317, 106, 104, 315], [417, 4, 416, 5], [1, 0, 4, 1], [3, 4, 8, 11], [254, 1, 83, 0]], 'adelic_image': '420.12.0.?', 'conductor': 47040, 'lmfdb_label': '47040.j2', 'prime': 0}
  • id: 203685
    {'conductor': 47040, 'elladic_image': '2.3.0.1', 'lmfdb_label': '47040.j2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 47040.j does not appear in ec_padic