Elliptic curve data - 5040.r2

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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': '5040bh', 'Clabel': '5040bh2', 'Cnumber': 2, 'abc_quality': 0.8466452702175264, 'absD': 411505920, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 420, 'ainvs': [0, 0, 0, 177, 362], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 5040, 'degree': 1536, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.34166608188998756168008405384', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 17, 'isogeny_degrees': [1, 2], 'jinv': [3286064, 2205], 'lmfdb_iso': '5040.r', 'lmfdb_label': '5040.r2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, 20, 20], 'min_quad_twist_disc': 12, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '20.6.0.a.1', '84.6.0.?', '420.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 45], [3, 8, 560], [5, 6, 1008], [7, 8, 720]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.66973818281736415696235997893', 'prec': 107}, 'szpiro_ratio': 3.183758181329384, '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, 1, 0, 0, 0, 2, 0, 4, 0, 0, 0, -2, 0, 2, 0], 'aplist': [0, 0, -1, 1, 2, 4, -2, 2, 4, 2, 6, -6, -6, 4, 0, -8, 0, -10, 12, -14, 4, 8, 12, 14, 8], 'class_deg': 2, 'class_size': 2, 'conductor': 5040, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '5040.r', 'trace_hash': 274597682481273089}
• 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': '0.50493167101607588630596977374', 'prec': 103}, 'conductor': 5040, 'gens': [], 'heights': [], 'lmfdb_label': '5040.r2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.0569807336605835118443105184', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.1139614673211670236886210368565111034', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-2, 0, 1]], 'xcoord_integral_points': [-2]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [0, 0], '7': [3, 0]}, 'iwp0': 3, 'lmfdb_label': '5040.r2'}
• ec_torsion_growth •

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

  
  
  • id: 264010
    {'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '5040.r2', 'torsion': [2, 2]}
  • id: 264011
    {'degree': 4, 'field': [-5, 0, -8, 0, 1], 'lmfdb_label': '5040.r2', 'torsion': [4]}
  • id: 264014
    {'degree': 8, 'field': [-675, 0, 0, 0, -90, 0, 4, 0, 1], 'lmfdb_label': '5040.r2', 'torsion': [6]}
  • id: 264013
    {'degree': 8, 'field': [606, 168, 136, 164, 44, 32, 14, -4, 1], 'lmfdb_label': '5040.r2', 'torsion': [2, 4]}
  • id: 264012
    {'degree': 8, 'field': [729, -486, 378, -306, 159, -30, 28, -4, 1], 'lmfdb_label': '5040.r2', 'torsion': [2, 4]}
  • id: 264015
    {'degree': 16, 'field': [-280791, -364392, 670908, 697536, -606080, -333488, 208898, 46956, -49673, -820, 6310, -1492, -386, 168, -10, -8, 1], 'lmfdb_label': '5040.r2', 'torsion': [8]}
  • id: 264016
    {'degree': 16, 'field': [33124, 0, 27636, 0, -8540, 0, 733, 0, 6810, 0, 553, 0, 277, 0, -30, 0, 1], 'lmfdb_label': '5040.r2', '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: 97950
    {'conductor': 5040, 'conductor_valuation': 4, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '5040.r2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 97951
    {'conductor': 5040, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '5040.r2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 97952
    {'conductor': 5040, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '5040.r2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 97953
    {'conductor': 5040, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '5040.r2', 'prime': 7, '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: 1696936
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [316, 109, 105, 316], [1, 2, 2, 5], [281, 4, 142, 9], [1, 4, 0, 1], [417, 4, 416, 5], [254, 1, 83, 0], [241, 4, 62, 9]], 'adelic_image': '420.12.0.?', 'conductor': 5040, 'lmfdb_label': '5040.r2', 'prime': 0}
  • id: 25074
    {'conductor': 5040, 'elladic_image': '2.3.0.1', 'lmfdb_label': '5040.r2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 5040.r does not appear in ec_padic