Elliptic curve data - 487872.qr2

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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': '487872qr', 'Clabel': '487872qr1', 'Cnumber': 1, 'abc_quality': 0.8118894454035532, 'absD': 40324547902205952, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 616, 'ainvs': [0, 0, 0, 59532, -7879520], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 11], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 487872, 'degree': 4915200, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8712303594475167456040312099', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 433, 'isogeny_degrees': [1, 2], 'jinv': [4410944, 7623], 'lmfdb_iso': '487872.qr', 'lmfdb_label': '487872.qr2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 14, -32], 'min_quad_twist_disc': 264, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '14.6.0.b.1', '88.6.0.?', '616.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 2, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '8.8772684906852793049529942844', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 7623], [3, 8, 54208], [7, 8, 69696], [11, 72, 4032]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.57017060184566868154179531900', 'prec': 107}, 'szpiro_ratio': 3.4572731102501684, '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, 4, 0, -1, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -2, 0], 'aplist': [0, 0, 4, -1, 0, 6, 0, -2, -4, 2, -2, -2, 0, -4, -6, 2, 0, 14, 12, -8, 4, -8, -2, 14, 2], 'class_deg': 2, 'class_size': 2, 'conductor': 487872, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '487872.qr', 'trace_hash': 1235682291491249343}
• 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': '0.023695722819122265678945924766', 'prec': 107}, 'conductor': 487872, 'gens': [[57506, 13863096, 5]], 'heights': [{'__RealLiteral__': 0, 'data': '8.8772684906852793049529942844', 'prec': 100}], 'lmfdb_label': '487872.qr2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.19061823324976861918121002897', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '13.537353886226143945927476596389041232', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[110, 0, 1]], 'xcoord_integral_points': [110]}
• lmfdb_label 487872.qr2 does not appear in ec_iwasawa
• lmfdb_label 487872.qr2 does not appear in ec_torsion_growth
• 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: 12030851
    {'conductor': 487872, 'conductor_valuation': 6, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -6, 'lmfdb_label': '487872.qr2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 12030852
    {'conductor': 487872, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '487872.qr2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 12030853
    {'conductor': 487872, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '487872.qr2', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 12030854
    {'conductor': 487872, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '487872.qr2', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 4654929
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [613, 4, 612, 5], [90, 1, 263, 0], [1, 2, 2, 5], [1, 4, 0, 1], [309, 4, 2, 9], [57, 4, 114, 9], [81, 540, 384, 231]], 'adelic_image': '616.12.0.?', 'conductor': 487872, 'lmfdb_label': '487872.qr2', 'prime': 0}
  • id: 1615633
    {'conductor': 487872, 'elladic_image': '2.3.0.1', 'lmfdb_label': '487872.qr2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 487872.qr does not appear in ec_padic