Elliptic curve data - 28224.by3

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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': '28224gd', 'Clabel': '28224gd2', 'Cnumber': 2, 'abc_quality': 1.0653400939100561, 'absD': 275417656786944, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 168, 'ainvs': [0, 0, 0, -33516, -2222640], 'analytic_rank': 0, 'bad_primes': [2, 3, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 28224, 'degree': 98304, 'elladic_images': ['8.12.0.3'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5202283920631240099037554532', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 50, 'isogeny_degrees': [1, 2], 'jinv': [740772, 49], 'lmfdb_iso': '28224.by', 'lmfdb_label': '28224.by3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -19, 30], 'min_quad_twist_disc': -168, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '8.12.0.a.1', '12.12.0-2.a.1.2', '24.24.0-8.a.1.4', '28.12.0.b.1', '56.24.0.d.1', '84.24.0.?', '168.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 441], [3, 6, 3136], [7, 32, 576]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.92622906754518123423618636560', 'prec': 107}, 'szpiro_ratio': 4.183571337763016, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, -2, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, -6, 0, -8, 0], 'aplist': [0, 0, -2, 0, 4, 2, -6, -8, 0, 6, 8, 2, 2, -4, 8, 6, 0, -6, -4, -8, -10, -16, 8, -6, 6], 'class_deg': 4, 'class_size': 4, 'conductor': 28224, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '28224.by', 'trace_hash': 80647020939366516}
• 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': '0.047813044265653245371781248640', 'prec': 107}, 'conductor': 28224, 'gens': [], 'heights': [], 'lmfdb_label': '28224.by3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.35431312011021212133294869837', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4172524804408484853317947934980228519', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[-84, 0, 1], [210, 0, 1]], 'xcoord_integral_points': [-126, -84, 210]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '7': 'a'}, 'iwp0': 3, 'lmfdb_label': '28224.by3'}
• ec_torsion_growth •

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

  
  
  • id: 1415492
    {'degree': 4, 'field': [4, 0, -10, 0, 1], 'lmfdb_label': '28224.by3', 'torsion': [2, 4]}
  • id: 1415491
    {'degree': 4, 'field': [22, -16, 17, -2, 1], 'lmfdb_label': '28224.by3', 'torsion': [2, 4]}
  • id: 1415490
    {'degree': 4, 'field': [121, 0, 20, 0, 1], 'lmfdb_label': '28224.by3', 'torsion': [2, 4]}
  • id: 1415493
    {'degree': 8, 'field': [-147, 0, -462, 0, 126, 0, 0, 0, 1], 'lmfdb_label': '28224.by3', 'torsion': [2, 6]}
  • id: 1415495
    {'degree': 16, 'field': [16, 0, 32, 0, 208, 0, 1048, 0, 1713, 0, 524, 0, 52, 0, 4, 0, 1], 'lmfdb_label': '28224.by3', 'torsion': [2, 8]}
  • id: 1415494
    {'degree': 16, 'field': [256, 0, 0, 0, -16, 0, 0, 0, -15, 0, 0, 0, -1, 0, 0, 0, 1], 'lmfdb_label': '28224.by3', 'torsion': [4, 4]}
  • id: 1415496
    {'degree': 16, 'field': [2401, 0, 5488, 0, 4361, 0, 616, 0, 1264, 0, -88, 0, 89, 0, -16, 0, 1], 'lmfdb_label': '28224.by3', 'torsion': [2, 8]}
  • id: 1415497
    {'degree': 16, 'field': [35344, 0, -47616, 0, 70016, 0, -61120, 0, 18360, 0, -640, 0, -96, 0, -16, 0, 1], 'lmfdb_label': '28224.by3', 'torsion': [2, 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: 654365
    {'conductor': 28224, 'conductor_valuation': 6, 'discriminant_valuation': 16, 'j_denominator_valuation': 0, 'kodaira_symbol': -10, 'lmfdb_label': '28224.by3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 654366
    {'conductor': 28224, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '28224.by3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 654367
    {'conductor': 28224, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '28224.by3', 'prime': 7, '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: 1852390
    {'adelic_gens': [[55, 0, 0, 167], [165, 4, 164, 5], [41, 108, 0, 167], [95, 108, 78, 47], [1, 4, 0, 1], [83, 54, 0, 167], [1, 0, 4, 1]], 'adelic_image': '168.48.0.?', 'conductor': 28224, 'lmfdb_label': '28224.by3', 'prime': 0}
  • id: 127486
    {'conductor': 28224, 'elladic_image': '8.12.0.3', 'lmfdb_label': '28224.by3', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 28224.by does not appear in ec_padic