Elliptic curve data - 4998.x2

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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': '4998x', 'Clabel': '4998x2', 'Cnumber': 2, 'abc_quality': 0.9489425211495345, 'absD': 5508090882, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 136, 'ainvs': [1, 0, 1, 366, -2306], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 4998, 'degree': 5760, 'elladic_images': ['8.6.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.55600047423932278169910899955', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 23, 'isogeny_degrees': [1, 2], 'jinv': [46268279, 46818], 'lmfdb_iso': '4998.x', 'lmfdb_label': '4998.x2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 8, 10], 'min_quad_twist_disc': -7, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.a.1', '68.6.0.c.1', '136.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 49], [3, 4, 1666], [7, 26, 102], [17, 18, 294]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.41695460028833387085356737217', 'prec': 107}, 'szpiro_ratio': 3.443247672713954, '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, -1, 1, 1, 4, -1, 0, -1, 1, -4, 0, 1, 6, 0, 4, 1, 1, -1, -4, 4], 'aplist': [-1, 1, 4, 0, 0, 6, 1, -4, 6, -4, 6, -4, 10, -4, -4, -2, -12, 4, -12, -6, -2, 10, 12, 2, -6], 'class_deg': 2, 'class_size': 2, 'conductor': 4998, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '4998.x', 'trace_hash': 1225801469266851830}
• 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': '0.32890018987681394709825847175', 'prec': 103}, 'conductor': 4998, 'gens': [], 'heights': [], 'lmfdb_label': '4998.x2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.73622095817823111780660553678', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.9448838327129244712264221471105890263', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[23, -27, 2]], 'xcoord_integral_points': []}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [5, 1], '3': [1, 0], '7': 'a', '17': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '4998.x2'}
• ec_torsion_growth •

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

  
  
  • id: 261300
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '4998.x2', 'torsion': [2, 2]}
  • id: 261301
    {'degree': 4, 'field': [-98, 0, -21, 0, 1], 'lmfdb_label': '4998.x2', 'torsion': [4]}
  • id: 261304
    {'degree': 8, 'field': [-3972, 7260, 4092, -724, -154, 122, 1, -2, 1], 'lmfdb_label': '4998.x2', 'torsion': [6]}
  • id: 261303
    {'degree': 8, 'field': [36, 0, -160, 0, 182, 0, -8, 0, 1], 'lmfdb_label': '4998.x2', 'torsion': [2, 4]}
  • id: 261302
    {'degree': 8, 'field': [3481, 0, 1086, 0, 226, 0, 30, 0, 1], 'lmfdb_label': '4998.x2', 'torsion': [2, 4]}
  • id: 261306
    {'degree': 16, 'field': [34012224, 0, 25036776, 0, 621108, 0, -302544, 0, -20652, 0, 4004, 0, 804, 0, 48, 0, 1], 'lmfdb_label': '4998.x2', 'torsion': [2, 6]}
  • id: 261305
    {'degree': 16, 'field': [592630336, 0, 493857072, 0, -13287676, 0, 8824632, 0, -1047864, 0, 26988, 0, 1013, 0, -66, 0, 1], 'lmfdb_label': '4998.x2', 'torsion': [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: 96876
    {'conductor': 4998, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '4998.x2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 96877
    {'conductor': 4998, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '4998.x2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 96878
    {'conductor': 4998, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '4998.x2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 96879
    {'conductor': 4998, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '4998.x2', 'prime': 17, '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: 1696664
    {'adelic_gens': [[133, 4, 132, 5], [2, 1, 67, 0], [1, 4, 0, 1], [52, 89, 17, 120], [1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [105, 4, 74, 9]], 'adelic_image': '136.12.0.?', 'conductor': 4998, 'lmfdb_label': '4998.x2', 'prime': 0}
  • id: 24834
    {'conductor': 4998, 'elladic_image': '8.6.0.5', 'lmfdb_label': '4998.x2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 4998.x does not appear in ec_padic