Elliptic curve data - 489762.dg5

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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': '489762dg', 'Clabel': '489762dg1', 'Cnumber': 1, 'abc_quality': 0.9458836476842432, 'absD': 2339020339139248128, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 100464, 'ainvs': [1, -1, 1, 191614, -66169983], 'analytic_rank': 2, 'bad_primes': [2, 3, 7, 13, 23], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 489762, 'degree': 9437184, 'elladic_images': ['16.24.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2080346052647429610235097391', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 2, 'iso_nlabel': 84, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [221115865823, 664731648], 'lmfdb_iso': '489762.dg', 'lmfdb_label': '489762.dg5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, 126, 1167], 'min_quad_twist_disc': -39, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '16.24.0.e.1', '46.6.0.a.1', '56.24.0.bv.1', '92.12.0.?', '112.48.0.?', '156.12.0.?', '184.24.0.?', '312.24.0.?', '368.48.0.?', '624.48.0.?', '1288.48.0.?', '2184.48.0.?', '2576.96.1.?', '3588.24.0.?', '4368.96.0.?', '7176.48.0.?', '14352.96.0.?', '50232.96.0.?', '100464.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 25, 'optimality': 4, 'potential_good_reduction': False, 'rank': 2, 'regulator': {'__RealLiteral__': 0, 'data': '1.2515986520108474009187657090', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 34983], [3, 8, 54418], [7, 8, 69966], [13, 86, 2898], [23, 24, 21294]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.37625378219991974729914339985', 'prec': 103}, 'szpiro_ratio': 3.7809801191147847, '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, 0, 1, -2, 0, -1, 1, 0, -2, -4, 0, 0, -1, 0, 1, 6, 0, -4, -2], 'aplist': [1, 0, -2, -1, -4, 0, 6, -4, 1, 2, 8, -6, -6, -4, -8, -6, 4, -10, -4, -8, 6, 0, -12, 2, -10], 'class_deg': 8, 'class_size': 6, 'conductor': 489762, 'isogeny_matrix': [[1, 8, 2, 4, 8, 4], [8, 1, 4, 2, 4, 8], [2, 4, 1, 2, 4, 2], [4, 2, 2, 1, 2, 4], [8, 4, 4, 2, 1, 8], [4, 8, 2, 4, 8, 1]], 'lmfdb_iso': '489762.dg', 'trace_hash': 420932400967085346}
• 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': '0.012081629411309191209405946745', 'prec': 107}, 'conductor': 489762, 'gens': [[725, 20931, 1], [413, 8919, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.0943007754603004021548174357', 'prec': 100}, {'__RealLiteral__': 0, 'data': '1.2004151751880972640681616352', 'prec': 100}], 'lmfdb_label': '489762.dg5', 'ngens': 2, 'rank_bounds': [2, 2], 'real_period': {'__RealLiteral__': 0, 'data': '0.13253139473177656265219506464', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '21.232142719412360774868436693980878737', 'prec': 130}, 'tamagawa_product': 512, 'torsion_generators': [[257, -129, 1]], 'xcoord_integral_points': [257, 273, 305, 413, 657, 725, 1089, 2753, 3329, 8369, 15285, 24593, 341429]}
• lmfdb_label 489762.dg5 does not appear in ec_iwasawa
• lmfdb_label 489762.dg5 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: 12075543
    {'conductor': 489762, 'conductor_valuation': 1, 'discriminant_valuation': 16, 'j_denominator_valuation': 16, 'kodaira_symbol': 20, 'lmfdb_label': '489762.dg5', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 16}
  • id: 12075544
    {'conductor': 489762, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '489762.dg5', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 12075545
    {'conductor': 489762, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '489762.dg5', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 12075546
    {'conductor': 489762, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '489762.dg5', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 12075547
    {'conductor': 489762, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '489762.dg5', 'prime': 23, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
• ec_galrep •

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

  
  
  • id: 4665551
    {'adelic_gens': [[100449, 16, 100448, 17], [15, 2, 100366, 100451], [1, 16, 0, 1], [49921, 79872, 69810, 45631], [70669, 79872, 71136, 4837], [5, 4, 100460, 100461], [1, 0, 16, 1], [1, 79872, 65052, 11077], [71800, 48945, 62127, 38650], [33487, 0, 0, 100463], [15455, 0, 0, 100463]], 'adelic_image': '100464.192.1.?', 'conductor': 489762, 'lmfdb_label': '489762.dg5', 'prime': 0}
  • id: 1620825
    {'conductor': 489762, 'elladic_image': '16.24.0.1', 'lmfdb_label': '489762.dg5', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 489762.dg does not appear in ec_padic