Elliptic curve data - 528.g3

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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': '528h', 'Clabel': '528h1', 'Cnumber': 1, 'abc_quality': 1.0970565641289056, 'absD': 1216512, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 264, 'ainvs': [0, 1, 0, -104, 372], 'analytic_rank': 1, 'bad_primes': [2, 3, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 528, 'degree': 96, 'elladic_images': ['8.12.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.012632067116688598242446120206', 'prec': 110}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 6, 'isogeny_degrees': [1, 2, 4], 'jinv': [30664297, 297], 'lmfdb_iso': '528.g', 'lmfdb_label': '528.g3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -6, -9], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.5', '12.12.0-4.c.1.1', '24.24.0-24.ba.1.12', '44.12.0-4.c.1.1', '66.6.0.a.1', '88.24.0.?', '132.24.0.?', '264.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 11, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.24159712687271798496632475006', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 2, 33], [3, 4, 176], [11, 12, 48]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.70577924767663390765967824166', 'prec': 107}, 'szpiro_ratio': 4.076564560790409, '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, 1, 0, -2, 0, -4, 0, 1, 0, -1, 0, -2, 0, -2, 0, -2, 0, 0, 0], 'aplist': [0, 1, -2, -4, -1, -2, -2, 0, -8, -6, 8, 6, -2, 0, -8, 6, 4, 6, 4, 0, -14, 4, -12, -6, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 528, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '528.g', 'trace_hash': 1774982305618068607}
• 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': '1.0255859771174331474340959251', 'prec': 100}, 'conductor': 528, 'gens': [[4, 6, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.24159712687271798496632475006', 'prec': 103}], 'lmfdb_label': '528.g3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '2.7446333574658941034508119070', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.9892866004483446548391692989102681967', 'prec': 130}, 'tamagawa_product': 12, 'torsion_generators': [[6, 0, 1]], 'xcoord_integral_points': [-12, -2, 4, 6, 7, 22]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [2, 0], '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '528.g3'}
• ec_torsion_growth •

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

  
  
  • id: 23943
    {'degree': 2, 'field': [-11, 0, 1], 'lmfdb_label': '528.g3', 'torsion': [4]}
  • id: 23941
    {'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '528.g3', 'torsion': [2, 2]}
  • id: 23942
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '528.g3', 'torsion': [4]}
  • id: 23945
    {'degree': 4, 'field': [1, 4, -3, -2, 1], 'lmfdb_label': '528.g3', 'torsion': [8]}
  • id: 23944
    {'degree': 4, 'field': [4, 0, -7, 0, 1], 'lmfdb_label': '528.g3', 'torsion': [2, 4]}
  • id: 23949
    {'degree': 8, 'field': [-3, 0, -19, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '528.g3', 'torsion': [6]}
  • id: 23948
    {'degree': 8, 'field': [1, 0, -11, 0, 24, 0, -11, 0, 1], 'lmfdb_label': '528.g3', 'torsion': [2, 8]}
  • id: 23947
    {'degree': 8, 'field': [16, 0, 12, 0, 13, 0, 3, 0, 1], 'lmfdb_label': '528.g3', 'torsion': [8]}
  • id: 23946
    {'degree': 8, 'field': [1089, 0, 0, 0, 33, 0, 0, 0, 1], 'lmfdb_label': '528.g3', 'torsion': [2, 4]}
  • id: 23953
    {'degree': 16, 'field': [1, 0, 13, 0, -104, 0, 223, 0, -149, 0, -29, 0, 40, 0, 13, 0, 1], 'lmfdb_label': '528.g3', 'torsion': [2, 6]}
  • id: 23950
    {'degree': 16, 'field': [1, 6, 18, 36, 85, 252, 630, 798, 84, -798, 630, -252, 85, -36, 18, -6, 1], 'lmfdb_label': '528.g3', 'torsion': [4, 4]}
  • id: 23954
    {'degree': 16, 'field': [9, 0, -24, 0, 34, 0, -30, 0, 15, 0, -17, 0, 15, 0, -6, 0, 1], 'lmfdb_label': '528.g3', 'torsion': [12]}
  • id: 23952
    {'degree': 16, 'field': [69, -72, -1002, 5484, -9648, 5244, 4422, -6684, 1501, 1468, -770, 52, -8, 4, 16, -8, 1], 'lmfdb_label': '528.g3', 'torsion': [16]}
  • id: 23955
    {'degree': 16, 'field': [169, 0, -505, 0, 361, 0, -92, 0, 86, 0, -137, 0, 67, 0, -13, 0, 1], 'lmfdb_label': '528.g3', 'torsion': [12]}
  • id: 23951
    {'degree': 16, 'field': [256, 0, -192, 0, -64, 0, -60, 0, 117, 0, -15, 0, -4, 0, -3, 0, 1], 'lmfdb_label': '528.g3', '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: 5975
    {'conductor': 528, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '528.g3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 5976
    {'conductor': 528, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '528.g3', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 5977
    {'conductor': 528, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '528.g3', 'prime': 11, '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: 1668185
    {'adelic_gens': [[235, 234, 178, 43], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [7, 6, 258, 259], [257, 8, 256, 9], [223, 228, 226, 97], [104, 3, 197, 2], [92, 1, 199, 6]], 'adelic_image': '264.48.0.?', 'conductor': 528, 'lmfdb_label': '528.g3', 'prime': 0}
  • id: 2375
    {'conductor': 528, 'elladic_image': '8.12.0.6', 'lmfdb_label': '528.g3', 'modell_image': '2B', 'prime': 2}
• ec_padic •

  Column	Type
  lmfdb_iso	text
  p	smallint
  prec	smallint
  unit	numeric
  val	smallint

  
  
  • id: 8340
    {'lmfdb_iso': '528.g', 'p': 5, 'prec': 20, 'unit': 19006617219036, 'val': 1}
  • id: 8341
    {'lmfdb_iso': '528.g', 'p': 7, 'prec': 20, 'unit': 2790486595005891, 'val': 1}
  • id: 8346
    {'lmfdb_iso': '528.g', 'p': 13, 'prec': 20, 'unit': 818322061843722253657, 'val': 1}
  • id: 8348
    {'lmfdb_iso': '528.g', 'p': 17, 'prec': 20, 'unit': 223355877051229651272789, 'val': 1}
  • id: 8344
    {'lmfdb_iso': '528.g', 'p': 23, 'prec': 20, 'unit': 3534608018948378245044766, 'val': 1}
  • id: 8345
    {'lmfdb_iso': '528.g', 'p': 29, 'prec': 20, 'unit': 967973756095690561458014250, 'val': 1}
  • id: 8342
    {'lmfdb_iso': '528.g', 'p': 31, 'prec': 20, 'unit': 15953785749675783167298487701, 'val': 1}
  • id: 8356
    {'lmfdb_iso': '528.g', 'p': 37, 'prec': 20, 'unit': 609186080348195490023484300214, 'val': 1}
  • id: 8343
    {'lmfdb_iso': '528.g', 'p': 41, 'prec': 20, 'unit': 1068938328387803856709087121984, 'val': 1}
  • id: 8354
    {'lmfdb_iso': '528.g', 'p': 47, 'prec': 20, 'unit': 47460995152603359931021435934546, 'val': 1}
  • id: 8350
    {'lmfdb_iso': '528.g', 'p': 53, 'prec': 20, 'unit': 93147639430079988379794787758690, 'val': 1}
  • id: 8351
    {'lmfdb_iso': '528.g', 'p': 59, 'prec': 20, 'unit': 2142124250718715094961578970928939, 'val': 1}
  • id: 8355
    {'lmfdb_iso': '528.g', 'p': 61, 'prec': 20, 'unit': 4069185066345650616863470252016859, 'val': 1}
  • id: 8339
    {'lmfdb_iso': '528.g', 'p': 67, 'prec': 20, 'unit': 11170979380603412758621281021003630, 'val': 1}
  • id: 8352
    {'lmfdb_iso': '528.g', 'p': 73, 'prec': 20, 'unit': 231253450838031221553378510530125349, 'val': 1}
  • id: 8347
    {'lmfdb_iso': '528.g', 'p': 79, 'prec': 20, 'unit': 80924452110949527682781547418127502, 'val': 1}
  • id: 8349
    {'lmfdb_iso': '528.g', 'p': 83, 'prec': 20, 'unit': 1248845479639809030300811880700222937, 'val': 1}
  • id: 8353
    {'lmfdb_iso': '528.g', 'p': 89, 'prec': 20, 'unit': 1980123700137903217023918180543289668, 'val': 1}
  • id: 8338
    {'lmfdb_iso': '528.g', 'p': 97, 'prec': 20, 'unit': 307427642247104590721929223758835251, 'val': 2}