Elliptic curve data - 28224.br3

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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
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '28224ce', 'Clabel': '28224ce2', 'Cnumber': 2, 'abc_quality': 0.9793898903636942, 'absD': 50194867949420544, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 168, 'ainvs': [0, 0, 0, -445116, 113793680], 'analytic_rank': 1, 'bad_primes': [2, 3, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 28224, 'degree': 294912, 'elladic_images': ['8.12.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0504501931621175254644462523', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 43, 'isogeny_degrees': [1, 2], 'jinv': [6940769488, 35721], 'lmfdb_iso': '28224.br', 'lmfdb_label': '28224.br3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -252, 1620], 'min_quad_twist_disc': 168, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '8.12.0-2.a.1.2', '12.12.0.b.1', '24.24.0-12.b.1.4', '28.12.0.a.1', '56.24.0-28.a.1.3', '84.24.0.?', '168.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 9, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.5117781414792678989115392584', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.28048273635286350043929021292', 'prec': 107}, 'szpiro_ratio': 4.940693751971743, '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, 0, 0, 6, 0, 0, 0, -2, 0, 4, 0], 'aplist': [0, 0, -2, 0, 0, 6, -2, 4, 4, -10, 8, -6, -2, 4, 8, -10, -12, -2, -12, 12, 14, -8, -12, -2, -10], '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.br', 'trace_hash': 1285778671289691584}
• 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': '0.016557760307154752633631141389', 'prec': 107}, 'conductor': 28224, 'gens': [[413, 637, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.5117781414792678989115392584', 'prec': 100}], 'lmfdb_label': '28224.br3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.35821666258424988522037019230', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.0319097823080922601220490024508796901', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[364, 0, 1], [406, 0, 1]], 'xcoord_integral_points': [-770, -608, 364, 406, 413, 7462]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': 'a', '11': [1, 1, 0], '13': [1, 0], '17': [1, 0], '19': [3, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '28224.br3'}
• ec_torsion_growth •

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

  
  
  • id: 1413408
    {'degree': 4, 'field': [4, 0, 10, 0, 1], 'lmfdb_label': '28224.br3', 'torsion': [2, 4]}
  • id: 1413407
    {'degree': 4, 'field': [81, 0, -24, 0, 1], 'lmfdb_label': '28224.br3', 'torsion': [2, 4]}
  • id: 1413406
    {'degree': 4, 'field': [196, 0, 14, 0, 1], 'lmfdb_label': '28224.br3', 'torsion': [2, 4]}
  • id: 1413409
    {'degree': 8, 'field': [-588, 0, 504, 0, 0, 0, -14, 0, 1], 'lmfdb_label': '28224.br3', 'torsion': [2, 6]}
  • id: 1413410
    {'degree': 16, 'field': [256, 0, 0, 0, -16, 0, 0, 0, -15, 0, 0, 0, -1, 0, 0, 0, 1], 'lmfdb_label': '28224.br3', 'torsion': [4, 4]}
  • id: 1413412
    {'degree': 16, 'field': [457, 1388, -2422, 624, 3698, -5588, 2086, 2052, -3497, 2136, -326, -388, 368, -168, 44, -8, 1], 'lmfdb_label': '28224.br3', 'torsion': [2, 8]}
  • id: 1413411
    {'degree': 16, 'field': [2401, 0, -3430, 0, 49, 0, 1484, 0, 1654, 0, 338, 0, -44, 0, -10, 0, 1], 'lmfdb_label': '28224.br3', 'torsion': [2, 8]}
  • id: 1413413
    {'degree': 16, 'field': [29584, 0, 9088, 0, -704, 0, -5120, 0, -680, 0, 352, 0, 160, 0, 16, 0, 1], 'lmfdb_label': '28224.br3', '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: 653729
    {'conductor': 28224, 'conductor_valuation': 6, 'discriminant_valuation': 14, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '28224.br3', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 653730
    {'conductor': 28224, 'conductor_valuation': 2, 'discriminant_valuation': 12, 'j_denominator_valuation': 6, 'kodaira_symbol': -10, 'lmfdb_label': '28224.br3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 653731
    {'conductor': 28224, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '28224.br3', '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: 1852373
    {'adelic_gens': [[165, 4, 164, 5], [125, 166, 0, 167], [83, 0, 0, 167], [29, 4, 58, 9], [87, 164, 88, 163], [1, 4, 0, 1], [95, 166, 0, 167], [1, 0, 4, 1]], 'adelic_image': '168.48.0.?', 'conductor': 28224, 'lmfdb_label': '28224.br3', 'prime': 0}
  • id: 127468
    {'conductor': 28224, 'elladic_image': '8.12.0.2', 'lmfdb_label': '28224.br3', 'modell_image': '2Cs', 'prime': 2}
• ec_padic •

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

  
  
  • id: 1356162
    {'lmfdb_iso': '28224.br', 'p': 5, 'prec': 20, 'unit': 4686239485923, 'val': 1}
  • id: 1356168
    {'lmfdb_iso': '28224.br', 'p': 13, 'prec': 20, 'unit': 1033909519857516649959, 'val': 1}
  • id: 1356170
    {'lmfdb_iso': '28224.br', 'p': 17, 'prec': 20, 'unit': 195202063320748916859246, 'val': 1}
  • id: 1356171
    {'lmfdb_iso': '28224.br', 'p': 19, 'prec': 20, 'unit': 3450609141418841646361, 'val': 3}
  • id: 1356175
    {'lmfdb_iso': '28224.br', 'p': 23, 'prec': 20, 'unit': 5450380861606731585438819, 'val': 1}
  • id: 1356167
    {'lmfdb_iso': '28224.br', 'p': 29, 'prec': 20, 'unit': 3395221786488301742465106648, 'val': 1}
  • id: 1356164
    {'lmfdb_iso': '28224.br', 'p': 31, 'prec': 20, 'unit': 7300072335067510719806157911, 'val': 1}
  • id: 1356179
    {'lmfdb_iso': '28224.br', 'p': 37, 'prec': 20, 'unit': 514014981637075448677874612374, 'val': 1}
  • id: 1356165
    {'lmfdb_iso': '28224.br', 'p': 41, 'prec': 20, 'unit': 3387979941081443255299708100413, 'val': 1}
  • id: 1356166
    {'lmfdb_iso': '28224.br', 'p': 43, 'prec': 20, 'unit': 1711111608251429585716878369927, 'val': 1}
  • id: 1356177
    {'lmfdb_iso': '28224.br', 'p': 47, 'prec': 20, 'unit': 42911405206491972845658631212100, 'val': 1}
  • id: 1356172
    {'lmfdb_iso': '28224.br', 'p': 53, 'prec': 20, 'unit': 215940182737877348500586046988397, 'val': 1}
  • id: 1356173
    {'lmfdb_iso': '28224.br', 'p': 59, 'prec': 20, 'unit': 3275255661253339756442071483597268, 'val': 1}
  • id: 1356178
    {'lmfdb_iso': '28224.br', 'p': 61, 'prec': 20, 'unit': 2167252458085646908986198811664817, 'val': 1}
  • id: 1356161
    {'lmfdb_iso': '28224.br', 'p': 67, 'prec': 20, 'unit': 35804250517059367369319416748468842, 'val': 1}
  • id: 1356163
    {'lmfdb_iso': '28224.br', 'p': 71, 'prec': 20, 'unit': 92457259889011142798229095985522353, 'val': 1}
  • id: 1356174
    {'lmfdb_iso': '28224.br', 'p': 73, 'prec': 20, 'unit': 232843692740564583408735535783040691, 'val': 1}
  • id: 1356169
    {'lmfdb_iso': '28224.br', 'p': 79, 'prec': 20, 'unit': 847937242311404289855493978855093173, 'val': 1}
  • id: 1356160
    {'lmfdb_iso': '28224.br', 'p': 83, 'prec': 20, 'unit': 2290494776192393267387917662776459814, 'val': 1}
  • id: 1356176
    {'lmfdb_iso': '28224.br', 'p': 89, 'prec': 20, 'unit': 5364678963572529182262155062841608155, 'val': 1}
  • id: 1356159
    {'lmfdb_iso': '28224.br', 'p': 97, 'prec': 20, 'unit': 8754730969117771230025339014560402796, 'val': 1}