Elliptic curve data - 54978.bi2

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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': '54978bv', 'Clabel': '54978bv2', 'Cnumber': 2, 'abc_quality': 0.9377066534403361, 'absD': 85605524467848, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 264, 'ainvs': [1, 1, 1, -7645, 510971], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 11, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 54978, 'degree': 276480, 'elladic_images': ['8.6.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3638965288755234983420036052', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 34, 'isogeny_degrees': [1, 2], 'jinv': [-420021471169, 727634952], 'lmfdb_iso': '54978.bi', 'lmfdb_label': '54978.bi2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -156, -1512], 'min_quad_twist_disc': -7, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.a.1', '132.6.0.?', '264.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 8, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.41144539361819317823001218814', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.39094145434786684578932723348', 'prec': 103}, 'szpiro_ratio': 3.64863480129934, '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, 1, -1, 0, 0, 4, 1, 1, 1, 0, -4], 'aplist': [1, -1, -4, 0, 1, 0, 1, 0, -6, -2, -4, 2, 6, -4, 6, 8, -8, 8, -4, -6, -10, -6, 4, 14, -14], 'class_deg': 2, 'class_size': 2, 'conductor': 54978, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '54978.bi', 'trace_hash': 1670298807490951838}
• 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': '0.065363383819192386503185325674', 'prec': 107}, 'conductor': 54978, 'gens': [[97, 784, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.41144539361819317823001218814', 'prec': 103}], 'lmfdb_label': '54978.bi2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.54212625287359189446838750514', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.3533283881039475425683185835884197350', 'prec': 130}, 'tamagawa_product': 96, 'torsion_generators': [[-445, 441, 2]], 'xcoord_integral_points': [-39, 29, 97, 293]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [8, 1], '3': [1, 0], '5': [1, 0], '7': 'a', '11': [2, 0], '13': [1, 1, 0], '17': [2, 0], '19': [1, 1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [3, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '54978.bi2'}
• ec_torsion_growth •

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

  
  
  • id: 2656721
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '54978.bi2', 'torsion': [2, 2]}
  • id: 2656722
    {'degree': 4, 'field': [-392, 0, -7, 0, 1], 'lmfdb_label': '54978.bi2', 'torsion': [4]}
  • id: 2656725
    {'degree': 8, 'field': [-18584, 10576, 52, -2235, 594, 177, -35, -2, 1], 'lmfdb_label': '54978.bi2', 'torsion': [6]}
  • id: 2656723
    {'degree': 8, 'field': [144, 0, 128, 0, 26, 0, -8, 0, 1], 'lmfdb_label': '54978.bi2', 'torsion': [2, 4]}
  • id: 2656724
    {'degree': 8, 'field': [4624, 0, 3912, 0, -223, 0, 24, 0, 1], 'lmfdb_label': '54978.bi2', 'torsion': [2, 4]}
  • id: 2656727
    {'degree': 16, 'field': [753898056, -1235520576, 469757212, 157931264, -115279610, 2141712, 13408329, -2544996, -536004, 321798, 1341, -16476, 1173, 438, -50, -4, 1], 'lmfdb_label': '54978.bi2', 'torsion': [2, 6]}
  • id: 2656726
    {'degree': 16, 'field': [713460651556, 0, -60163165824, 0, -5805413324, 0, 399796704, 0, -1261419, 0, -615696, 0, 18082, 0, -192, 0, 1], 'lmfdb_label': '54978.bi2', '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: 1320813
    {'conductor': 54978, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '54978.bi2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
  • id: 1320814
    {'conductor': 54978, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '54978.bi2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1320815
    {'conductor': 54978, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '54978.bi2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1320816
    {'conductor': 54978, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '54978.bi2', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1320817
    {'conductor': 54978, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '54978.bi2', 'prime': 17, 'reduction_type': 1, '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: 2029391
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [145, 4, 26, 9], [1, 4, 0, 1], [261, 4, 260, 5], [2, 1, 131, 0], [100, 169, 33, 232], [89, 4, 178, 9]], 'adelic_image': '264.12.0.?', 'conductor': 54978, 'lmfdb_label': '54978.bi2', 'prime': 0}
  • id: 234345
    {'conductor': 54978, 'elladic_image': '8.6.0.5', 'lmfdb_label': '54978.bi2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 2781600
    {'lmfdb_iso': '54978.bi', 'p': 5, 'prec': 20, 'unit': 34474439414744, 'val': -1}
  • id: 2781596
    {'lmfdb_iso': '54978.bi', 'p': 23, 'prec': 20, 'unit': 63498155319787212296536993, 'val': 1}
  • id: 2781590
    {'lmfdb_iso': '54978.bi', 'p': 29, 'prec': 20, 'unit': 2489926292758687700908698871, 'val': 1}
  • id: 2781587
    {'lmfdb_iso': '54978.bi', 'p': 31, 'prec': 20, 'unit': 19717739454239424471621343136, 'val': 1}
  • id: 2781585
    {'lmfdb_iso': '54978.bi', 'p': 37, 'prec': 20, 'unit': 5138763958389921486011754170, 'val': 2}
  • id: 2781588
    {'lmfdb_iso': '54978.bi', 'p': 41, 'prec': 20, 'unit': 3533918306070063440961242706877, 'val': 1}
  • id: 2781589
    {'lmfdb_iso': '54978.bi', 'p': 43, 'prec': 20, 'unit': 7590585860950791378589974623209, 'val': 1}
  • id: 2781598
    {'lmfdb_iso': '54978.bi', 'p': 47, 'prec': 20, 'unit': 1236417984913836299576573505200, 'val': 1}
  • id: 2781594
    {'lmfdb_iso': '54978.bi', 'p': 53, 'prec': 20, 'unit': 91859626592851058569935549937909, 'val': 1}
  • id: 2781592
    {'lmfdb_iso': '54978.bi', 'p': 59, 'prec': 20, 'unit': 796797765686973775492513651140040, 'val': 1}
  • id: 2781599
    {'lmfdb_iso': '54978.bi', 'p': 61, 'prec': 20, 'unit': 2017365969580932740252861066956004, 'val': 1}
  • id: 2781584
    {'lmfdb_iso': '54978.bi', 'p': 67, 'prec': 20, 'unit': 19870260658478473089363587093557827, 'val': 1}
  • id: 2781586
    {'lmfdb_iso': '54978.bi', 'p': 71, 'prec': 20, 'unit': 79297305631420658585081408256357989, 'val': 1}
  • id: 2781595
    {'lmfdb_iso': '54978.bi', 'p': 73, 'prec': 20, 'unit': 236469510624353581590540604310339967, 'val': 1}
  • id: 2781591
    {'lmfdb_iso': '54978.bi', 'p': 79, 'prec': 20, 'unit': 748276553106639697380312320392637220, 'val': 1}
  • id: 2781593
    {'lmfdb_iso': '54978.bi', 'p': 83, 'prec': 20, 'unit': 2846139687466268858318757728604870345, 'val': 1}
  • id: 2781597
    {'lmfdb_iso': '54978.bi', 'p': 89, 'prec': 20, 'unit': 9749901940842731424820381015889447135, 'val': 1}
  • id: 2781583
    {'lmfdb_iso': '54978.bi', 'p': 97, 'prec': 20, 'unit': 38826064458214264598568924750213919566, 'val': 1}