Elliptic curve data - 52878.f1

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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': '52878h', 'Clabel': '52878h1', 'Cnumber': 1, 'abc_quality': 0.9597874935926854, 'absD': 2303563655232, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 211512, 'ainvs': [1, 0, 0, -5459, 136545], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 1259], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 52878, 'degree': 158400, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.1010036725574314627105918221', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 5, 'isogeny_degrees': [1, 2], 'jinv': [17991524611989937, 2303563655232], 'lmfdb_iso': '52878.f', 'lmfdb_label': '52878.f1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -5459, 136545], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '56.6.0.c.1', '7554.6.0.?', '211512.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 11, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.26856342824151435923565913902', 'prec': 103}, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1010036725574314627105918221', 'prec': 100}, 'szpiro_ratio': 3.4414824241009083, '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, -2, 1, 1, 1, 1, -2, -4, 1, -6, 1, -2, 1, 4, 1, 0, -2], 'aplist': [1, 1, -2, 1, -4, -6, 4, 0, 8, 6, 6, 2, -2, -12, -4, -12, -4, -2, 12, 12, -2, -8, -12, 2, 18], 'class_deg': 2, 'class_size': 2, 'conductor': 52878, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '52878.f', 'trace_hash': 1347106138442677858}
• 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': '0.11058096127141707560091162370', 'prec': 103}, 'conductor': 52878, 'gens': [[58, 97, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.26856342824151435923565913902', 'prec': 103}], 'lmfdb_label': '52878.f1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.78972184502036474684949757549', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '9.5440682725147373219437127757609462075', 'prec': 130}, 'tamagawa_product': 180, 'torsion_generators': [[30, -15, 1]], 'xcoord_integral_points': [-68, -2, 16, 30, 58, 226]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [4, 0], '3': [4, 0], '5': [1, 0], '7': [6, 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, 0], '47': [1, 0], '1259': 'o?'}, 'iwp0': 0, 'lmfdb_label': '52878.f1'}
• ec_torsion_growth •

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

  
  
  • id: 2561107
    {'degree': 2, 'field': [-944, -1, 1], 'lmfdb_label': '52878.f1', 'torsion': [2, 2]}
  • id: 2561108
    {'degree': 4, 'field': [743, -28, 68, 0, 1], 'lmfdb_label': '52878.f1', 'torsion': [4]}
  • id: 2561111
    {'degree': 8, 'field': [-588, 0, -361, 0, 84, 0, 0, 0, 1], 'lmfdb_label': '52878.f1', 'torsion': [6]}
  • id: 2561110
    {'degree': 8, 'field': [2458624, 0, 375648, 0, 19364, 0, 300, 0, 1], 'lmfdb_label': '52878.f1', 'torsion': [2, 4]}
  • id: 2561109
    {'degree': 8, 'field': [13845841, 0, -907924, 0, -38106, 0, -244, 0, 1], 'lmfdb_label': '52878.f1', 'torsion': [2, 4]}
  • id: 2561113
    {'degree': 16, 'field': [17526632712192, 32296461015168, 26913181590720, 2131811582472, 1942461190944, -519367484736, 19266204357, 4197724794, -743559690, 130262118, 6062059, -64098, -49947, -5510, 84, 0, 1], 'lmfdb_label': '52878.f1', 'torsion': [2, 6]}
  • id: 2561112
    {'degree': 16, 'field': [111670305173741700, 5376167092489248, -5218769573793936, -312796358457408, 151420998624644, 5918064854688, -1882053064976, -77119300560, 18572251741, 467886712, -89758732, -2069816, 334110, 4984, -692, -8, 1], 'lmfdb_label': '52878.f1', '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: 1268062
    {'conductor': 52878, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '52878.f1', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 1268063
    {'conductor': 52878, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '52878.f1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 5}
  • id: 1268064
    {'conductor': 52878, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '52878.f1', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 1268065
    {'conductor': 52878, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '52878.f1', 'prime': 1259, '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: 2015573
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [120865, 4, 30218, 9], [1, 4, 0, 1], [2522, 1, 104495, 0], [211509, 4, 211508, 5], [141010, 1, 141007, 0], [26441, 185074, 185072, 26439], [105757, 4, 2, 9]], 'adelic_image': '211512.12.0.?', 'conductor': 52878, 'lmfdb_label': '52878.f1', 'prime': 0}
  • id: 226149
    {'conductor': 52878, 'elladic_image': '2.3.0.1', 'lmfdb_label': '52878.f1', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 2666877
    {'lmfdb_iso': '52878.f', 'p': 5, 'prec': 20, 'unit': 18348221979126, 'val': 0}
  • id: 2666876
    {'lmfdb_iso': '52878.f', 'p': 11, 'prec': 20, 'unit': 35320082193132783769, 'val': 1}
  • id: 2666883
    {'lmfdb_iso': '52878.f', 'p': 13, 'prec': 20, 'unit': 821859796674260853234, 'val': 1}
  • id: 2666885
    {'lmfdb_iso': '52878.f', 'p': 17, 'prec': 20, 'unit': 128263230093536228441775, 'val': 1}
  • id: 2666890
    {'lmfdb_iso': '52878.f', 'p': 23, 'prec': 20, 'unit': 12068816883434021394938471, 'val': 1}
  • id: 2666882
    {'lmfdb_iso': '52878.f', 'p': 29, 'prec': 20, 'unit': 3203746772292037441217893617, 'val': 1}
  • id: 2666879
    {'lmfdb_iso': '52878.f', 'p': 31, 'prec': 20, 'unit': 17696330557238612535690911174, 'val': 1}
  • id: 2666894
    {'lmfdb_iso': '52878.f', 'p': 37, 'prec': 20, 'unit': 151789819329592900027963152805, 'val': 1}
  • id: 2666880
    {'lmfdb_iso': '52878.f', 'p': 41, 'prec': 20, 'unit': 1037261126521755345822500141841, 'val': 1}
  • id: 2666881
    {'lmfdb_iso': '52878.f', 'p': 43, 'prec': 20, 'unit': 9124638194120936661162772423784, 'val': 1}
  • id: 2666892
    {'lmfdb_iso': '52878.f', 'p': 47, 'prec': 20, 'unit': 4788732671513830105362107287925, 'val': 1}
  • id: 2666887
    {'lmfdb_iso': '52878.f', 'p': 53, 'prec': 20, 'unit': 292125288205962932023754489276406, 'val': 1}
  • id: 2666888
    {'lmfdb_iso': '52878.f', 'p': 59, 'prec': 20, 'unit': 4345180383304782123226512105677750, 'val': 1}
  • id: 2666893
    {'lmfdb_iso': '52878.f', 'p': 61, 'prec': 20, 'unit': 105425396205126050887112559793387, 'val': 1}
  • id: 2666886
    {'lmfdb_iso': '52878.f', 'p': 67, 'prec': 20, 'unit': 27888922340079211706321789201805559, 'val': 1}
  • id: 2666878
    {'lmfdb_iso': '52878.f', 'p': 71, 'prec': 20, 'unit': 87741232084757478160170149430933213, 'val': 1}
  • id: 2666889
    {'lmfdb_iso': '52878.f', 'p': 73, 'prec': 20, 'unit': 106482945969507609764141305669533037, 'val': 1}
  • id: 2666884
    {'lmfdb_iso': '52878.f', 'p': 79, 'prec': 20, 'unit': 289451239232900075986523324535835986, 'val': 1}
  • id: 2666875
    {'lmfdb_iso': '52878.f', 'p': 83, 'prec': 20, 'unit': 496800097494230601408131248156934871, 'val': 1}
  • id: 2666891
    {'lmfdb_iso': '52878.f', 'p': 89, 'prec': 20, 'unit': 10195148070928424956787883944109100534, 'val': 1}
  • id: 2666874
    {'lmfdb_iso': '52878.f', 'p': 97, 'prec': 20, 'unit': 28559462287565507031606185198212978341, 'val': 1}