Elliptic curve data - 54720.ex2

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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': '54720bx', 'Clabel': '54720bx3', 'Cnumber': 3, 'abc_quality': 1.081271340032757, 'absD': 31650906595820175360000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 2280, 'ainvs': [0, 0, 0, -17948172, -27987358736], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 54720, 'degree': 5898240, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.0765153030943843332276030794', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 127, 'isogeny_degrees': [1, 2, 4], 'jinv': [3345930611358906241, 165622259047500], 'lmfdb_iso': '54720.ex', 'lmfdb_label': '54720.ex2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -31160, 2011565], 'min_quad_twist_disc': -24, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '24.12.0-4.c.1.1', '40.12.0-4.c.1.4', '76.12.0.?', '120.24.0.?', '456.24.0.?', '760.24.0.?', '2280.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '14.177646904547838923172837088', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 171], [3, 8, 6080], [5, 6, 10944], [19, 20, 2880]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.4874883879204115234041322788', 'prec': 100}, 'szpiro_ratio': 5.657441513750763, '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, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 6, 0, 0, 0, -2, 0, -1, 0], 'aplist': [0, 0, 1, 4, 0, 6, -2, -1, -8, 2, -8, -10, -6, 8, 0, -2, -12, 2, 12, 8, 2, -16, -4, -6, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 54720, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '54720.ex', 'trace_hash': 1898390553580246883}
• 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': '0.0021270258146522459797015615710', 'prec': 110}, 'conductor': 54720, 'gens': [[-30954508, 34106774040, 107]], 'heights': [{'__RealLiteral__': 0, 'data': '14.177646904547838923172837088', 'prec': 100}], 'lmfdb_label': '54720.ex2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.073574407834510793848879456889', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '8.3448958039111378010182849421006212829', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[4868, 0, 1]], 'xcoord_integral_points': [4868]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': 'a', '5': [2, 0], '7': [1, 0], '11': [1, 1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '54720.ex2'}
• ec_torsion_growth •

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

  
  
  • id: 2645024
    {'degree': 2, 'field': [-114, 0, 1], 'lmfdb_label': '54720.ex2', 'torsion': [4]}
  • id: 2645023
    {'degree': 2, 'field': [-19, 0, 1], 'lmfdb_label': '54720.ex2', 'torsion': [2, 2]}
  • id: 2645025
    {'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '54720.ex2', 'torsion': [4]}
  • id: 2645026
    {'degree': 4, 'field': [169, 0, -50, 0, 1], 'lmfdb_label': '54720.ex2', 'torsion': [2, 4]}
  • id: 2645030
    {'degree': 8, 'field': [-108, 0, 102, 0, -36, 0, 0, 0, 1], 'lmfdb_label': '54720.ex2', 'torsion': [6]}
  • id: 2645029
    {'degree': 8, 'field': [16, 0, 50, 0, 33, 0, -10, 0, 1], 'lmfdb_label': '54720.ex2', 'torsion': [8]}
  • id: 2645028
    {'degree': 8, 'field': [81, 0, -450, 0, 358, 0, -50, 0, 1], 'lmfdb_label': '54720.ex2', 'torsion': [8]}
  • id: 2645027
    {'degree': 8, 'field': [17700, -7680, 2896, -1192, 156, 16, 12, -4, 1], 'lmfdb_label': '54720.ex2', 'torsion': [2, 4]}
  • id: 2645035
    {'degree': 16, 'field': [-2035440, -8562240, 37975920, 66813264, 22793164, -21672360, -4396092, 3709560, 469740, -329040, -32684, 14220, 1302, -264, -36, 0, 1], 'lmfdb_label': '54720.ex2', 'torsion': [12]}
  • id: 2645031
    {'degree': 16, 'field': [55225, -55460, 27848, -15252, 49174, -43840, 21336, -9404, -297, 1360, -216, 164, 22, -60, 32, -8, 1], 'lmfdb_label': '54720.ex2', 'torsion': [4, 4]}
  • id: 2645033
    {'degree': 16, 'field': [207310, -160820, -80286, 10916, 119763, -43452, -15926, -12076, 19905, -5036, 70, -756, 381, 28, -18, -4, 1], 'lmfdb_label': '54720.ex2', 'torsion': [2, 8]}
  • id: 2645036
    {'degree': 16, 'field': [254016, 0, -1950912, 0, 2073636, 0, -1048464, 0, 151776, 0, -12756, 0, 936, 0, -48, 0, 1], 'lmfdb_label': '54720.ex2', 'torsion': [12]}
  • id: 2645032
    {'degree': 16, 'field': [291600, 0, -25103520, 0, 23343696, 0, -7779072, 0, 1249324, 0, -106576, 0, 4884, 0, -112, 0, 1], 'lmfdb_label': '54720.ex2', 'torsion': [2, 8]}
  • id: 2645034
    {'degree': 16, 'field': [14197914025, 0, -7235840900, 0, 1454714800, 0, -153741056, 0, 9615802, 0, -386636, 0, 10036, 0, -152, 0, 1], 'lmfdb_label': '54720.ex2', 'torsion': [2, 6]}
• 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: 1314363
    {'conductor': 54720, 'conductor_valuation': 6, 'discriminant_valuation': 20, 'j_denominator_valuation': 2, 'kodaira_symbol': -14, 'lmfdb_label': '54720.ex2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 1314364
    {'conductor': 54720, 'conductor_valuation': 2, 'discriminant_valuation': 26, 'j_denominator_valuation': 20, 'kodaira_symbol': -24, 'lmfdb_label': '54720.ex2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1314365
    {'conductor': 54720, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '54720.ex2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1314366
    {'conductor': 54720, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '54720.ex2', 'prime': 19, '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: 2027922
    {'adelic_gens': [[1688, 3, 485, 2], [457, 8, 1828, 33], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [1519, 2272, 1516, 2247], [288, 1433, 313, 360], [1421, 1422, 1982, 845], [7, 6, 2274, 2275], [2273, 8, 2272, 9]], 'adelic_image': '2280.48.0.?', 'conductor': 54720, 'lmfdb_label': '54720.ex2', 'prime': 0}
  • id: 233538
    {'conductor': 54720, 'elladic_image': '4.6.0.1', 'lmfdb_label': '54720.ex2', 'modell_image': '2B', 'prime': 2}
• ec_padic •

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

  
  
  • id: 2767932
    {'lmfdb_iso': '54720.ex', 'p': 7, 'prec': 20, 'unit': 4883066462641824, 'val': 1}
  • id: 2767936
    {'lmfdb_iso': '54720.ex', 'p': 13, 'prec': 20, 'unit': 672303230651438352351, 'val': 1}
  • id: 2767938
    {'lmfdb_iso': '54720.ex', 'p': 17, 'prec': 20, 'unit': 79140691266114222458475, 'val': 1}
  • id: 2767942
    {'lmfdb_iso': '54720.ex', 'p': 23, 'prec': 20, 'unit': 18528598956452909923541707, 'val': 1}
  • id: 2767935
    {'lmfdb_iso': '54720.ex', 'p': 29, 'prec': 20, 'unit': 2923123338370811061287391277, 'val': 1}
  • id: 2767947
    {'lmfdb_iso': '54720.ex', 'p': 31, 'prec': 20, 'unit': 3108144828102949952769924618, 'val': 1}
  • id: 2767931
    {'lmfdb_iso': '54720.ex', 'p': 37, 'prec': 20, 'unit': 215786460954906230324614346378, 'val': 1}
  • id: 2767933
    {'lmfdb_iso': '54720.ex', 'p': 41, 'prec': 20, 'unit': 2118134923651611176373183354873, 'val': 1}
  • id: 2767934
    {'lmfdb_iso': '54720.ex', 'p': 43, 'prec': 20, 'unit': 8542425422250237967189667336324, 'val': 1}
  • id: 2767940
    {'lmfdb_iso': '54720.ex', 'p': 53, 'prec': 20, 'unit': 417810675291535370321286809361643, 'val': 1}
  • id: 2767945
    {'lmfdb_iso': '54720.ex', 'p': 59, 'prec': 20, 'unit': 48586294015700613762562900034854, 'val': 2}
  • id: 2767946
    {'lmfdb_iso': '54720.ex', 'p': 61, 'prec': 20, 'unit': 7565607357516265074397797826700599, 'val': 1}
  • id: 2767930
    {'lmfdb_iso': '54720.ex', 'p': 67, 'prec': 20, 'unit': 15231950057558490322929089899860945, 'val': 1}
  • id: 2767944
    {'lmfdb_iso': '54720.ex', 'p': 71, 'prec': 20, 'unit': 124359484717079763575576958261292960, 'val': 1}
  • id: 2767941
    {'lmfdb_iso': '54720.ex', 'p': 73, 'prec': 20, 'unit': 70382833471448881762077122071269104, 'val': 1}
  • id: 2767937
    {'lmfdb_iso': '54720.ex', 'p': 79, 'prec': 20, 'unit': 754027099045271515726453979972651645, 'val': 1}
  • id: 2767939
    {'lmfdb_iso': '54720.ex', 'p': 83, 'prec': 20, 'unit': 1219173763628097104887038241110291086, 'val': 1}
  • id: 2767943
    {'lmfdb_iso': '54720.ex', 'p': 89, 'prec': 20, 'unit': 5091182808508672065879729525573214125, 'val': 1}
  • id: 2767929
    {'lmfdb_iso': '54720.ex', 'p': 97, 'prec': 20, 'unit': 18335492993993612956016534459384493088, 'val': 1}