Elliptic curve data - 53361.p5

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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': '53361bo', 'Clabel': '53361bo2', 'Cnumber': 2, 'abc_quality': 1.1486166056524132, 'absD': 603049522971892689, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 1848, 'ainvs': [1, -1, 1, -214556, 8256966], 'analytic_rank': 0, 'bad_primes': [3, 7, 11], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 53361, 'degree': 491520, 'elladic_images': ['8.24.0.10'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1022670580918912316223045124', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 15, 'isogeny_degrees': [1, 2, 4], 'jinv': [7189057, 3969], 'lmfdb_iso': '53361.p', 'lmfdb_label': '53361.p5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -4, -1], 'min_quad_twist_disc': -231, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.24.0.e.2', '24.48.0.w.2', '28.24.0.c.1', '56.48.0.i.1', '88.48.0.?', '132.24.0.?', '168.96.1.?', '264.96.0.?', '616.96.0.?', '924.48.0.?', '1848.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[3, 8, 5929], [7, 32, 1089], [11, 62, 441]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.61894179716900553865896626677', 'prec': 107}, 'szpiro_ratio': 4.450464794000622, '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, -1, 0, -1, -2, 0, 0, 3, 0, 2, 0, 0, -2, 0, 0, -1, 6, 0, 4, 2], 'aplist': [-1, 0, -2, 0, 0, -2, 6, 4, 0, -2, 0, 6, -2, 4, 0, -6, 12, -2, 4, 0, -6, 16, 12, -14, -18], 'class_deg': 8, 'class_size': 6, 'conductor': 53361, 'isogeny_matrix': [[1, 2, 8, 4, 4, 8], [2, 1, 4, 2, 2, 4], [8, 4, 1, 8, 2, 4], [4, 2, 8, 1, 4, 8], [4, 2, 2, 4, 1, 2], [8, 4, 4, 8, 2, 1]], 'lmfdb_iso': '53361.p', 'trace_hash': 1235016221343198693}
• 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': '0.014927739041335532132227831465', 'prec': 107}, 'conductor': 53361, 'gens': [], 'heights': [], 'lmfdb_label': '53361.p5', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.25146779305929266843100218318', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.0058711722371706737240087327313882978', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[-481, 240, 1], [443, -222, 1]], 'xcoord_integral_points': [-481, 443]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'o?', '3': 'a', '7': 'a', '11': 'a'}, 'iwp0': 3, 'lmfdb_label': '53361.p5'}
• ec_torsion_growth •

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

  
  
  • id: 2584063
    {'degree': 2, 'field': [58, -1, 1], 'lmfdb_label': '53361.p5', 'torsion': [2, 4]}
  • id: 2584064
    {'degree': 4, 'field': [-6, 30, -29, -2, 1], 'lmfdb_label': '53361.p5', 'torsion': [2, 4]}
  • id: 2584066
    {'degree': 4, 'field': [361, 19, 20, -1, 1], 'lmfdb_label': '53361.p5', 'torsion': [2, 8]}
  • id: 2584065
    {'degree': 4, 'field': [994, -70, 71, -2, 1], 'lmfdb_label': '53361.p5', 'torsion': [2, 4]}
  • id: 2584069
    {'degree': 8, 'field': [-4759, -3143, 6133, -3089, 809, -127, 44, -2, 1], 'lmfdb_label': '53361.p5', 'torsion': [2, 6]}
  • id: 2584068
    {'degree': 8, 'field': [564, -276, 322, -94, 53, -10, 8, -4, 1], 'lmfdb_label': '53361.p5', 'torsion': [2, 8]}
  • id: 2584067
    {'degree': 8, 'field': [1864, -2016, 2542, -1094, 653, -130, 48, -4, 1], 'lmfdb_label': '53361.p5', 'torsion': [4, 4]}
  • id: 2584072
    {'degree': 16, 'field': [71824, 0, -41752, 0, -799, 0, 5004, 0, -868, 0, -222, 0, 92, 0, 20, 0, 1], 'lmfdb_label': '53361.p5', 'torsion': [4, 8]}
  • id: 2584070
    {'degree': 16, 'field': [2527897, 9200252, -3281198, -10024084, 796952, 4196084, -61542, -953620, 12377, 128524, -4554, -10268, 680, 448, -44, -8, 1], 'lmfdb_label': '53361.p5', 'torsion': [2, 8]}
  • id: 2584071
    {'degree': 16, 'field': [4359744, 0, -1550016, 0, 451188, 0, -398628, 0, 158833, 0, -27760, 0, 2238, 0, -76, 0, 1], 'lmfdb_label': '53361.p5', 'torsion': [2, 8]}
  • id: 2584073
    {'degree': 16, 'field': [21687649, 0, -15486963, 0, 5139541, 0, -1056618, 0, 150651, 0, -15396, 0, 1090, 0, -48, 0, 1], 'lmfdb_label': '53361.p5', 'torsion': [2, 16]}
  • id: 2584074
    {'degree': 16, 'field': [168703539, -138367248, 126740757, 61007679, 7481631, 5320176, 3037372, -155488, 551858, -108372, 57698, -9962, 3351, -458, 101, -8, 1], 'lmfdb_label': '53361.p5', 'torsion': [2, 12]}
• 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: 1280602
    {'conductor': 53361, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '53361.p5', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1280603
    {'conductor': 53361, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '53361.p5', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1280604
    {'conductor': 53361, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '53361.p5', 'prime': 11, '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: 2018792
    {'adelic_gens': [[329, 330, 1782, 1517], [1, 0, 8, 1], [5, 4, 1844, 1845], [1, 8, 0, 1], [1841, 8, 1840, 9], [89, 1056, 1716, 749], [1231, 836, 0, 1847], [1013, 132, 330, 1211], [1175, 0, 0, 1847]], 'adelic_image': '1848.192.1.?', 'conductor': 53361, 'lmfdb_label': '53361.p5', 'prime': 0}
  • id: 228092
    {'conductor': 53361, 'elladic_image': '8.24.0.10', 'lmfdb_label': '53361.p5', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 53361.p does not appear in ec_padic