Elliptic curve data - 53361.bm4

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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': '53361bj', 'Clabel': '53361bj3', 'Cnumber': 3, 'abc_quality': 1.0376318384434067, 'absD': 888218104538866678731, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1848, 'ainvs': [1, -1, 0, 2320092, -454331025], 'analytic_rank': 0, 'bad_primes': [3, 7, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 53361, 'degree': 1658880, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.7085767881442081720388246590', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 38, 'isogeny_degrees': [1, 2, 4], 'jinv': [9090072503, 5845851], 'lmfdb_iso': '53361.bm', 'lmfdb_label': '53361.bm4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 44, 55], 'min_quad_twist_disc': -231, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '22.6.0.a.1', '24.12.0.ba.1', '44.12.0.g.1', '56.12.0-4.c.1.3', '84.12.0.?', '168.24.0.?', '264.24.0.?', '616.24.0.?', '924.24.0.?', '1848.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[3, 6, 5929], [7, 26, 1089], [11, 72, 441]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.012632067116688598242446120166', 'prec': 110}, 'szpiro_ratio': 5.106641748289579, '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, 0, -1, -2, 0, 0, -3, 0, -2, 0, 0, -2, 0, 0, -1, 2, 0, 0, 2], 'aplist': [1, 0, -2, 0, 0, -2, 2, 0, -8, -6, 8, 6, 2, 0, 8, -6, -4, 6, -4, 0, -14, 4, -12, -6, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 53361, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '53361.bm', 'trace_hash': 740424081454027113}
• 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': '0.0044397661347075028027450040047', 'prec': 110}, 'conductor': 53361, 'gens': [], 'heights': [], 'lmfdb_label': '53361.bm4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.090291808479390327678494942183', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.72233446783512262142795953746730963002', 'prec': 133}, 'tamagawa_product': 32, 'torsion_generators': [[771, -771, 2]], 'xcoord_integral_points': []}
• 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.bm4'}
• ec_torsion_growth •

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

  
  
  • id: 2583986
    {'degree': 2, 'field': [-231, 0, 1], 'lmfdb_label': '53361.bm4', 'torsion': [4]}
  • id: 2583985
    {'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '53361.bm4', 'torsion': [2, 2]}
  • id: 2583987
    {'degree': 2, 'field': [21, 0, 1], 'lmfdb_label': '53361.bm4', 'torsion': [4]}
  • id: 2583988
    {'degree': 4, 'field': [345, -48, 49, -2, 1], 'lmfdb_label': '53361.bm4', 'torsion': [2, 4]}
  • id: 2583992
    {'degree': 8, 'field': [-1113, 3773, 184, 696, 19, 5, 15, -1, 1], 'lmfdb_label': '53361.bm4', 'torsion': [6]}
  • id: 2583990
    {'degree': 8, 'field': [529, 0, -492, 0, -37, 0, 36, 0, 1], 'lmfdb_label': '53361.bm4', 'torsion': [8]}
  • id: 2583989
    {'degree': 8, 'field': [1527, -204, 376, -324, 113, 56, -14, -4, 1], 'lmfdb_label': '53361.bm4', 'torsion': [2, 4]}
  • id: 2583991
    {'degree': 8, 'field': [1258884, 0, 33396, 0, 3157, 0, 88, 0, 1], 'lmfdb_label': '53361.bm4', 'torsion': [8]}
  • id: 2583997
    {'degree': 16, 'field': [-11071287, -18396, -7220391, -5156466, 5676441, -108660, -570678, 281400, -183233, 60814, -8702, 3574, 151, 16, 31, -2, 1], 'lmfdb_label': '53361.bm4', 'torsion': [12]}
  • id: 2583998
    {'degree': 16, 'field': [81, 0, 330222, 0, 136129, 0, -27801, 0, -1644, 0, 3250, 0, 633, 0, 42, 0, 1], 'lmfdb_label': '53361.bm4', 'torsion': [12]}
  • id: 2583996
    {'degree': 16, 'field': [12951, -1935, -26594, 15436, 802, -9600, 16332, -13404, 8878, -4577, 2386, -861, 345, -99, 25, -5, 1], 'lmfdb_label': '53361.bm4', 'torsion': [2, 6]}
  • id: 2583995
    {'degree': 16, 'field': [17725, -30460, 54922, -52756, 37508, -18868, 19290, -19732, 17909, -12332, 6510, -2684, 872, -224, 52, -8, 1], 'lmfdb_label': '53361.bm4', 'torsion': [2, 8]}
  • id: 2583994
    {'degree': 16, 'field': [531441, 0, 519048, 0, -477206, 0, 856224, 0, 1770507, 0, 95776, 0, 3834, 0, 72, 0, 1], 'lmfdb_label': '53361.bm4', 'torsion': [2, 8]}
  • id: 2583993
    {'degree': 16, 'field': [662596, 0, -948640, 0, 794420, 0, -280500, 0, 58301, 0, -7740, 0, 710, 0, -40, 0, 1], 'lmfdb_label': '53361.bm4', 'torsion': [4, 4]}
• 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: 1280575
    {'conductor': 53361, 'conductor_valuation': 2, 'discriminant_valuation': 18, 'j_denominator_valuation': 12, 'kodaira_symbol': -16, 'lmfdb_label': '53361.bm4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 1280576
    {'conductor': 53361, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '53361.bm4', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
  • id: 1280577
    {'conductor': 53361, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '53361.bm4', '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: 2018745
    {'adelic_gens': [[1555, 1288, 1442, 1821], [263, 0, 0, 1847], [1841, 8, 1840, 9], [1555, 1554, 1498, 43], [1231, 784, 700, 1287], [1, 0, 8, 1], [1532, 791, 889, 258], [7, 6, 1842, 1843], [1, 8, 0, 1], [1, 4, 4, 17]], 'adelic_image': '1848.48.0.?', 'conductor': 53361, 'lmfdb_label': '53361.bm4', 'prime': 0}
  • id: 228054
    {'conductor': 53361, 'elladic_image': '4.6.0.1', 'lmfdb_label': '53361.bm4', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 53361.bm does not appear in ec_padic