Elliptic curve data - 54208.u2

Formats: - HTML - YAML - JSON - 2025-10-09T14:23:05.106580

• 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': '54208t', 'Clabel': '54208t1', 'Cnumber': 1, 'abc_quality': 1.0348177494302118, 'absD': 812707151872, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 56, 'ainvs': [0, 1, 0, -161, 43327], 'analytic_rank': 0, 'bad_primes': [2, 7, 11], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 54208, 'degree': 92160, 'elladic_images': ['8.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.96427880083904262331964694958', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 20, 'isogeny_degrees': [1, 2], 'jinv': [-4, 7], 'lmfdb_iso': '54208.u', 'lmfdb_label': '54208.u2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, 0, -4], 'min_quad_twist_disc': -88, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.c.1', '14.6.0.b.1', '56.12.0.n.1'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 847], [7, 8, 7744], [11, 62, 448]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1588650763067363946009676680', 'prec': 103}, 'szpiro_ratio': 3.1997081961509473, '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, -2, 0, 4, 0, -1, 0, 1, 0, 0, 0, 0, 0, -8, 0, 2, 0, -2, 0], 'aplist': [0, -2, 4, -1, 0, 0, 2, -2, 8, 2, 4, 6, 2, 8, -4, 10, -6, 4, 12, 0, 14, 8, 6, 10, -2], 'class_deg': 2, 'class_size': 2, 'conductor': 54208, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '54208.u', 'trace_hash': 1167295580620958239}
• 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': '0.14535771106551926328415847732', 'prec': 103}, 'conductor': 54208, 'gens': [], 'heights': [], 'lmfdb_label': '54208.u2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.71917125674422247695207837302', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.8766850269768899078083134920820139917', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-37, 0, 1]], 'xcoord_integral_points': [-37]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '7': [0, 0], '11': 'a'}, 'iwp0': 3, 'lmfdb_label': '54208.u2'}
• ec_torsion_growth •

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

  
  
  • id: 2621169
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '54208.u2', 'torsion': [2, 2]}
  • id: 2621170
    {'degree': 4, 'field': [-46, -16, -5, -2, 1], 'lmfdb_label': '54208.u2', 'torsion': [4]}
  • id: 2621173
    {'degree': 8, 'field': [-3557763, 0, 191664, 0, -2178, 0, -66, 0, 1], 'lmfdb_label': '54208.u2', 'torsion': [6]}
  • id: 2621172
    {'degree': 8, 'field': [526, 348, -13, -82, -11, 16, 1, -2, 1], 'lmfdb_label': '54208.u2', 'torsion': [2, 4]}
  • id: 2621171
    {'degree': 8, 'field': [29968, 13344, 5664, -184, 854, 44, 29, -2, 1], 'lmfdb_label': '54208.u2', 'torsion': [2, 4]}
  • id: 2621174
    {'degree': 16, 'field': [293764, 0, -350352, 0, -62536, 0, 34896, 0, -5792, 0, -696, 0, 172, 0, -16, 0, 1], 'lmfdb_label': '54208.u2', 'torsion': [8]}
  • id: 2621175
    {'degree': 16, 'field': [30867678864, 0, 16836915744, 0, 2111700712, 0, -131417616, 0, 2064381, 0, -39930, 0, 2178, 0, 0, 0, 1], 'lmfdb_label': '54208.u2', '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: 1301189
    {'conductor': 54208, 'conductor_valuation': 6, 'discriminant_valuation': 16, 'j_denominator_valuation': 0, 'kodaira_symbol': -10, 'lmfdb_label': '54208.u2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 1301190
    {'conductor': 54208, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '54208.u2', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
  • id: 1301191
    {'conductor': 54208, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '54208.u2', '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: 2024393
    {'adelic_gens': [[1, 2, 2, 5], [29, 4, 2, 9], [3, 4, 8, 11], [9, 50, 48, 7], [34, 1, 39, 0], [53, 4, 52, 5], [1, 4, 0, 1], [1, 0, 4, 1]], 'adelic_image': '56.12.0.?', 'conductor': 54208, 'lmfdb_label': '54208.u2', 'prime': 0}
  • id: 231422
    {'conductor': 54208, 'elladic_image': '8.6.0.1', 'lmfdb_label': '54208.u2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 54208.u does not appear in ec_padic