Elliptic curve data - 55.a1

Formats: - HTML - YAML - JSON - 2024-04-25T12:45:54.311248

• 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': '55a', 'Clabel': '55a3', 'Cnumber': 3, 'abc_quality': 1.0771710471613196, 'absD': 6875, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 440, 'ainvs': [1, -1, 0, -59, 190], 'analytic_rank': 0, 'bad_primes': [5, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 55, 'degree': 4, 'elladic_images': ['4.12.0.7'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.28566547997475890066298740964', 'prec': 107}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [22930509321, 6875], 'lmfdb_iso': '55.a', 'lmfdb_label': '55.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -59, 190], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '40.24.0-40.z.1.4', '44.24.0-44.h.1.2', '440.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.28566547997475890066298740964', 'prec': 107}, 'szpiro_ratio': 5.953019887009635, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
• 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, 1, 0, 0, -3, -3, 1, -1, 0, 2, 0, 0, -1, 6, -3, -4, -1], 'aplist': [1, 0, 1, 0, -1, 2, 6, -4, 4, 6, -8, -2, 2, 4, -12, -2, 4, -10, -16, 8, 14, 8, -4, 10, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 55, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '55.a', 'trace_hash': 467045135390574132}
• 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': '1.7706221109565404793015936143', 'prec': 100}, 'conductor': 55, 'gens': [], 'heights': [], 'lmfdb_label': '55.a1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '4.1146794247127563394669761001', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.0286698561781890848667440250290006511', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[6, 2, 1]], 'xcoord_integral_points': [6]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [0, 0], '5': [1, 0], '11': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '55.a1'}
• ec_torsion_growth •

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

  
  
  • id: 1920
    {'degree': 2, 'field': [-11, 0, 1], 'lmfdb_label': '55.a1', 'torsion': [2, 4]}
  • id: 1921
    {'degree': 4, 'field': [11, 0, -7, 0, 1], 'lmfdb_label': '55.a1', 'torsion': [8]}
  • id: 1925
    {'degree': 8, 'field': [-3, 0, 3, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '55.a1', 'torsion': [12]}
  • id: 1924
    {'degree': 8, 'field': [5, -110, -74, 154, 119, -22, -24, 0, 1], 'lmfdb_label': '55.a1', 'torsion': [2, 8]}
  • id: 1922
    {'degree': 8, 'field': [100, 0, 136, 0, -16, 0, 4, 0, 1], 'lmfdb_label': '55.a1', 'torsion': [4, 4]}
  • id: 1923
    {'degree': 8, 'field': [23716, 0, 7260, 0, 693, 0, 0, 0, 1], 'lmfdb_label': '55.a1', 'torsion': [2, 8]}
  • id: 1926
    {'degree': 16, 'field': [14641, 0, -42592, 0, 42108, 0, -22264, 0, 7865, 0, -2024, 0, 348, 0, -32, 0, 1], 'lmfdb_label': '55.a1', 'torsion': [16]}
  • id: 1927
    {'degree': 16, 'field': [96721, 0, -411088, 0, 150316, 0, -46126, 0, 11206, 0, -1864, 0, 241, 0, -22, 0, 1], 'lmfdb_label': '55.a1', '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: 272
    {'conductor': 55, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '55.a1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
  • id: 273
    {'conductor': 55, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '55.a1', 'prime': 11, '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: 1666013
    {'adelic_gens': [[168, 393, 193, 240], [1, 0, 8, 1], [433, 8, 432, 9], [1, 8, 0, 1], [404, 1, 343, 6], [1, 4, 4, 17], [7, 6, 434, 435], [177, 8, 268, 33], [59, 58, 178, 395]], 'adelic_image': '440.48.0.?', 'conductor': 55, 'lmfdb_label': '55.a1', 'prime': 0}
  • id: 166
    {'conductor': 55, 'elladic_image': '4.12.0.7', 'lmfdb_label': '55.a1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 55.a does not appear in ec_padic