Elliptic curve data - 264.a1

Formats: - HTML - YAML - JSON - 2025-10-21T02:03:41.998479

• 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': '264b', 'Clabel': '264b3', 'Cnumber': 3, 'abc_quality': 0.9748605365818221, 'absD': 1824768, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 264, 'ainvs': [0, -1, 0, -472, 4108], 'analytic_rank': 0, 'bad_primes': [2, 3, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 264, 'degree': 64, 'elladic_images': ['8.12.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.21241299985567583103979130813', 'prec': 103}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [5690357426, 891], 'lmfdb_iso': '264.a', 'lmfdb_label': '264.a1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -472, 4108], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.4', '24.24.0-24.bb.1.16', '44.12.0-4.c.1.1', '88.24.0.?', '264.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 11], [3, 4, 88], [11, 12, 24]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.42297191565760736925933813654', 'prec': 107}, 'szpiro_ratio': 5.395791340493858, '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, -1, 0, 2, 0, 0, 0, 1, 0, 1, 0, 2, 0, -2, 0, 6, 0, 0, 0], 'aplist': [0, -1, 2, 0, 1, 2, 6, 0, 4, 2, 0, -10, 6, -8, -4, -6, -12, 2, 4, 12, -14, 16, -12, 10, -14], 'class_deg': 4, 'class_size': 4, 'conductor': 264, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '264.a', 'trace_hash': 679666520955609094}
• 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': '0.65388355115854330939694131016', 'prec': 103}, 'conductor': 264, 'gens': [], 'heights': [], 'lmfdb_label': '264.a1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '2.5539883832590008329284197600', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2769941916295004164642098800115256210', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [[13, 0, 1]], 'xcoord_integral_points': [13]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '11': [3, 0]}, 'iwp0': 3, 'lmfdb_label': '264.a1'}
• ec_torsion_growth •

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

  
  
  • id: 11270
    {'degree': 2, 'field': [-22, 0, 1], 'lmfdb_label': '264.a1', 'torsion': [2, 2]}
  • id: 11271
    {'degree': 2, 'field': [-11, 0, 1], 'lmfdb_label': '264.a1', 'torsion': [4]}
  • id: 11272
    {'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '264.a1', 'torsion': [4]}
  • id: 11273
    {'degree': 4, 'field': [25, 0, -12, 0, 1], 'lmfdb_label': '264.a1', 'torsion': [2, 4]}
  • id: 11277
    {'degree': 8, 'field': [-48, 0, 112, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '264.a1', 'torsion': [6]}
  • id: 11275
    {'degree': 8, 'field': [49, -28, -191, -34, 126, 28, -23, -2, 1], 'lmfdb_label': '264.a1', 'torsion': [8]}
  • id: 11274
    {'degree': 8, 'field': [324, 0, 560, 0, -20, 0, 8, 0, 1], 'lmfdb_label': '264.a1', 'torsion': [2, 4]}
  • id: 11276
    {'degree': 8, 'field': [484, 0, 176, 0, 42, 0, 8, 0, 1], 'lmfdb_label': '264.a1', 'torsion': [8]}
  • id: 11279
    {'degree': 16, 'field': [64, 0, -13888, 0, 42032, 0, -42096, 0, 19604, 0, -4776, 0, 620, 0, -40, 0, 1], 'lmfdb_label': '264.a1', 'torsion': [2, 8]}
  • id: 11283
    {'degree': 16, 'field': [289, 0, 1772, 0, 1672, 0, -6840, 0, 2694, 0, -468, 0, 100, 0, -16, 0, 1], 'lmfdb_label': '264.a1', 'torsion': [12]}
  • id: 11280
    {'degree': 16, 'field': [2401, 0, 11956, 0, 21848, 0, 18816, 0, 9191, 0, 2592, 0, 392, 0, 28, 0, 1], 'lmfdb_label': '264.a1', 'torsion': [2, 8]}
  • id: 11278
    {'degree': 16, 'field': [14641, 0, 0, 0, 0, 0, 0, 0, 4114, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '264.a1', 'torsion': [4, 4]}
  • id: 11282
    {'degree': 16, 'field': [17424, 0, -50688, 0, 119232, 0, -53312, 0, 4856, 0, -2960, 0, -140, 0, -40, 0, 1], 'lmfdb_label': '264.a1', 'torsion': [12]}
  • id: 11281
    {'degree': 16, 'field': [13630864, 0, 6907456, 0, 153184, 0, -491664, 0, 71496, 0, -6816, 0, 700, 0, -44, 0, 1], 'lmfdb_label': '264.a1', '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: 2413
    {'conductor': 264, 'conductor_valuation': 3, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '264.a1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
  • id: 2414
    {'conductor': 264, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '264.a1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 2415
    {'conductor': 264, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '264.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: 1666871
    {'adelic_gens': [[52, 1, 167, 6], [89, 8, 92, 33], [1, 0, 8, 1], [232, 107, 169, 198], [168, 41, 193, 240], [1, 8, 0, 1], [7, 6, 258, 259], [1, 4, 4, 17], [257, 8, 256, 9]], 'adelic_image': '264.48.0.?', 'conductor': 264, 'lmfdb_label': '264.a1', 'prime': 0}
  • id: 1096
    {'conductor': 264, 'elladic_image': '8.12.0.8', 'lmfdb_label': '264.a1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 264.a does not appear in ec_padic