Elliptic curve data - 1056.i2

Formats: - HTML - YAML - JSON - 2026-01-31T04:29:58.843651

• 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': '1056j', 'Clabel': '1056j2', 'Cnumber': 2, 'abc_quality': 1.1220261923101509, 'absD': 45163008, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 264, 'ainvs': [0, 1, 0, -88, -484], 'analytic_rank': 0, 'bad_primes': [2, 3, 11], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 1056, 'degree': 192, 'elladic_images': ['8.6.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.17125906209420359718275793882', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 8, 'isogeny_degrees': [1, 2], 'jinv': [-148877000, 88209], 'lmfdb_iso': '1056.i', 'lmfdb_label': '1056.i2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -88, 484], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.a.1', '132.6.0.?', '264.12.0.?'], '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, 1], [3, 4, 352], [11, 12, 96]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.34860132332575538488016615227', 'prec': 107}, 'szpiro_ratio': 3.700236698662009, '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, 0, 0, 2, 0, 1, 0, 1, 0, 4, 0, 0, 0, -2, 0, 0, 0], 'aplist': [0, 1, 0, 2, 1, 4, -2, 0, 2, -2, 4, 6, -6, 12, 6, 0, 0, 0, -4, 10, 2, -2, 4, -14, -2], 'class_deg': 2, 'class_size': 2, 'conductor': 1056, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '1056.i', 'trace_hash': 704926749122745581}
• 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': '0.70998025145309838939654688963', 'prec': 103}, 'conductor': 1056, 'gens': [], 'heights': [], 'lmfdb_label': '1056.i2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.75805214245121546604779223033', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.2741564273536463981433766909910874447', 'prec': 130}, 'tamagawa_product': 12, 'torsion_generators': [[11, 0, 1]], 'xcoord_integral_points': [11]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [1, 0], '11': [1, 0]}, 'iwp0': 5, 'lmfdb_label': '1056.i2'}
• ec_torsion_growth •

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

  
  
  • id: 52078
    {'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '1056.i2', 'torsion': [2, 2]}
  • id: 52079
    {'degree': 4, 'field': [-8, 0, 1, 0, 1], 'lmfdb_label': '1056.i2', 'torsion': [4]}
  • id: 52082
    {'degree': 8, 'field': [-27, 0, -144, 0, -18, 0, 0, 0, 1], 'lmfdb_label': '1056.i2', 'torsion': [6]}
  • id: 52080
    {'degree': 8, 'field': [16, 0, -32, 0, 26, 0, -8, 0, 1], 'lmfdb_label': '1056.i2', 'torsion': [2, 4]}
  • id: 52081
    {'degree': 8, 'field': [36, 0, 204, 0, 13, 0, 10, 0, 1], 'lmfdb_label': '1056.i2', 'torsion': [2, 4]}
  • id: 52083
    {'degree': 16, 'field': [16, 0, 16, 0, 40, 0, -2168, 0, -8960, 0, 1084, 0, 10, 0, -2, 0, 1], 'lmfdb_label': '1056.i2', 'torsion': [8]}
  • id: 52084
    {'degree': 16, 'field': [6633, 6336, 26532, 15072, 35724, 8544, 18572, -768, 3326, -864, -148, -96, -68, 0, 4, 0, 1], 'lmfdb_label': '1056.i2', '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: 15026
    {'conductor': 1056, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '1056.i2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
  • id: 15027
    {'conductor': 1056, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '1056.i2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
  • id: 15028
    {'conductor': 1056, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '1056.i2', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1671237
    {'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [145, 4, 26, 9], [1, 4, 0, 1], [261, 4, 260, 5], [2, 1, 131, 0], [100, 169, 33, 232], [89, 4, 178, 9]], 'adelic_image': '264.12.0.?', 'conductor': 1056, 'lmfdb_label': '1056.i2', 'prime': 0}
  • id: 5016
    {'conductor': 1056, 'elladic_image': '8.6.0.5', 'lmfdb_label': '1056.i2', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 1056.i does not appear in ec_padic