Elliptic curve data - 4056.m1

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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
  intrinsic_torsion	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
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '4056f', 'Clabel': '4056f3', 'Cnumber': 3, 'abc_quality': 1.052193877800105, 'absD': 192763444224, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 312, 'ainvs': [0, 1, 0, -140664, -20352864], 'analytic_rank': 0, 'bad_primes': [2, 3, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 4056, 'degree': 10752, 'elladic_images': ['4.12.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4856000032334873463367410613', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'intrinsic_torsion': 2, 'iso_nlabel': 12, 'isogeny_degrees': [1, 2, 4], 'jinv': [62275269892, 39], 'lmfdb_iso': '4056.m', 'lmfdb_label': '4056.m1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -832, -9520], 'min_quad_twist_disc': 13, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '24.24.0-24.z.1.1', '104.24.0.?', '156.24.0.?', '312.48.0.?'], '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, 2, 507], [3, 4, 1352], [13, 98, 24]], 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.37449732596390211287102942737', 'prec': 107}, 'szpiro_ratio': 5.6784144980679985, '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, 0, 0, 0, 0, -2, 0, 2, 0, 4, 0], 'aplist': [0, 1, -2, 0, 0, 0, 2, 4, 0, 6, 0, 2, -6, -12, 4, 6, 8, -2, -4, 12, 14, 0, -8, 18, 6], 'class_deg': 4, 'class_size': 4, 'conductor': 4056, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '4056.m', 'trace_hash': 1238606247498279165}
• 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': '0.051241782951754020026665824783', 'prec': 107}, 'conductor': 4056, 'gens': [], 'heights': [], 'lmfdb_label': '4056.m1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.24652080256487923295473231358', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.9721664205190338636378585086300995179', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-217, 0, 1]], 'xcoord_integral_points': [-217]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [7, 0], '13': 'a'}, 'iwp0': 3, 'lmfdb_label': '4056.m1'}
• ec_torsion_growth •

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

  
  
  • id: 212615
    {'degree': 2, 'field': [-39, 0, 1], 'lmfdb_label': '4056.m1', 'torsion': [2, 2]}
  • id: 212617
    {'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '4056.m1', 'torsion': [4]}
  • id: 212616
    {'degree': 2, 'field': [10, -1, 1], 'lmfdb_label': '4056.m1', 'torsion': [4]}
  • id: 212619
    {'degree': 4, 'field': [-56, -20, 21, -2, 1], 'lmfdb_label': '4056.m1', 'torsion': [2, 4]}
  • id: 212618
    {'degree': 4, 'field': [100, 0, -19, 0, 1], 'lmfdb_label': '4056.m1', 'torsion': [2, 4]}
  • id: 212623
    {'degree': 8, 'field': [-507, 0, 728, 0, -78, 0, 0, 0, 1], 'lmfdb_label': '4056.m1', 'torsion': [6]}
  • id: 212620
    {'degree': 8, 'field': [256, 0, -191, 0, 291, 0, -29, 0, 1], 'lmfdb_label': '4056.m1', 'torsion': [4, 4]}
  • id: 212621
    {'degree': 8, 'field': [1296, 0, 0, 0, 84, 0, 0, 0, 1], 'lmfdb_label': '4056.m1', 'torsion': [8]}
  • id: 212622
    {'degree': 8, 'field': [1521, 0, 0, 0, 91, 0, 0, 0, 1], 'lmfdb_label': '4056.m1', 'torsion': [8]}
  • id: 212627
    {'degree': 16, 'field': [-642758, 1594496, 2059004, -2199140, -4397546, -2095776, 281998, 551216, 111410, -45272, -20252, 1818, 1828, 26, -70, -2, 1], 'lmfdb_label': '4056.m1', 'torsion': [2, 6]}
  • id: 212629
    {'degree': 16, 'field': [81, -1296, 10368, -5760, 1332, 2268, -1984, 2824, -986, -696, 904, -472, 200, -84, 32, -8, 1], 'lmfdb_label': '4056.m1', 'torsion': [12]}
  • id: 212625
    {'degree': 16, 'field': [6561, 0, 0, 0, 1701, 0, 0, 0, 360, 0, 0, 0, 21, 0, 0, 0, 1], 'lmfdb_label': '4056.m1', 'torsion': [2, 8]}
  • id: 212628
    {'degree': 16, 'field': [81796, 0, -23660, 0, 55432, 0, 22204, 0, 8593, 0, 1456, 0, 274, 0, 28, 0, 1], 'lmfdb_label': '4056.m1', 'torsion': [12]}
  • id: 212626
    {'degree': 16, 'field': [950625, 0, 0, 0, -4788108, 0, 0, 0, 115050, 0, 0, 0, -780, 0, 0, 0, 1], 'lmfdb_label': '4056.m1', 'torsion': [2, 8]}
  • id: 212624
    {'degree': 16, 'field': [2313441, 0, 0, 0, -138411, 0, 0, 0, 6760, 0, 0, 0, -91, 0, 0, 0, 1], 'lmfdb_label': '4056.m1', 'torsion': [2, 8]}
• 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: 76241
    {'conductor': 4056, 'conductor_valuation': 3, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '4056.m1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
  • id: 76242
    {'conductor': 4056, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '4056.m1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
  • id: 76243
    {'conductor': 4056, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '4056.m1', 'prime': 13, '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: 1690464
    {'adelic_gens': [[44, 311, 97, 306], [7, 6, 306, 307], [120, 281, 145, 192], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [43, 42, 130, 283], [112, 3, 109, 2], [305, 8, 304, 9]], 'adelic_image': '312.48.0.?', 'conductor': 4056, 'lmfdb_label': '4056.m1', 'prime': 0}
  • id: 20311
    {'conductor': 4056, 'elladic_image': '4.12.0.8', 'lmfdb_label': '4056.m1', 'modell_image': '2B', 'prime': 2}
• lmfdb_iso 4056.m does not appear in ec_padic