Elliptic curve data - 112.c2

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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': '112c', 'Clabel': '112c5', 'Cnumber': 5, 'abc_quality': 1.0293250379726038, 'absD': 7516192768, 'adelic_genus': 21, 'adelic_index': 864, 'adelic_level': 504, 'ainvs': [0, -1, 0, -2728, 55920], 'analytic_rank': 0, 'bad_primes': [2, 7], 'class_deg': 18, 'class_size': 6, 'cm': 0, 'conductor': 112, 'degree': 72, 'elladic_images': ['8.6.0.1', '9.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.75967457070305711228939841557', 'prec': 103}, 'faltings_index': 4, 'faltings_ratio': 9, 'intrinsic_torsion': 1, 'iso_nlabel': 2, 'isogeny_degrees': [1, 2, 3, 6, 9, 18], 'jinv': [-548347731625, 1835008], 'lmfdb_iso': '112.c', 'lmfdb_label': '112.c2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -171, -874], 'min_quad_twist_disc': -4, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '8.6.0.c.1', '9.12.0.a.1', '12.24.0-6.a.1.9', '14.6.0.b.1', '18.36.0.a.1', '24.48.0-24.bw.1.3', '36.72.0-18.a.1.10', '42.24.0.b.1', '56.12.0.n.1', '63.36.0.d.1', '72.144.1.?', '84.48.0.?', '126.216.7.?', '168.96.1.?', '252.432.7.?', '504.864.21.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 2, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 7], [7, 8, 16]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.066527390143111802872166294112', 'prec': 107}, 'szpiro_ratio': 7.4925751978471435, '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, 0, 0, -1, 0, 1, 0, 0, 0, -4, 0, 0, 0, 6, 0, -2, 0], 'aplist': [0, 2, 0, -1, 0, -4, 6, -2, 0, -6, 4, 2, 6, -8, 12, 6, 6, 8, 4, 0, 2, -8, 6, -6, -10], 'class_deg': 18, 'class_size': 6, 'conductor': 112, 'isogeny_matrix': [[1, 2, 3, 9, 18, 6], [2, 1, 6, 18, 9, 3], [3, 6, 1, 3, 6, 2], [9, 18, 3, 1, 2, 6], [18, 9, 6, 2, 1, 3], [6, 3, 2, 6, 3, 1]], 'lmfdb_iso': '112.c', 'trace_hash': 2000533991094873398}
• 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': '0.21885428379850134887482124741', 'prec': 103}, 'conductor': 112, 'gens': [], 'heights': [], 'lmfdb_label': '112.c2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.3254912396824867143349662920', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.3254912396824867143349662920288834551', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[-60, 0, 1]], 'xcoord_integral_points': [-60]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': 'a', '3': [0, 0], '7': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '112.c2'}
• ec_torsion_growth •

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

  
  
  • id: 4201
    {'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '112.c2', 'torsion': [6]}
  • id: 4200
    {'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '112.c2', 'torsion': [2, 2]}
  • id: 4202
    {'degree': 4, 'field': [-2, -4, -2, 0, 1], 'lmfdb_label': '112.c2', 'torsion': [4]}
  • id: 4203
    {'degree': 4, 'field': [22, 2, -1, -2, 1], 'lmfdb_label': '112.c2', 'torsion': [2, 6]}
  • id: 4205
    {'degree': 6, 'field': [-588, 0, 441, 0, -42, 0, 1], 'lmfdb_label': '112.c2', 'torsion': [18]}
  • id: 4204
    {'degree': 6, 'field': [49, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '112.c2', 'torsion': [6]}
  • id: 4208
    {'degree': 8, 'field': [-2, 4, -2, 0, 7, -4, -6, 0, 1], 'lmfdb_label': '112.c2', 'torsion': [12]}
  • id: 4207
    {'degree': 8, 'field': [1, 0, -3, 0, 6, 0, -3, 0, 1], 'lmfdb_label': '112.c2', 'torsion': [2, 4]}
  • id: 4206
    {'degree': 8, 'field': [1, 0, 2, 0, 10, 0, 2, 0, 1], 'lmfdb_label': '112.c2', 'torsion': [2, 4]}
  • id: 4210
    {'degree': 12, 'field': [49, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '112.c2', 'torsion': [18]}
  • id: 4211
    {'degree': 12, 'field': [64, 0, -204, 0, 225, 0, 6, 0, 15, 0, 6, 0, 1], 'lmfdb_label': '112.c2', 'torsion': [2, 6]}
  • id: 4209
    {'degree': 12, 'field': [4096, 0, 2496, 0, 1329, 0, 245, 0, 48, 0, -3, 0, 1], 'lmfdb_label': '112.c2', 'torsion': [3, 6]}
  • id: 4212
    {'degree': 12, 'field': [28224, 0, 15876, 0, 7497, 0, -252, 0, 126, 0, 0, 0, 1], 'lmfdb_label': '112.c2', 'torsion': [2, 18]}
  • id: 4213
    {'degree': 16, 'field': [-28, 32, 320, 224, -72, 48, 208, 384, 464, 256, 48, 16, 12, -8, -8, 0, 1], 'lmfdb_label': '112.c2', 'torsion': [8]}
  • id: 4214
    {'degree': 16, 'field': [4, 0, -8, 40, 48, -152, 280, -332, 341, -344, 338, -256, 146, -56, 18, -4, 1], 'lmfdb_label': '112.c2', 'torsion': [2, 12]}
  • id: 4215
    {'degree': 16, 'field': [484, 0, 212, 0, 485, 0, 920, 0, 811, 0, 388, 0, 107, 0, 16, 0, 1], 'lmfdb_label': '112.c2', '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: 733
    {'conductor': 112, 'conductor_valuation': 4, 'discriminant_valuation': 30, 'j_denominator_valuation': 18, 'kodaira_symbol': -26, 'lmfdb_label': '112.c2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 734
    {'conductor': 112, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '112.c2', 'prime': 7, '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: 1666212
    {'adelic_gens': [[1, 36, 0, 1], [253, 36, 10, 361], [1, 0, 36, 1], [397, 36, 88, 29], [469, 36, 468, 37], [19, 36, 216, 91], [377, 468, 242, 143], [292, 9, 223, 178], [1, 18, 14, 253]], 'adelic_image': '504.864.21.?', 'conductor': 112, 'lmfdb_label': '112.c2', 'prime': 0}
  • id: 396
    {'conductor': 112, 'elladic_image': '8.6.0.1', 'lmfdb_label': '112.c2', 'modell_image': '2B', 'prime': 2}
  • id: 397
    {'conductor': 112, 'elladic_image': '9.12.0.1', 'lmfdb_label': '112.c2', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 112.c does not appear in ec_padic