Elliptic curve data - 1050.c6

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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
  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': '1050c', 'Clabel': '1050c2', 'Cnumber': 2, 'abc_quality': 1.0190986885579905, 'absD': 803722500000000, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 1680, 'ainvs': [1, 1, 0, -26750, 976500], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 1050, 'degree': 6144, 'elladic_images': ['16.96.0.44'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5594276022726952701275697318', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 2, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [135487869158881, 51438240000], 'lmfdb_iso': '1050.c', 'lmfdb_label': '1050.c6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -1070, 7812], 'min_quad_twist_disc': 5, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.48.0.l.2', '16.96.0-8.l.2.4', '20.24.0-4.b.1.3', '28.24.0.c.1', '40.96.0-8.l.2.2', '48.192.1-48.f.2.16', '56.96.1.cd.2', '80.192.2.?', '112.192.1.?', '140.48.0.?', '240.384.5.?', '280.192.1.?', '336.384.5.?', '560.384.5.?', '1680.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 25], [3, 4, 350], [5, 18, 42], [7, 8, 150]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.75470864605564508282719006519', 'prec': 103}, 'szpiro_ratio': 6.065730619481999, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 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, -1, -1, 1, 0, 1, 1, -1, 1, 0, -4, -1, 2, -1, 0, 1, -2, -1, 4, 0], 'aplist': [-1, -1, 0, 1, -4, 2, -2, 4, 8, -2, 0, -6, -6, 4, 0, 10, 12, 14, 12, -8, -10, 16, 12, 10, -2], 'class_deg': 16, 'class_size': 8, 'conductor': 1050, 'isogeny_matrix': [[1, 2, 4, 16, 4, 8, 16, 8], [2, 1, 2, 8, 2, 4, 8, 4], [4, 2, 1, 16, 4, 8, 16, 8], [16, 8, 16, 1, 4, 2, 4, 8], [4, 2, 4, 4, 1, 2, 4, 2], [8, 4, 8, 2, 2, 1, 2, 4], [16, 8, 16, 4, 4, 2, 1, 8], [8, 4, 8, 8, 2, 4, 8, 1]], 'lmfdb_iso': '1050.c', 'trace_hash': 1840108885404238702}
• 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': '0.044207748291667939517513770716', 'prec': 107}, 'conductor': 1050, 'gens': [], 'heights': [], 'lmfdb_label': '1050.c6', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.45881119015292984437388985970', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.91762238030585968874777971940783629772', 'prec': 133}, 'tamagawa_product': 32, 'torsion_generators': [[-180, 90, 1], [140, -70, 1]], 'xcoord_integral_points': [-180, 140]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 0], '3': [0, 0], '5': 'a', '7': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '1050.c6'}
• ec_torsion_growth •

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

  
  
  • id: 51129
    {'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '1050.c6', 'torsion': [2, 8]}
  • id: 51131
    {'degree': 4, 'field': [9, 0, -1, 0, 1], 'lmfdb_label': '1050.c6', 'torsion': [2, 4]}
  • id: 51130
    {'degree': 4, 'field': [14, -14, 15, -2, 1], 'lmfdb_label': '1050.c6', 'torsion': [2, 4]}
  • id: 51135
    {'degree': 8, 'field': [-75, 0, -20, 0, 30, 0, 0, 0, 1], 'lmfdb_label': '1050.c6', 'torsion': [2, 6]}
  • id: 51133
    {'degree': 8, 'field': [-5, 180, -56, -224, 53, 68, -18, -4, 1], 'lmfdb_label': '1050.c6', 'torsion': [2, 16]}
  • id: 51132
    {'degree': 8, 'field': [16, 0, -36, 0, 37, 0, -9, 0, 1], 'lmfdb_label': '1050.c6', 'torsion': [4, 8]}
  • id: 51134
    {'degree': 8, 'field': [16, 0, 24, 0, 32, 0, 6, 0, 1], 'lmfdb_label': '1050.c6', 'torsion': [2, 16]}
  • id: 51137
    {'degree': 16, 'field': [81, 0, 232, 0, 1193, 0, -496, 0, 1536, 0, 240, 0, 89, 0, 8, 0, 1], 'lmfdb_label': '1050.c6', 'torsion': [2, 8]}
  • id: 51136
    {'degree': 16, 'field': [256, 0, -576, 0, 1953, 0, -2100, 0, 1120, 0, -252, 0, 0, 0, 12, 0, 1], 'lmfdb_label': '1050.c6', 'torsion': [2, 8]}
  • id: 51138
    {'degree': 16, 'field': [320, 440, -1095, 1200, -150, -990, 931, -128, -645, 730, -377, 48, 83, -70, 30, -8, 1], 'lmfdb_label': '1050.c6', 'torsion': [2, 24]}
• 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: 14728
    {'conductor': 1050, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '1050.c6', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 14729
    {'conductor': 1050, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '1050.c6', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 14730
    {'conductor': 1050, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '1050.c6', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
  • id: 14731
    {'conductor': 1050, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '1050.c6', 'prime': 7, '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: 1671161
    {'adelic_gens': [[15, 16, 74, 289], [327, 1664, 604, 1559], [1121, 8, 0, 1], [1, 16, 0, 1], [13, 8, 320, 617], [241, 16, 1446, 97], [1, 0, 16, 1], [1, 16, 4, 65], [1665, 16, 1664, 17]], 'adelic_image': '1680.768.13.?', 'conductor': 1050, 'lmfdb_label': '1050.c6', 'prime': 0}
  • id: 4942
    {'conductor': 1050, 'elladic_image': '16.96.0.44', 'lmfdb_label': '1050.c6', 'modell_image': '2Cs', 'prime': 2}
• lmfdb_iso 1050.c does not appear in ec_padic