Modular curve data - 56.768.49.nw.1

Formats: - HTML - YAML - JSON - 2024-06-03T09:27:02.407755

• gps_gl2zhat_fine •

  Column	Type
  CPlabel	text
  Glabel	text
  RSZBlabel	text
  RZBlabel	text
  SZlabel	text
  Slabel	text
  all_degree1_points_known	boolean
  bad_primes	integer[]
  canonical_conjugator	integer[]
  canonical_generators	integer[]
  cm_discriminants	integer[]
  coarse_class	text
  coarse_class_num	integer
  coarse_index	integer
  coarse_label	text
  coarse_level	integer
  coarse_num	integer
  conductor	integer[]
  contains_negative_one	boolean
  curve_label	text
  cusp_orbits	integer[]
  cusp_widths	integer[]
  cusps	integer
  determinant_label	text
  dims	integer[]
  factorization	text[]
  fine_num	integer
  generators	integer[]
  genus	integer
  genus_minus_rank	integer
  has_obstruction	smallint
  index	integer
  isogeny_orbits	integer[]
  kummer_orbits	integer[]
  label	text
  lattice_labels	text[]
  lattice_x	integer[]
  level	integer
  level_is_squarefree	boolean
  level_radical	integer
  log_conductor	numeric
  models	smallint
  mults	integer[]
  name	text
  newforms	text[]
  nu2	integer
  nu3	integer
  num_bad_primes	integer
  num_known_degree1_noncm_points	integer
  num_known_degree1_noncusp_points	integer
  num_known_degree1_points	integer
  obstructions	integer[]
  orbits	integer[]
  parents	text[]
  parents_conj	integer[]
  pointless	boolean
  power	boolean
  psl2index	integer
  psl2label	text
  psl2level	integer
  q_gonality	integer
  q_gonality_bounds	integer[]
  qbar_gonality	integer
  qbar_gonality_bounds	integer[]
  rank	integer
  rational_cusps	integer
  reductions	text[]
  scalar_label	text
  simple	boolean
  sl2label	text
  sl2level	integer
  squarefree	boolean
  trace_hash	bigint
  traces	integer[]

  
  {'CPlabel': None, 'Glabel': None, 'RSZBlabel': '56.768.49.157', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 7], 'canonical_conjugator': [35, 6, 50, 41], 'canonical_generators': [[1, 0, 4, 1], [3, 0, 2, 17], [5, 0, 2, 37], [11, 0, 2, 25], [11, 28, 2, 53], [15, 0, 4, 15], [17, 0, 4, 33], [41, 0, 4, 41]], 'cm_discriminants': [], 'coarse_class': '56.768.49.nw', 'coarse_class_num': 361, 'coarse_index': 768, 'coarse_label': '56.768.49.nw.1', 'coarse_level': 56, 'coarse_num': 1, 'conductor': [[2, 196], [7, 75]], 'contains_negative_one': True, 'curve_label': None, 'cusp_orbits': [[2, 8], [4, 4]], 'cusp_widths': [[4, 8], [8, 8], [28, 8], [56, 8]], 'cusps': 32, 'determinant_label': '1.1.1', 'dims': [1, 1, 1, 2, 4, 1, 1, 1, 2, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 2, 2, 1, 1, 1], 'factorization': [], 'fine_num': 0, 'generators': [[17, 0, 48, 39], [17, 20, 12, 11], [23, 32, 20, 7], [39, 40, 10, 41], [47, 52, 10, 5]], 'genus': 49, 'genus_minus_rank': 41, 'has_obstruction': 1, 'index': 768, 'isogeny_orbits': [[2, 1, 3], [4, 1, 2], [4, 2, 2], [7, 1, 1], [7, 7, 1], [8, 2, 2], [8, 4, 2], [14, 1, 3], [14, 7, 3], [28, 1, 2], [28, 2, 2], [28, 7, 2], [28, 14, 2], [56, 2, 2], [56, 4, 2], [56, 14, 2], [56, 28, 2]], 'kummer_orbits': [[2, 1, 3], [4, 1, 2], [4, 2, 2], [7, 3, 1], [7, 21, 1], [8, 2, 2], [8, 4, 3], [8, 8, 1], [14, 3, 3], [14, 21, 3], [28, 6, 2], [28, 12, 2], [28, 42, 2], [28, 84, 2], [56, 12, 2], [56, 24, 3], [56, 48, 1], [56, 84, 2], [56, 168, 3], [56, 336, 1]], 'label': '56.768.49.nw.1', 'lattice_labels': None, 'lattice_x': None, 'level': 56, 'level_is_squarefree': False, 'level_radical': 14, 'log_conductor': {'__RealLiteral__': 0, 'data': '281.80010856889777852868', 'prec': 80}, 'models': None, 'mults': [3, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1], 'name': None, 'newforms': ['14.2.a.a', '56.2.a.a', '56.2.a.b', '56.2.b.a', '56.2.b.b', '98.2.a.a', '392.2.a.b', '392.2.a.d', '392.2.b.b', '392.2.b.c', '448.2.a.a', '448.2.a.c', '448.2.a.d', '448.2.a.e', '448.2.a.g', '448.2.a.h', '784.2.a.b', '784.2.a.e', '784.2.a.i', '1568.2.b.a', '1568.2.b.d', '3136.2.a.bf', '3136.2.a.by', '3136.2.a.f', '3136.2.a.m', '3136.2.a.y'], 'nu2': 0, 'nu3': 0, 'num_bad_primes': 2, 'num_known_degree1_noncm_points': 0, 'num_known_degree1_noncusp_points': 0, 'num_known_degree1_points': 0, 'obstructions': [5, 13], 'orbits': [[2, 1, 3], [4, 2, 2], [4, 4, 2], [7, 6, 1], [7, 42, 1], [8, 4, 2], [8, 8, 3], [8, 16, 1], [14, 6, 3], [14, 42, 3], [28, 12, 2], [28, 24, 2], [28, 84, 2], [28, 168, 2], [56, 24, 2], [56, 48, 3], [56, 96, 1], [56, 168, 2], [56, 336, 3], [56, 672, 1]], 'parents': ['56.96.1.by.1', '56.384.23.x.1', '56.384.23.y.1', '56.384.23.df.1', '56.384.23.di.1', '56.384.25.eh.2', '56.384.25.ei.1', '56.384.25.ew.1'], 'parents_conj': [[21, 13, 38, 7], [1, 0, 0, 1], [37, 16, 51, 17], [31, 43, 33, 20], [25, 25, 23, 34], [1, 0, 0, 1], [37, 8, 23, 51], [37, 37, 31, 22]], 'pointless': True, 'power': False, 'psl2index': 768, 'psl2label': '56.768.49.c.1', 'psl2level': 56, 'q_gonality': None, 'q_gonality_bounds': [8, 16], 'qbar_gonality': None, 'qbar_gonality_bounds': [8, 16], 'rank': 8, 'rational_cusps': 0, 'reductions': ['2.6.0.a.1', '4.12.0.b.1', '7.8.0.a.1', '8.48.0.i.1', '14.48.2.a.1', '28.192.11.e.1'], 'scalar_label': '8.2.2', 'simple': False, 'sl2label': '56.768.49.c.1', 'sl2level': 56, 'squarefree': False, 'trace_hash': 2062534015337916962, 'traces': [-7, -4, 6, -1, -4, 14, 10, 12, -8, 6, -32, -18, 34, 28, -48, 30, -12, -2, -28, -72, 2, 64, -4, -46, -102, -26, -104, 12, -42, 82, 32, 76, -22, 52, -66, 120, 30, -44, 152, -146, -44, -138, 176, -222, -82, 56, 20, -224, 60, 38, -54, 112, -22, -44, 122, 88, 78, 80, 62, -134, -60, -154, -4, -56, -14, 6, 28, 306, -84, 158, -102, -344, -48, -34, -52, 96, 142, 14, -270, 82, 28, -50, 16, -214, -56, -4, -94, -214, 270, 192, -20, -160, 40, -84, -12, 328, -130, 66, -60, 230, 52, -202, 156, 26, 108, 58, -140, 138, -24, 210, 288, 46, -182, 52, -216, -414, 44, -40, 118, -124, -106, -382, 294, 12, -132, 166, -306, -112, 328, -98, 20, 72, -16, -2, -78, -134, -186, -84, 94, 394, 52, 30, 40, -100, -2, 216, 22, 18, -12, 208, 86, -150, 20, 8, 76, 144, 168, 218, 226, -18, 164, -614, -152, 4, 50, -376, -336, -26]}
• modcurve 56.768.49.nw.1 does not appear in modcurve_models
• domain_label 56.768.49.nw.1 does not appear in modcurve_modelmaps
• curve_label 56.768.49.nw.1 does not appear in modcurve_points