Modular curve data - 120.36.1-12.b.1.16

Formats: - HTML - YAML - JSON - 2024-05-24T21:52:58.541407

• 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': '12B1', 'Glabel': None, 'RSZBlabel': None, 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3, 5], 'canonical_conjugator': [1, 0, 0, 1], 'canonical_generators': [[13, 12, 108, 109], [23, 0, 0, 119], [24, 95, 95, 14], [59, 0, 0, 119], [69, 110, 110, 89], [94, 95, 65, 44], [94, 115, 85, 44], [96, 5, 55, 6], [96, 25, 35, 6], [96, 25, 55, 106], [96, 55, 5, 6], [119, 0, 108, 119], [119, 108, 0, 119]], 'cm_discriminants': [], 'coarse_class': '12.18.1.b', 'coarse_class_num': 2, 'coarse_index': 18, 'coarse_label': '12.18.1.b.1', 'coarse_level': 12, 'coarse_num': 1, 'conductor': None, 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[1, 1], [2, 1]], 'cusp_widths': [[3, 2], [12, 1]], 'cusps': 3, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': ['3.3.0.a.1', '40.12.0-4.b.1.3'], 'fine_num': 16, 'generators': [[13, 58, 10, 71], [30, 17, 89, 80], [31, 94, 70, 17], [73, 40, 108, 83], [119, 36, 96, 65], [119, 106, 106, 57]], 'genus': 1, 'genus_minus_rank': None, 'has_obstruction': 0, 'index': 36, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [3, 4, 1], [4, 2, 1], [4, 4, 1], [5, 6, 1], [6, 4, 1], [6, 8, 1], [8, 4, 1], [8, 8, 1], [10, 6, 1], [10, 12, 1], [12, 8, 1], [12, 16, 1], [15, 24, 1], [20, 12, 1], [20, 24, 1], [24, 16, 1], [24, 32, 1], [30, 24, 1], [30, 48, 1], [40, 24, 1], [40, 48, 1], [60, 48, 1], [60, 96, 1], [120, 96, 1], [120, 192, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [3, 4, 1], [4, 2, 1], [4, 4, 1], [5, 12, 1], [6, 4, 1], [6, 8, 1], [8, 8, 1], [8, 16, 1], [10, 12, 1], [10, 24, 1], [12, 16, 1], [12, 32, 1], [15, 96, 1], [20, 48, 1], [20, 96, 1], [24, 64, 1], [24, 128, 1], [30, 96, 1], [30, 192, 1], [40, 192, 1], [40, 384, 1], [60, 384, 1], [60, 768, 1], [120, 1536, 1], [120, 3072, 1]], 'label': '120.36.1-12.b.1.16', 'lattice_labels': None, 'lattice_x': None, 'level': 120, 'level_is_squarefree': False, 'level_radical': 30, 'log_conductor': None, 'models': None, 'mults': [1], 'name': None, 'newforms': None, 'nu2': 0, 'nu3': 0, 'num_bad_primes': 3, 'num_known_degree1_noncm_points': None, 'num_known_degree1_noncusp_points': None, 'num_known_degree1_points': None, 'obstructions': None, 'orbits': [[2, 1, 1], [2, 2, 1], [3, 8, 1], [4, 4, 1], [4, 8, 1], [5, 24, 1], [6, 8, 1], [6, 16, 1], [8, 16, 1], [8, 32, 1], [10, 24, 1], [10, 48, 1], [12, 32, 1], [12, 64, 1], [15, 192, 1], [20, 96, 1], [20, 192, 1], [24, 128, 1], [24, 256, 1], [30, 192, 1], [30, 384, 1], [40, 384, 1], [40, 768, 1], [60, 768, 1], [60, 1536, 1], [120, 3072, 1], [120, 6144, 1]], 'parents': ['40.12.0-4.b.1.3'], 'parents_conj': None, 'pointless': False, 'power': True, 'psl2index': 18, 'psl2label': '12.18.1.a.1', 'psl2level': 12, 'q_gonality': 2, 'q_gonality_bounds': [2, 2], 'qbar_gonality': 2, 'qbar_gonality_bounds': [2, 2], 'rank': None, 'rational_cusps': 1, 'reductions': ['1.1.0.a.1', '2.3.0.a.1', '2.3.0.a.1', '3.3.0.a.1', '3.3.0.a.1', '4.6.0.b.1', '4.6.0.b.1', '4.6.0.b.1', '6.9.0.a.1', '6.9.0.a.1', '12.18.1.b.1', '12.18.1.b.1', '12.18.1.b.1', '40.12.0-4.b.1.3'], 'scalar_label': '4.2.1', 'simple': True, 'sl2label': '12.18.1.a.1', 'sl2level': 24, 'squarefree': True, 'trace_hash': None, 'traces': None}
• 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': '12B1', 'Glabel': '256.15435', 'RSZBlabel': '12.18.1.2', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3], 'canonical_conjugator': [7, 0, 11, 11], 'canonical_generators': [[0, 1, 1, 10], [0, 1, 7, 10], [0, 1, 11, 6], [0, 5, 7, 6], [0, 7, 5, 6], [2, 1, 7, 4], [2, 5, 11, 4], [3, 10, 10, 7]], 'cm_discriminants': [-4], 'coarse_class': '12.18.1.b', 'coarse_class_num': 2, 'coarse_index': 18, 'coarse_label': '12.18.1.b.1', 'coarse_level': 12, 'coarse_num': 1, 'conductor': [[2, 4], [3, 2]], 'contains_negative_one': True, 'curve_label': '144.a3', 'cusp_orbits': [[1, 1], [2, 1]], 'cusp_widths': [[3, 2], [12, 1]], 'cusps': 3, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': ['3.3.0.a.1', '4.6.0.b.1'], 'fine_num': 0, 'generators': [[1, 5, 10, 1], [3, 1, 10, 3], [5, 4, 8, 5], [11, 11, 4, 11]], 'genus': 1, 'genus_minus_rank': 1, 'has_obstruction': -1, 'index': 18, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [3, 4, 1], [4, 2, 1], [4, 4, 1], [6, 4, 1], [6, 8, 1], [12, 8, 1], [12, 16, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [3, 4, 1], [4, 2, 1], [4, 4, 1], [6, 4, 1], [6, 8, 1], [12, 16, 1], [12, 32, 1]], 'label': '12.18.1.b.1', 'lattice_labels': ['1.1.0.a.1', '2.3.0.a.1', '3.3.0.a.1', '4.6.0.b.1', '6.9.0.a.1', '12.18.1.b.1'], 'lattice_x': [5269, 8011, 2527, 8011, 4140, 6075], 'level': 12, 'level_is_squarefree': False, 'level_radical': 6, 'log_conductor': {'__RealLiteral__': 0, 'data': '4.96981329957600062046', 'prec': 74}, 'models': 1, 'mults': [1], 'name': None, 'newforms': ['144.2.a.a'], 'nu2': 0, 'nu3': 0, 'num_bad_primes': 2, 'num_known_degree1_noncm_points': 0, 'num_known_degree1_noncusp_points': 1, 'num_known_degree1_points': 2, 'obstructions': [], 'orbits': [[2, 1, 1], [2, 2, 1], [3, 8, 1], [4, 4, 1], [4, 8, 1], [6, 8, 1], [6, 16, 1], [12, 32, 1], [12, 64, 1]], 'parents': ['4.6.0.b.1', '6.9.0.a.1'], 'parents_conj': [[1, 0, 0, 1], [1, 0, 0, 1]], 'pointless': False, 'power': True, 'psl2index': 18, 'psl2label': '12.18.1.a.1', 'psl2level': 12, 'q_gonality': 2, 'q_gonality_bounds': [2, 2], 'qbar_gonality': 2, 'qbar_gonality_bounds': [2, 2], 'rank': 0, 'rational_cusps': 1, 'reductions': ['2.3.0.a.1', '3.3.0.a.1', '4.6.0.b.1', '6.9.0.a.1'], 'scalar_label': '1.1.1', 'simple': True, 'sl2label': '12.18.1.a.1', 'sl2level': 12, 'squarefree': True, 'trace_hash': 497432316503275046, 'traces': [0, 0, 0, 4, 0, 2, 0, -8, 0, 0, 4, -10, 0, -8, 0, 0, 0, 14, 16, 0, -10, 4, 0, 0, 14, 0, -20, 0, 2, 0, -20, 0, 0, 16, 0, 4, 14, -8, 0, 0, 0, 26, 0, 2, 0, 28, 16, 28, 0, -22, 0, 0, 14, 0, 0, 0, 0, 28, 26, 0, -32, 0, 16, 0, -22, 0, -32, -34, 0, 14, 0, 0, 4, 38, -8, 0, 0, -34, 0, 38, 0, -22, 0, 2, 28, 0, 0, -10, 0, -20, 0, 0, -44, 0, -32, 0, 0, 0, -8, -46, 40, 0, 0, 0, 16, -46, 0, 0, 0, 26, -20, -10, 0, -32, -44, 0, 40, 0, 0, 0, 38, 50, 0, 0, -8, 0, -22, 0, -44, 50, 16, 0, 52, 26, 0, 2, 0, -56, 0, 0, -56, 0, 52, 0, -46, 0, -58, 0, -56, 0, -34, 0, -8, 0, 40, 0, 52, 0, 26, 0, 0, 0, -20, 0, 0, 0, -44, -10]}
• modcurve_models •

  Column	Type
  dont_display	boolean
  equation	text[]
  modcurve	text
  model_type	smallint
  number_variables	smallint
  smooth	boolean
  upload_id	bigint

  
  {'dont_display': False, 'equation': ['x^3-y^2*z-z^3'], 'modcurve': '12.18.1.b.1', 'model_type': 5, 'number_variables': 3, 'smooth': True, 'upload_id': None}
• modcurve_modelmaps •

  Column	Type
  codomain_label	text
  codomain_model_type	smallint
  coordinates	text[]
  degree	integer
  domain_label	text
  domain_model_type	smallint
  dont_display	boolean
  factored	boolean
  leading_coefficients	text[]
  upload_id	bigint

  
  {'codomain_label': '1.1.0.a.1', 'codomain_model_type': 1, 'coordinates': ['(4*y^2+3*z^2)^3', 'z^4*(y^2+z^2)'], 'degree': 18, 'domain_label': '12.18.1.b.1', 'domain_model_type': 5, 'dont_display': False, 'factored': True, 'leading_coefficients': ['2^6', '1'], 'upload_id': None}
• modcurve_points •

  Column	Type
  Elabel	text
  ainvs	text
  cardinality	integer
  cm	smallint
  conductor_norm	numeric
  coordinates	jsonb
  curve_genus	integer
  curve_index	integer
  curve_label	text
  curve_level	integer
  curve_name	text
  cusp	boolean
  degree	smallint
  isolated	smallint
  j_field	text
  j_height	double precision
  jinv	text
  jorig	text
  quo_info	smallint[]
  residue_field	text
  upload_id	bigint

  
  
  • id: 1157
    {'Elabel': '32.a3', 'ainvs': None, 'cardinality': None, 'cm': -4, 'conductor_norm': 32, 'coordinates': {'5': ['1:0:1']}, 'curve_genus': 1, 'curve_index': 18, 'curve_label': '12.18.1.b.1', 'curve_level': 12, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': 4, 'j_field': '1.1.1.1', 'j_height': 7.454719949364, 'jinv': '1728', 'jorig': '1728', 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
  • id: 1658631
    {'Elabel': None, 'ainvs': None, 'cardinality': 1, 'cm': 0, 'conductor_norm': None, 'coordinates': {'5': ['0:1:0']}, 'curve_genus': 1, 'curve_index': 18, 'curve_label': '12.18.1.b.1', 'curve_level': 12, 'curve_name': None, 'cusp': True, 'degree': 1, 'isolated': None, 'j_field': '1.1.1.1', 'j_height': 0.0, 'jinv': None, 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
  • id: 1658953
    {'Elabel': None, 'ainvs': None, 'cardinality': 1, 'cm': 0, 'conductor_norm': None, 'coordinates': {'5': ['0,0:0,-1:1,0']}, 'curve_genus': 1, 'curve_index': 18, 'curve_label': '12.18.1.b.1', 'curve_level': 12, 'curve_name': None, 'cusp': True, 'degree': 2, 'isolated': None, 'j_field': '1.1.1.1', 'j_height': 0.0, 'jinv': None, 'jorig': None, 'quo_info': None, 'residue_field': '2.0.4.1', 'upload_id': None}