Modular curve data - 232.96.0-8.c.1.6

Formats: - HTML - YAML - JSON - 2024-06-02T06:52:37.429911

• 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': '8N0', 'Glabel': None, 'RSZBlabel': None, 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 29], 'canonical_conjugator': [1, 0, 0, 1], 'canonical_generators': [[1, 0, 0, 59], [1, 0, 8, 1], [1, 0, 116, 1], [1, 8, 0, 1], [9, 8, 224, 225], [57, 0, 0, 115], [143, 0, 0, 231], [175, 116, 116, 175], [231, 0, 0, 57], [231, 116, 0, 231]], 'cm_discriminants': [], 'coarse_class': '8.48.0.c', 'coarse_class_num': 3, 'coarse_index': 48, 'coarse_label': '8.48.0.c.1', 'coarse_level': 8, 'coarse_num': 1, 'conductor': None, 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[1, 4], [2, 3]], 'cusp_widths': [[4, 8], [8, 2]], 'cusps': 10, 'determinant_label': '1.1.1', 'dims': None, 'factorization': [], 'fine_num': 6, 'generators': [[39, 104, 64, 125], [79, 116, 32, 161], [111, 180, 80, 139], [113, 216, 20, 99], [151, 144, 56, 33]], 'genus': 0, 'genus_minus_rank': None, 'has_obstruction': 0, 'index': 96, 'isogeny_orbits': [[2, 1, 3], [4, 1, 4], [4, 2, 1], [8, 2, 4], [8, 4, 1], [29, 30, 1], [58, 30, 3], [116, 30, 4], [116, 60, 1], [232, 60, 4], [232, 120, 1]], 'kummer_orbits': [[2, 1, 3], [4, 1, 4], [4, 2, 1], [8, 2, 4], [8, 4, 2], [8, 8, 1], [29, 420, 1], [58, 420, 3], [116, 840, 4], [116, 1680, 1], [232, 1680, 4], [232, 3360, 2], [232, 6720, 1]], 'label': '232.96.0-8.c.1.6', 'lattice_labels': None, 'lattice_x': None, 'level': 232, 'level_is_squarefree': False, 'level_radical': 58, 'log_conductor': None, 'models': None, 'mults': None, 'name': None, 'newforms': None, 'nu2': 0, 'nu3': 0, 'num_bad_primes': 2, 'num_known_degree1_noncm_points': None, 'num_known_degree1_noncusp_points': None, 'num_known_degree1_points': None, 'obstructions': None, 'orbits': [[2, 1, 3], [4, 2, 4], [4, 4, 1], [8, 4, 4], [8, 8, 2], [8, 16, 1], [29, 840, 1], [58, 840, 3], [116, 1680, 4], [116, 3360, 1], [232, 3360, 4], [232, 6720, 2], [232, 13440, 1]], 'parents': ['232.48.0-4.b.1.4', '232.48.0-4.b.1.5', '232.48.0-8.e.1.4', '232.48.0-8.e.1.5', '232.48.0-8.e.1.12', '232.48.0-8.e.1.13'], 'parents_conj': None, 'pointless': False, 'power': None, 'psl2index': 48, 'psl2label': '8.48.0.a.1', 'psl2level': 8, 'q_gonality': 1, 'q_gonality_bounds': [1, 1], 'qbar_gonality': 1, 'qbar_gonality_bounds': [1, 1], 'rank': None, 'rational_cusps': 4, 'reductions': ['1.1.0.a.1', '2.6.0.a.1', '2.6.0.a.1', '4.24.0.b.1', '4.24.0.b.1', '8.48.0.c.1'], 'scalar_label': '8.4.1', 'simple': None, 'sl2label': '8.48.0.a.1', 'sl2level': 8, 'squarefree': None, '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': '8N0', 'Glabel': '32.51', 'RSZBlabel': '8.48.0.45', 'RZBlabel': 'X189', 'SZlabel': '8N0-8f', 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2], 'canonical_conjugator': [1, 0, 0, 1], 'canonical_generators': [[1, 0, 0, 3], [1, 0, 0, 7], [1, 0, 4, 1], [1, 4, 0, 1], [7, 0, 0, 5], [7, 4, 4, 7]], 'cm_discriminants': [], 'coarse_class': '8.48.0.c', 'coarse_class_num': 3, 'coarse_index': 48, 'coarse_label': '8.48.0.c.1', 'coarse_level': 8, 'coarse_num': 1, 'conductor': None, 'contains_negative_one': True, 'curve_label': None, 'cusp_orbits': [[1, 4], [2, 3]], 'cusp_widths': [[4, 8], [8, 2]], 'cusps': 10, 'determinant_label': '1.1.1', 'dims': None, 'factorization': [], 'fine_num': 0, 'generators': [[1, 0, 4, 1], [1, 4, 0, 1], [7, 4, 0, 1], [7, 4, 0, 3], [7, 4, 4, 7]], 'genus': 0, 'genus_minus_rank': 0, 'has_obstruction': -1, 'index': 48, 'isogeny_orbits': [[2, 1, 3], [4, 1, 4], [4, 2, 1], [8, 2, 4], [8, 4, 1]], 'kummer_orbits': [[2, 1, 3], [4, 1, 4], [4, 2, 1], [8, 2, 4], [8, 4, 2], [8, 8, 1]], 'label': '8.48.0.c.1', 'lattice_labels': ['1.1.0.a.1', '2.2.0.a.1', '2.3.0.a.1', '2.6.0.a.1', '4.6.0.b.1', '4.6.0.c.1', '4.6.0.d.1', '4.6.0.e.1', '4.12.0.a.1', '4.12.0.b.1', '4.12.0.f.1', '4.24.0.b.1', '8.24.0.e.1', '8.24.0.e.2', '8.48.0.c.1'], 'lattice_x': [5838, 7056, 4619, 6827, 4848, 2767, 685, 8807, 6472, 3350, 8807, 6472, 2462, 4289, 4289], 'level': 8, 'level_is_squarefree': False, 'level_radical': 2, 'log_conductor': None, 'models': 1, 'mults': None, 'name': None, 'newforms': [], 'nu2': 0, 'nu3': 0, 'num_bad_primes': 1, 'num_known_degree1_noncm_points': 6, 'num_known_degree1_noncusp_points': 6, 'num_known_degree1_points': 7, 'obstructions': [], 'orbits': [[2, 1, 3], [4, 2, 4], [4, 4, 1], [8, 4, 4], [8, 8, 2], [8, 16, 1]], 'parents': ['4.24.0.b.1', '8.24.0.e.1', '8.24.0.e.2'], 'parents_conj': [[1, 0, 0, 1], [0, 3, 7, 0], [1, 0, 0, 1]], 'pointless': False, 'power': None, 'psl2index': 48, 'psl2label': '8.48.0.a.1', 'psl2level': 8, 'q_gonality': 1, 'q_gonality_bounds': [1, 1], 'qbar_gonality': 1, 'qbar_gonality_bounds': [1, 1], 'rank': 0, 'rational_cusps': 4, 'reductions': ['2.6.0.a.1', '4.24.0.b.1'], 'scalar_label': '8.2.2', 'simple': None, 'sl2label': '8.48.0.a.1', 'sl2level': 8, 'squarefree': None, 'trace_hash': 0, 'traces': []}
• modcurve 8.48.0.c.1 does not appear in modcurve_models
• 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': ['x^48*(x^8-4*x^7*y+4*x^6*y^2+28*x^5*y^3+6*x^4*y^4-28*x^3*y^5+4*x^2*y^6+4*x*y^7+y^8)^3*(x^8+4*x^7*y+4*x^6*y^2-28*x^5*y^3+6*x^4*y^4+28*x^3*y^5+4*x^2*y^6-4*x*y^7+y^8)^3', 'y^4*x^52*(x-y)^4*(x+y)^4*(x^2+y^2)^8*(x^2-2*x*y-y^2)^4*(x^2+2*x*y-y^2)^4'], 'degree': 48, 'domain_label': '8.48.0.c.1', 'domain_model_type': 1, 'dont_display': False, 'factored': True, 'leading_coefficients': None, '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: 1848091
    {'Elabel': None, 'ainvs': None, 'cardinality': 4, 'cm': 0, 'conductor_norm': None, 'coordinates': {'1': ['-1:1', '0:1', '1:1', '1:0']}, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '8.48.0.c.1', 'curve_level': 8, '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: 3970
    {'Elabel': '210.e5', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 210, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '8.48.0.c.1', 'curve_level': 8, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 38.4015198375872, 'jinv': '47595748626367201/1215506250000', 'jorig': '47595748626367201/1215506250000', 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
  • id: 208846
    {'Elabel': '46410.ck5', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 46410, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '8.48.0.c.1', 'curve_level': 8, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 60.6958083852378, 'jinv': '229010110533436633465952161/132501160769452503210000', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
  • id: 320220
    {'Elabel': '82110.bs4', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 82110, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '8.48.0.c.1', 'curve_level': 8, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 67.2745948422986, 'jinv': '164810665209657549410090824321/60743509039087274201760000', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
  • id: 401590
    {'Elabel': '110670.cm4', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 110670, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '8.48.0.c.1', 'curve_level': 8, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 76.5629502872005, 'jinv': '1781832302709884421209712638637121/585975791707934414062500000000', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
  • id: 743019
    {'Elabel': '249690.cj4', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 249690, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '8.48.0.c.1', 'curve_level': 8, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 80.8079782974004, 'jinv': '124296548246895698958145872007982881/2749138304449961117564010000', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
  • id: 782309
    {'Elabel': '266910.ck4', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 266910, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '8.48.0.c.1', 'curve_level': 8, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 88.6388811999355, 'jinv': '312879412318855009716463045818793383361/44626411898210828624928814208160000', 'jorig': '312879412318855009716463045818793383361/44626411898210828624928814208160000', 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}