Modular curve data - 40.96.0-40.b.2.10

Formats: - HTML - YAML - JSON - 2024-05-15T22:14:03.554517

• 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': '40.96.0.200', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 5], 'canonical_conjugator': [12, 3, 15, 18], 'canonical_generators': [[1, 0, 8, 1], [1, 0, 20, 1], [1, 4, 32, 5], [1, 8, 0, 1], [1, 20, 0, 1], [9, 8, 32, 33], [9, 20, 20, 9], [37, 38, 4, 27], [39, 38, 16, 5], [39, 38, 36, 5]], 'cm_discriminants': [], 'coarse_class': '40.48.0.b', 'coarse_class_num': 2, 'coarse_index': 48, 'coarse_label': '40.48.0.b.2', 'coarse_level': 40, 'coarse_num': 2, 'conductor': None, 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[1, 2], [2, 2], [4, 1]], 'cusp_widths': [[4, 8], [8, 2]], 'cusps': 10, 'determinant_label': '1.1.1', 'dims': None, 'factorization': [], 'fine_num': 10, 'generators': [[1, 16, 14, 23], [7, 24, 32, 11], [31, 8, 12, 35], [37, 12, 28, 9], [37, 32, 20, 1]], 'genus': 0, 'genus_minus_rank': 0, 'has_obstruction': -1, 'index': 96, 'isogeny_orbits': [[2, 1, 3], [4, 1, 4], [4, 2, 1], [5, 6, 1], [8, 2, 4], [8, 4, 1], [10, 6, 3], [20, 6, 4], [20, 12, 1], [40, 12, 4], [40, 24, 1]], 'kummer_orbits': [[2, 1, 3], [4, 1, 4], [4, 2, 1], [5, 12, 1], [8, 4, 4], [8, 8, 1], [10, 12, 3], [20, 24, 4], [20, 48, 1], [40, 96, 4], [40, 192, 1]], 'label': '40.96.0-40.b.2.10', 'lattice_labels': None, 'lattice_x': None, 'level': 40, 'level_is_squarefree': False, 'level_radical': 10, 'log_conductor': None, 'models': None, 'mults': None, 'name': None, 'newforms': None, 'nu2': 0, 'nu3': 0, 'num_bad_primes': 2, 'num_known_degree1_noncm_points': 3, 'num_known_degree1_noncusp_points': 3, 'num_known_degree1_points': 4, 'obstructions': None, 'orbits': [[2, 1, 3], [4, 2, 4], [4, 4, 1], [5, 24, 1], [8, 4, 2], [8, 8, 3], [8, 16, 1], [10, 24, 3], [20, 48, 4], [20, 96, 1], [40, 96, 2], [40, 192, 3], [40, 384, 1]], 'parents': ['8.48.0-4.b.1.4', '40.48.0-4.b.1.1', '40.48.0-40.h.1.6', '40.48.0-40.h.1.19', '40.48.0-40.i.2.6', '40.48.0-40.i.2.25'], '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': 0, 'rational_cusps': 2, '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', '8.48.0-4.b.1.4'], 'scalar_label': '8.4.1', 'simple': None, 'sl2label': '8.96.0-8.a.1.1', 'sl2level': 8, 'squarefree': None, 'trace_hash': 0, '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': None, 'RSZBlabel': '40.48.0.44', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 5], 'canonical_conjugator': [32, 25, 25, 32], 'canonical_generators': [[1, 0, 8, 1], [1, 0, 20, 1], [1, 2, 4, 35], [1, 2, 24, 35], [1, 4, 32, 5], [1, 8, 0, 1], [1, 20, 0, 1], [3, 2, 36, 13], [9, 8, 32, 33], [31, 20, 20, 31]], 'cm_discriminants': [], 'coarse_class': '40.48.0.b', 'coarse_class_num': 2, 'coarse_index': 48, 'coarse_label': '40.48.0.b.2', 'coarse_level': 40, 'coarse_num': 2, 'conductor': None, 'contains_negative_one': True, 'curve_label': None, 'cusp_orbits': [[1, 2], [2, 2], [4, 1]], 'cusp_widths': [[4, 8], [8, 2]], 'cusps': 10, 'determinant_label': '1.1.1', 'dims': None, 'factorization': [], 'fine_num': 0, 'generators': [[9, 28, 0, 21], [19, 8, 0, 27], [29, 28, 2, 11], [31, 0, 38, 1], [35, 8, 14, 33], [37, 12, 6, 7]], 'genus': 0, 'genus_minus_rank': 0, 'has_obstruction': -1, 'index': 48, 'isogeny_orbits': [[2, 1, 3], [4, 1, 4], [4, 2, 1], [5, 6, 1], [8, 2, 4], [8, 4, 1], [10, 6, 3], [20, 6, 4], [20, 12, 1], [40, 12, 4], [40, 24, 1]], 'kummer_orbits': [[2, 1, 3], [4, 1, 4], [4, 2, 1], [5, 12, 1], [8, 4, 4], [8, 8, 1], [10, 12, 3], [20, 24, 4], [20, 48, 1], [40, 96, 4], [40, 192, 1]], 'label': '40.48.0.b.2', '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', '40.24.0.h.1', '40.24.0.i.2', '40.48.0.b.2'], 'lattice_x': [5838, 7056, 4619, 6827, 4848, 2767, 685, 8807, 6472, 3350, 8807, 6472, 4289, 2462, 4289], 'level': 40, 'level_is_squarefree': False, 'level_radical': 10, 'log_conductor': None, 'models': 1, 'mults': None, 'name': None, 'newforms': [], 'nu2': 0, 'nu3': 0, 'num_bad_primes': 2, 'num_known_degree1_noncm_points': 3, 'num_known_degree1_noncusp_points': 3, 'num_known_degree1_points': 4, 'obstructions': [], 'orbits': [[2, 1, 3], [4, 2, 4], [4, 4, 1], [5, 24, 1], [8, 8, 4], [8, 16, 1], [10, 24, 3], [20, 48, 4], [20, 96, 1], [40, 192, 4], [40, 384, 1]], 'parents': ['4.24.0.b.1', '40.24.0.h.1', '40.24.0.i.2'], 'parents_conj': [[12, 37, 9, 1], [33, 14, 36, 9], [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': 2, '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', '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 40.48.0.b.2 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+y)^48*(64*x^8+1280*x^7*y+11040*x^6*y^2+53600*x^5*y^3+160200*x^4*y^4+302000*x^3*y^5+351500*x^2*y^6+232500*x*y^7+68125*y^8)^3*(64*x^8+1280*x^7*y+11360*x^6*y^2+58400*x^5*y^3+190200*x^4*y^4+402000*x^3*y^5+538500*x^2*y^6+417500*x*y^7+143125*y^8)^3', 'y^8*(x+y)^48*(2*x+5*y)^8*(x^2+5*x*y+5*y^2)^4*(2*x^2+10*x*y+15*y^2)^4*(8*x^4+80*x^3*y+300*x^2*y^2+500*x*y^3+325*y^4)^4'], 'degree': 48, 'domain_label': '40.48.0.b.2', 'domain_model_type': 1, 'dont_display': False, 'factored': True, 'leading_coefficients': ['1', '5^4'], '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: 1848494
    {'Elabel': None, 'ainvs': None, 'cardinality': 2, 'cm': 0, 'conductor_norm': None, 'coordinates': {'1': ['-5/2:1', '-1:1']}, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '40.48.0.b.2', 'curve_level': 40, '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: 3411
    {'Elabel': '195.a4', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 195, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '40.48.0.b.2', 'curve_level': 40, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 30.3752096573502, 'jinv': '15551989015681/1445900625', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
  • id: 13663
    {'Elabel': '1230.f4', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 1230, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '40.48.0.b.2', 'curve_level': 40, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 44.4220184019965, 'jinv': '19599160390581221281/185398179210000', 'jorig': '19599160390581221281/185398179210000', 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
  • id: 42703
    {'Elabel': '5565.b3', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 5565, 'coordinates': None, 'curve_genus': 0, 'curve_index': 48, 'curve_label': '40.48.0.b.2', 'curve_level': 40, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 46.9695521652557, 'jinv': '250390197566955663841/77686524665150625', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}