Modular curve data - 120.96.1-24.bi.2.3

Formats: - HTML - YAML - JSON - 2024-06-11T04:16:43.514229

• 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': '8G1', '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': [[1, 0, 24, 1], [1, 0, 80, 1], [1, 24, 0, 1], [1, 50, 0, 61], [1, 50, 40, 21], [1, 80, 0, 1], [1, 90, 60, 1], [19, 70, 80, 19], [23, 0, 0, 119], [25, 24, 96, 97], [81, 80, 40, 41], [89, 30, 60, 89], [119, 20, 80, 69]], 'cm_discriminants': [], 'coarse_class': '24.48.1.bi', 'coarse_class_num': 35, 'coarse_index': 48, 'coarse_label': '24.48.1.bi.2', 'coarse_level': 24, 'coarse_num': 2, 'conductor': None, 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[1, 2], [2, 3]], 'cusp_widths': [[4, 4], [8, 4]], 'cusps': 8, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': [], 'fine_num': 3, 'generators': [[21, 62, 80, 77], [45, 76, 104, 91], [47, 46, 76, 79], [55, 62, 48, 113], [113, 116, 72, 43]], 'genus': 1, 'genus_minus_rank': None, 'has_obstruction': 0, 'index': 96, 'isogeny_orbits': [[2, 1, 3], [3, 4, 1], [4, 1, 2], [4, 2, 2], [5, 6, 1], [6, 4, 3], [8, 2, 2], [8, 4, 2], [10, 6, 3], [12, 4, 2], [12, 8, 2], [15, 24, 1], [20, 6, 2], [20, 12, 2], [24, 8, 2], [24, 16, 2], [30, 24, 3], [40, 12, 2], [40, 24, 2], [60, 24, 2], [60, 48, 2], [120, 48, 2], [120, 96, 2]], 'kummer_orbits': [[2, 1, 3], [3, 4, 1], [4, 1, 2], [4, 2, 2], [5, 12, 1], [6, 4, 3], [8, 4, 4], [8, 8, 1], [10, 12, 3], [12, 8, 2], [12, 16, 2], [15, 96, 1], [20, 24, 2], [20, 48, 2], [24, 32, 4], [24, 64, 1], [30, 96, 3], [40, 96, 4], [40, 192, 1], [60, 192, 2], [60, 384, 2], [120, 768, 4], [120, 1536, 1]], 'label': '120.96.1-24.bi.2.3', '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, 3], [3, 8, 1], [4, 2, 2], [4, 4, 2], [5, 24, 1], [6, 8, 3], [8, 8, 4], [8, 16, 1], [10, 24, 3], [12, 16, 2], [12, 32, 2], [15, 192, 1], [20, 48, 2], [20, 96, 2], [24, 64, 4], [24, 128, 1], [30, 192, 3], [40, 192, 4], [40, 384, 1], [60, 384, 2], [60, 768, 2], [120, 1536, 4], [120, 3072, 1]], 'parents': ['40.48.0-8.e.1.5', '120.48.0-8.e.1.9', '120.48.0-24.h.2.6', '120.48.0-24.h.2.21', '120.48.1-24.d.1.11', '120.48.1-24.d.1.12'], 'parents_conj': None, 'pointless': False, 'power': True, 'psl2index': 48, 'psl2label': '8.48.1.b.1', 'psl2level': 8, 'q_gonality': 2, 'q_gonality_bounds': [2, 2], 'qbar_gonality': 2, 'qbar_gonality_bounds': [2, 2], 'rank': None, 'rational_cusps': 2, 'reductions': ['1.1.0.a.1', '1.1.0.a.1', '1.1.0.a.1', '2.6.0.a.1', '2.6.0.a.1', '2.6.0.a.1', '2.6.0.a.1', '4.12.0.b.1', '4.12.0.b.1', '4.12.0.b.1', '8.24.0.e.1', '24.48.1.bi.2', '40.48.0-8.e.1.5', '60.24.0-4.b.1.3'], 'scalar_label': '8.4.1', 'simple': True, 'sl2label': '8.48.1.b.1', 'sl2level': 8, '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': '8G1', 'Glabel': None, 'RSZBlabel': '24.48.1.117', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3], 'canonical_conjugator': [1, 0, 0, 1], 'canonical_generators': [[1, 0, 8, 1], [1, 2, 0, 13], [1, 2, 16, 21], [1, 4, 16, 3], [1, 8, 0, 1], [1, 18, 12, 1], [5, 2, 16, 5], [7, 18, 12, 7], [9, 8, 16, 17]], 'cm_discriminants': [], 'coarse_class': '24.48.1.bi', 'coarse_class_num': 35, 'coarse_index': 48, 'coarse_label': '24.48.1.bi.2', 'coarse_level': 24, 'coarse_num': 2, 'conductor': [[2, 6], [3, 2]], 'contains_negative_one': True, 'curve_label': '576.c2', 'cusp_orbits': [[1, 2], [2, 3]], 'cusp_widths': [[4, 4], [8, 4]], 'cusps': 8, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': [], 'fine_num': 0, 'generators': [[3, 22, 16, 11], [7, 22, 0, 19], [7, 22, 20, 15], [11, 8, 12, 19], [21, 22, 20, 11]], 'genus': 1, 'genus_minus_rank': 0, 'has_obstruction': -1, 'index': 48, 'isogeny_orbits': [[2, 1, 3], [3, 4, 1], [4, 1, 2], [4, 2, 2], [6, 4, 3], [8, 2, 2], [8, 4, 2], [12, 4, 2], [12, 8, 2], [24, 8, 2], [24, 16, 2]], 'kummer_orbits': [[2, 1, 3], [3, 4, 1], [4, 1, 2], [4, 2, 2], [6, 4, 3], [8, 4, 4], [8, 8, 1], [12, 8, 2], [12, 16, 2], [24, 32, 4], [24, 64, 1]], 'label': '24.48.1.bi.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.c.1', '4.6.0.d.1', '4.12.0.b.1', '8.24.0.e.1', '24.12.0.bz.1', '24.12.1.bw.1', '24.24.0.h.2', '24.24.1.d.1', '24.48.1.bi.2'], 'lattice_x': [2834, 1306, 4363, 1433, 4236, 6847, 3662, 4554, 6847, 9140, 2261, 6847, 4554], 'level': 24, 'level_is_squarefree': False, 'level_radical': 6, 'log_conductor': {'__RealLiteral__': 0, 'data': '6.35610766069589123929', 'prec': 74}, 'models': 1, 'mults': [1], 'name': None, 'newforms': ['576.2.a.c'], 'nu2': 0, 'nu3': 0, 'num_bad_primes': 2, 'num_known_degree1_noncm_points': 2, 'num_known_degree1_noncusp_points': 2, 'num_known_degree1_points': 3, 'obstructions': [], 'orbits': [[2, 1, 3], [3, 8, 1], [4, 2, 2], [4, 4, 2], [6, 8, 3], [8, 8, 4], [8, 16, 1], [12, 16, 2], [12, 32, 2], [24, 64, 4], [24, 128, 1]], 'parents': ['8.24.0.e.1', '24.24.0.h.2', '24.24.1.d.1'], 'parents_conj': [[23, 15, 22, 1], [17, 11, 22, 11], [1, 0, 0, 1]], 'pointless': False, 'power': True, 'psl2index': 48, 'psl2label': '8.48.1.b.1', 'psl2level': 8, 'q_gonality': 2, 'q_gonality_bounds': [2, 2], 'qbar_gonality': 2, 'qbar_gonality_bounds': [2, 2], 'rank': 1, 'rational_cusps': 2, 'reductions': ['1.1.0.a.1', '2.6.0.a.1', '2.6.0.a.1', '4.12.0.b.1', '4.12.0.b.1', '8.24.0.e.1'], 'scalar_label': '8.2.2', 'simple': True, 'sl2label': '8.48.1.b.1', 'sl2level': 8, 'squarefree': True, 'trace_hash': 1086616701052248176, 'traces': [0, 0, -2, 0, 0, -6, -2, 0, 0, -10, 0, 2, -10, 0, 0, 14, 0, 10, 0, 0, -6, 0, 0, -10, 18, -2, 0, 0, -6, 14, 0, 0, 22, 0, 14, 0, -22, 0, 0, -26, 0, 18, 0, -14, -2, 0, 0, 0, 0, -30, -26, 0, -30, 0, -2, 0, -26, 0, 18, -10, 0, -34, 0, 0, 26, 22, 0, 18, 0, 10, -34, 0, 0, -14, 0, 0, -34, -38, -2, -6, 0, -30, 0, 34, 0, 0, 14, 42, 38, 0, 0, 0, 0, 0, 0, 0, -10, 22, 0, 42, 0, 38, 0, -26, 0, 2, 0, 46, 0, 10, 0, 34, 38, 0, 0, -50, 0, 0, -26, 0, 50, -46, -2, 0, 0, -10, -30, 0, 0, -54, 0, 0, 0, 18, 38, 50, -34, 0, 22, -10, 0, -50, 0, 0, -54, 0, -46, -58, 0, 0, 58, -50, 0, 0, 0, 0, 0, 46, -38, -58, 0, -26, 0, 0, 62, 0, 0, -62]}
• 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-396*x*z^2+3024*z^3'], 'modcurve': '24.48.1.bi.2', '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': ['144*x^2*y^14-550522656*x^2*y^12*z^2+283165527573504*x^2*y^10*z^4-35589093251396649984*x^2*y^8*z^6+1435852678252338286166016*x^2*y^6*z^8-23600740106397378551611981824*x^2*y^4*z^10+166825072115401190726981684035584*x^2*y^2*z^12-421596930836809960564255254978232320*x^2*z^14-37296*x*y^14*z+51202720512*x*y^12*z^3-17060703549398784*x*y^10*z^5+1487230108714945769472*x*y^8*z^7-47478377603511577592856576*x*y^6*z^9+665298645524533817351278166016*x*y^4*z^11-4187262207135015339241996903514112*x*y^2*z^13+9684318754352320554987748010250731520*x*z^15-y^16+4344192*y^14*z^2-4058589950208*y^12*z^4+792268224762138624*y^10*z^6-43843111579283454738432*y^8*z^8+944128051414930556653142016*y^6*z^10-9065075431123430510805612232704*y^4*z^12+38280102371311259261797843561611264*y^2*z^14-55501867011727212343338600744464941056*z^16', 'z*y^4*(10332*x^2*y^8*z-519436800*x^2*y^6*z^3+3852738452736*x^2*y^4*z^5-1451188224*x^2*y^2*z^7+78364164096*x^2*z^9+x*y^10-516240*x*y^8*z^2+15177570048*x*y^6*z^4-88499423895552*x*y^4*z^6-15237476352*x*y^2*z^8+940369969152*x*z^10-144*y^10*z+16907616*y^8*z^3-217503553536*y^6*z^5+507198870484992*y^4*z^7+417942208512*y^2*z^9-19747769352192*z^11)'], 'degree': 48, 'domain_label': '24.48.1.bi.2', 'domain_model_type': 5, 'dont_display': False, 'factored': True, 'leading_coefficients': ['-1', '2^2*3^2'], '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: 1720213
    {'Elabel': None, 'ainvs': None, 'cardinality': 2, 'cm': 0, 'conductor_norm': None, 'coordinates': {'5': ['12:0:1', '0:1:0']}, 'curve_genus': 1, 'curve_index': 48, 'curve_label': '24.48.1.bi.2', 'curve_level': 24, '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: 1720214
    {'Elabel': None, 'ainvs': None, 'cardinality': 1, 'cm': 0, 'conductor_norm': None, 'coordinates': {'5': ['18,0:0,-24:1,0']}, 'curve_genus': 1, 'curve_index': 48, 'curve_label': '24.48.1.bi.2', 'curve_level': 24, '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': '2.2.12.1', 'upload_id': None}
  • id: 1720215
    {'Elabel': None, 'ainvs': None, 'cardinality': 1, 'cm': 0, 'conductor_norm': None, 'coordinates': {'5': ['6,0:0,12:1,0']}, 'curve_genus': 1, 'curve_index': 48, 'curve_label': '24.48.1.bi.2', 'curve_level': 24, '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': '2.2.24.1', 'upload_id': None}
  • id: 1720216
    {'Elabel': None, 'ainvs': None, 'cardinality': 1, 'cm': 0, 'conductor_norm': None, 'coordinates': {'5': ['-6,-12:0,0:1,0']}, 'curve_genus': 1, 'curve_index': 48, 'curve_label': '24.48.1.bi.2', 'curve_level': 24, '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': '2.2.8.1', 'upload_id': None}
  • id: 764
    {'Elabel': '24.a4', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 24, 'coordinates': {'5': ['-6:-72:1', '-6:72:1', '10:-8:1', '10:8:1']}, 'curve_genus': 1, 'curve_index': 48, 'curve_label': '24.48.1.bi.2', 'curve_level': 24, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': 2, 'j_field': '1.1.1.1', 'j_height': 10.4674367946244, 'jinv': '35152/9', 'jorig': '35152/9', 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
  • id: 3895
    {'Elabel': '210.e2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 210, 'coordinates': {'5': ['16:-28:1', '16:28:1', '21:-63:1', '21:63:1']}, 'curve_genus': 1, 'curve_index': 48, 'curve_label': '24.48.1.bi.2', 'curve_level': 24, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': 2, 'j_field': '1.1.1.1', 'j_height': 46.7005943582882, 'jinv': '191342053882402567201/129708022500', 'jorig': '191342053882402567201/129708022500', 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}