Modular curve data - 312.48.0-24.bk.1.1

Formats: - HTML - YAML - JSON - 2024-06-11T13:03:53.427585

• 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': '8G0', 'Glabel': None, 'RSZBlabel': None, 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3, 13], 'canonical_conjugator': [1, 0, 0, 1], 'canonical_generators': [[1, 0, 24, 1], [1, 0, 104, 1], [1, 0, 169, 209], [1, 0, 169, 235], [1, 0, 234, 1], [1, 24, 0, 1], [1, 52, 221, 27], [1, 104, 0, 1], [1, 104, 169, 27], [25, 24, 288, 289], [77, 0, 78, 77], [105, 104, 208, 209], [157, 0, 234, 157], [167, 0, 0, 311]], 'cm_discriminants': [], 'coarse_class': '24.24.0.bk', 'coarse_class_num': 37, 'coarse_index': 24, 'coarse_label': '24.24.0.bk.1', 'coarse_level': 24, 'coarse_num': 1, 'conductor': None, 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[2, 3]], 'cusp_widths': [[2, 4], [8, 2]], 'cusps': 6, 'determinant_label': '1.1.1', 'dims': None, 'factorization': [], 'fine_num': 1, 'generators': [[3, 308, 2, 69], [7, 304, 48, 221], [63, 308, 91, 237], [169, 48, 40, 107]], 'genus': 0, 'genus_minus_rank': None, 'has_obstruction': -1, 'index': 48, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [3, 4, 1], [4, 1, 2], [4, 4, 1], [6, 4, 1], [6, 8, 1], [8, 2, 2], [8, 8, 1], [12, 4, 2], [12, 16, 1], [13, 14, 1], [24, 8, 2], [24, 32, 1], [26, 14, 1], [26, 28, 1], [39, 56, 1], [52, 14, 2], [52, 56, 1], [78, 56, 1], [78, 112, 1], [104, 28, 2], [104, 112, 1], [156, 56, 2], [156, 224, 1], [312, 112, 2], [312, 448, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [3, 4, 1], [4, 1, 2], [4, 4, 1], [6, 4, 1], [6, 8, 1], [8, 4, 2], [8, 16, 1], [12, 8, 2], [12, 32, 1], [13, 84, 1], [24, 32, 2], [24, 128, 1], [26, 84, 1], [26, 168, 1], [39, 672, 1], [52, 168, 2], [52, 672, 1], [78, 672, 1], [78, 1344, 1], [104, 672, 2], [104, 2688, 1], [156, 1344, 2], [156, 5376, 1], [312, 5376, 2], [312, 21504, 1]], 'label': '312.48.0-24.bk.1.1', 'lattice_labels': None, 'lattice_x': None, 'level': 312, 'level_is_squarefree': False, 'level_radical': 78, 'log_conductor': None, 'models': None, 'mults': None, '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, 2, 2], [4, 8, 1], [6, 8, 1], [6, 16, 1], [8, 8, 2], [8, 32, 1], [12, 16, 2], [12, 64, 1], [13, 168, 1], [24, 64, 2], [24, 256, 1], [26, 168, 1], [26, 336, 1], [39, 1344, 1], [52, 336, 2], [52, 1344, 1], [78, 1344, 1], [78, 2688, 1], [104, 1344, 2], [104, 5376, 1], [156, 2688, 2], [156, 10752, 1], [312, 10752, 2], [312, 43008, 1]], 'parents': ['104.24.0-8.m.1.3', '156.24.0-12.h.1.1', '312.24.0-8.m.1.6', '312.24.0-12.h.1.3', '312.24.0-24.y.1.1', '312.24.0-24.y.1.11'], 'parents_conj': None, 'pointless': None, 'power': None, 'psl2index': 24, 'psl2label': '8.24.0.b.1', 'psl2level': 8, 'q_gonality': None, 'q_gonality_bounds': [1, 2], 'qbar_gonality': 1, 'qbar_gonality_bounds': [1, 1], 'rank': None, 'rational_cusps': 0, 'reductions': ['1.1.0.a.1', '1.1.0.a.1', '1.1.0.a.1', '2.3.0.a.1', '2.3.0.a.1', '2.3.0.a.1', '2.3.0.a.1', '4.6.0.c.1', '8.12.0.m.1', '12.12.0.h.1', '24.24.0.bk.1', '52.12.0-4.c.1.1', '104.24.0-8.m.1.3', '156.24.0-12.h.1.1'], 'scalar_label': '4.2.1', 'simple': None, 'sl2label': '8.24.0.b.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': '8G0', 'Glabel': None, 'RSZBlabel': '24.24.0.228', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3], 'canonical_conjugator': [4, 23, 23, 2], 'canonical_generators': [[1, 0, 1, 17], [1, 0, 1, 19], [1, 0, 8, 1], [1, 0, 18, 1], [1, 4, 5, 3], [1, 8, 0, 1], [1, 8, 1, 3], [9, 8, 16, 17], [13, 0, 18, 13], [19, 0, 18, 19]], 'cm_discriminants': [], 'coarse_class': '24.24.0.bk', 'coarse_class_num': 37, 'coarse_index': 24, 'coarse_label': '24.24.0.bk.1', 'coarse_level': 24, 'coarse_num': 1, 'conductor': None, 'contains_negative_one': True, 'curve_label': None, 'cusp_orbits': [[2, 3]], 'cusp_widths': [[2, 4], [8, 2]], 'cusps': 6, 'determinant_label': '1.1.1', 'dims': None, 'factorization': [], 'fine_num': 0, 'generators': [[3, 11, 4, 9], [3, 19, 8, 17], [15, 16, 20, 3], [21, 10, 16, 19]], 'genus': 0, 'genus_minus_rank': 0, 'has_obstruction': 0, 'index': 24, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [3, 4, 1], [4, 1, 2], [4, 4, 1], [6, 4, 1], [6, 8, 1], [8, 2, 2], [8, 8, 1], [12, 4, 2], [12, 16, 1], [24, 8, 2], [24, 32, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [3, 4, 1], [4, 1, 2], [4, 4, 1], [6, 4, 1], [6, 8, 1], [8, 4, 2], [8, 16, 1], [12, 8, 2], [12, 32, 1], [24, 32, 2], [24, 128, 1]], 'label': '24.24.0.bk.1', 'lattice_labels': ['1.1.0.a.1', '2.3.0.a.1', '4.6.0.c.1', '8.12.0.m.1', '12.2.0.a.1', '12.6.0.a.1', '12.6.0.g.1', '12.12.0.h.1', '24.12.0.y.1', '24.24.0.bk.1'], 'lattice_x': [2473, 3964, 6764, 9018, 982, 1164, 3782, 3782, 6400, 6400], 'level': 24, 'level_is_squarefree': False, 'level_radical': 6, 'log_conductor': None, 'models': None, 'mults': None, 'name': None, 'newforms': [], 'nu2': 0, 'nu3': 0, 'num_bad_primes': 2, 'num_known_degree1_noncm_points': 13, 'num_known_degree1_noncusp_points': 13, 'num_known_degree1_points': 14, 'obstructions': [], 'orbits': [[2, 1, 1], [2, 2, 1], [3, 8, 1], [4, 2, 2], [4, 8, 1], [6, 8, 1], [6, 16, 1], [8, 8, 2], [8, 32, 1], [12, 16, 2], [12, 64, 1], [24, 64, 2], [24, 256, 1]], 'parents': ['8.12.0.m.1', '12.12.0.h.1', '24.12.0.y.1'], 'parents_conj': [[1, 0, 0, 1], [1, 0, 0, 1], [19, 16, 6, 5]], 'pointless': None, 'power': None, 'psl2index': 24, 'psl2label': '8.24.0.b.1', 'psl2level': 8, 'q_gonality': None, 'q_gonality_bounds': [1, 2], 'qbar_gonality': 1, 'qbar_gonality_bounds': [1, 1], 'rank': 0, 'rational_cusps': 0, 'reductions': ['1.1.0.a.1', '2.3.0.a.1', '2.3.0.a.1', '4.6.0.c.1', '8.12.0.m.1', '12.12.0.h.1'], 'scalar_label': '1.1.1', 'simple': None, 'sl2label': '8.24.0.b.1', 'sl2level': 8, 'squarefree': None, 'trace_hash': 0, 'traces': []}
• modcurve 24.24.0.bk.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': ['(4*x+y)^24*(2368*x^4+2688*x^3*y+1728*x^2*y^2+1008*x*y^3+333*y^4)^3*(4672*x^4-8448*x^3*y+6912*x^2*y^2-3168*x*y^3+657*y^4)^3', '(4*x+y)^24*(8*x^2-3*y^2)^2*(8*x^2-36*x*y+3*y^2)^8*(24*x^2-8*x*y+9*y^2)^2'], 'degree': 24, 'domain_label': '24.24.0.bk.1', 'domain_model_type': 1, 'dont_display': False, 'factored': True, 'leading_coefficients': ['2^6', '3*5^2'], '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: 2172
    {'Elabel': '96.a2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 96, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '24.24.0.bk.1', 'curve_level': 24, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 11.8537311557443, 'jinv': '140608/3', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
  • id: 1848273
    {'Elabel': None, 'ainvs': None, 'cardinality': 0, 'cm': 0, 'conductor_norm': None, 'coordinates': {'1': ['-1/4:1']}, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '24.24.0.bk.1', '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: 6653
    {'Elabel': '480.a1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 480, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '24.24.0.bk.1', 'curve_level': 24, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 27.8630151447375, 'jinv': '1261112198464/675', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
  • id: 12097
    {'Elabel': '1056.e2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 1056, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '24.24.0.bk.1', 'curve_level': 24, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 33.1264606219842, 'jinv': '243578556889408/52089208083', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
  • id: 111697
    {'Elabel': '20064.d1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 20064, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '24.24.0.bk.1', 'curve_level': 24, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 43.6676142678193, 'jinv': '9217304063844205888/131043', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
  • id: 233404
    {'Elabel': '53664.g1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 53664, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '24.24.0.bk.1', 'curve_level': 24, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 53.9611174834427, 'jinv': '272279886183701546713408/3298621707543123', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
  • id: 280609
    {'Elabel': '68640.c2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 68640, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '24.24.0.bk.1', 'curve_level': 24, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 37.3988884760561, 'jinv': '17463484154200384/7402756293075', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
  • id: 342387
    {'Elabel': '89760.o1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 89760, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '24.24.0.bk.1', 'curve_level': 24, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 47.946334272067, 'jinv': '665010345830133070144/116155718641875', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
  • id: 422348
    {'Elabel': '118560.a1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 118560, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '24.24.0.bk.1', 'curve_level': 24, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 85.573380821401, 'jinv': '14589724413269994983274047124347838784/124578331982157421875', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
  • id: 650725
    {'Elabel': '209760.u2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 209760, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '24.24.0.bk.1', 'curve_level': 24, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 42.7662549473179, 'jinv': '3742385616402382144/2120269926483075', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
  • id: 808930
    {'Elabel': '279456.d1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 279456, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '24.24.0.bk.1', 'curve_level': 24, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 59.4711147246997, 'jinv': '67294095100778815199864128/25421763', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
  • id: 1127051
    {'Elabel': '432480.g1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 432480, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '24.24.0.bk.1', 'curve_level': 24, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 75.2746095171477, 'jinv': '491300878519727165939145648825664/4931691075', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
  • id: 1138492
    {'Elabel': '438240.l1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 438240, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '24.24.0.bk.1', 'curve_level': 24, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 68.2306961237848, 'jinv': '428760553581943126732238250304/1034752320337253476921875', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}
  • id: 1234709
    {'Elabel': '487968.n1', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 487968, 'coordinates': None, 'curve_genus': 0, 'curve_index': 24, 'curve_label': '24.24.0.bk.1', 'curve_level': 24, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': -2, 'j_field': '1.1.1.1', 'j_height': 47.4721931951588, 'jinv': '413915365292619112768/374129185071603', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}