Modular curve data - 60.72.1.fo.1

Formats: - HTML - YAML - JSON - 2024-06-08T07:36:11.056769

• 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': '30D1', 'Glabel': None, 'RSZBlabel': '60.72.1.396', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3, 5], 'canonical_conjugator': [21, 59, 59, 0], 'canonical_generators': [[0, 31, 29, 27], [0, 49, 11, 3], [1, 0, 30, 1], [1, 1, 28, 29], [1, 30, 0, 1], [2, 1, 23, 35], [2, 1, 29, 14], [2, 7, 23, 11], [2, 19, 1, 55], [2, 19, 11, 35], [31, 30, 30, 31]], 'cm_discriminants': [], 'coarse_class': '60.72.1.fo', 'coarse_class_num': 145, 'coarse_index': 72, 'coarse_label': '60.72.1.fo.1', 'coarse_level': 60, 'coarse_num': 1, 'conductor': [[2, 4], [3, 2], [5, 2]], 'contains_negative_one': True, 'curve_label': None, 'cusp_orbits': [[2, 2]], 'cusp_widths': [[6, 2], [30, 2]], 'cusps': 4, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': [], 'fine_num': 0, 'generators': [[29, 15, 3, 22], [37, 40, 41, 7], [53, 50, 25, 11], [59, 25, 29, 14]], 'genus': 1, 'genus_minus_rank': 0, 'has_obstruction': 0, 'index': 72, 'isogeny_orbits': [[2, 3, 1], [3, 4, 1], [4, 6, 1], [5, 1, 1], [5, 5, 1], [6, 12, 1], [10, 3, 1], [10, 15, 1], [12, 24, 1], [15, 4, 1], [15, 20, 1], [20, 6, 1], [20, 30, 1], [30, 12, 1], [30, 60, 1], [60, 24, 1], [60, 120, 1]], 'kummer_orbits': [[2, 3, 1], [3, 4, 1], [4, 6, 1], [5, 2, 1], [5, 10, 1], [6, 12, 1], [10, 6, 1], [10, 30, 1], [12, 48, 1], [15, 16, 1], [15, 80, 1], [20, 24, 1], [20, 120, 1], [30, 48, 1], [30, 240, 1], [60, 192, 1], [60, 960, 1]], 'label': '60.72.1.fo.1', 'lattice_labels': ['1.1.0.a.1', '3.3.0.a.1', '5.6.0.a.1', '10.12.0.a.2', '15.18.0.a.1', '30.36.0.f.1', '60.6.0.i.1', '60.36.0.j.2', '60.36.1.fz.1', '60.72.1.fo.1'], 'lattice_x': [6287, 4455, 8168, 8465, 4901, 8465, 1782, 4901, 1337, 4901], 'level': 60, 'level_is_squarefree': False, 'level_radical': 30, 'log_conductor': {'__RealLiteral__': 0, 'data': '8.18868912444420136966', 'prec': 74}, 'models': 2, 'mults': [1], 'name': None, 'newforms': ['3600.2.a.be'], 'nu2': 16, 'nu3': 0, 'num_bad_primes': 3, 'num_known_degree1_noncm_points': 0, 'num_known_degree1_noncusp_points': 0, 'num_known_degree1_points': 0, 'obstructions': [], 'orbits': [[2, 3, 1], [3, 8, 1], [4, 12, 1], [5, 4, 1], [5, 20, 1], [6, 24, 1], [10, 12, 1], [10, 60, 1], [12, 96, 1], [15, 32, 1], [15, 160, 1], [20, 48, 1], [20, 240, 1], [30, 96, 1], [30, 480, 1], [60, 384, 1], [60, 1920, 1]], 'parents': ['30.36.0.f.1', '60.36.0.j.2', '60.36.1.fz.1'], 'parents_conj': [[1, 0, 0, 1], [1, 0, 0, 1], [51, 44, 55, 49]], 'pointless': None, 'power': True, 'psl2index': 72, 'psl2label': '30.72.1.a.1', 'psl2level': 30, 'q_gonality': 2, 'q_gonality_bounds': [2, 2], 'qbar_gonality': 2, 'qbar_gonality_bounds': [2, 2], 'rank': 1, 'rational_cusps': 0, 'reductions': ['1.1.0.a.1', '1.1.0.a.1', '3.3.0.a.1', '3.3.0.a.1', '3.3.0.a.1', '5.6.0.a.1', '10.12.0.a.2', '10.12.0.a.2', '15.18.0.a.1', '30.36.0.f.1'], 'scalar_label': '5.2.1', 'simple': True, 'sl2label': '30.72.1.a.1', 'sl2level': 30, 'squarefree': True, 'trace_hash': 494513997903162760, 'traces': [0, 0, 0, 2, 0, -2, -6, 4, -6, -6, 4, -2, -6, -10, 6, -6, 12, 2, 2, -12, -2, -8, -6, 6, -2, -6, 14, 6, 2, -6, 2, 0, 18, 4, 6, -20, 22, -10, -18, -6, -12, -10, -12, -26, 18, -8, 16, -10, 6, 14, -6, -24, 14, 0, -6, 18, -18, -20, -26, -6, 14, -30, 2, 12, 22, -6, -8, -2, 30, -10, 18, 24, -22, -26, 28, -6, 6, -2, 30, -34, 36, 26, 36, -2, -8, -6, -6, -26, -30, 14, 30, -24, 26, 0, 4, 18, -6, 6, 14, 14, 26, -30, 18, -30, -8, 22, 6, 18, 0, -10, -22, -2, -6, -20, 28, 18, 14, -42, 42, 36, -22, 46, 18, 42, -8, 30, -34, -24, -46, 22, -20, -6, 4, 22, -42, 2, -30, 26, 42, 6, 16, 54, 38, 30, 2, -48, -50, 18, 4, -6, -26, 18, 14, -18, -46, 12, 16, 42, 22, 18, -18, -6, -22, -24, 18, 18, 4, -26]}
• modcurve_models •

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

  
  
  • id: 92450
    {'dont_display': False, 'equation': ['y^2+5*x*w', '5*x^2-3*z^2+2*x*w+w^2'], 'modcurve': '60.72.1.fo.1', 'model_type': 8, 'number_variables': 4, 'smooth': True, 'upload_id': None}
  • id: 92451
    {'dont_display': False, 'equation': ['x^4-2*x^2*z^2-15*y^2*z^2+5*z^4'], 'modcurve': '60.72.1.fo.1', 'model_type': 2, 'number_variables': 3, 'smooth': False, '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

  
  
  • id: 91789
    {'codomain_label': '1.1.0.a.1', 'codomain_model_type': 1, 'coordinates': ['1708593750*x*z^16*w+6264843750*x*z^14*w^3+21740906250*x*z^12*w^5+50177981250*x*z^10*w^7+31569243750*x*z^8*w^9+32664890250*x*z^6*w^11+2447671500*x*z^4*w^13-253083840*x*z^2*w^15-4376384*x*w^17-284765625*z^18-1879453125*z^16*w^2-11390625000*z^14*w^4-14144878125*z^12*w^6-24959137500*z^10*w^8-25000214625*z^8*w^10+11568316725*z^6*w^12-1568527200*z^4*w^14-133433904*z^2*w^16+515968*w^18', 'w^3*(170859375*x*z^14+877078125*x*z^12*w^2-621928125*x*z^10*w^4+33665625*x*z^8*w^6+65188125*x*z^6*w^8-19269225*x*z^4*w^10+2021745*x*z^2*w^12-68381*x*w^14-478406250*z^14*w+95681250*z^12*w^3+312558750*z^10*w^5-215763750*z^8*w^7+57233250*z^6*w^9-6634170*z^4*w^11+222954*z^2*w^13+8062*w^15)'], 'degree': 72, 'domain_label': '60.72.1.fo.1', 'domain_model_type': 8, 'dont_display': False, 'factored': True, 'leading_coefficients': ['3^3', '1'], 'upload_id': None}
  • id: 91790
    {'codomain_label': '60.72.1.fo.1', 'codomain_model_type': 2, 'coordinates': ['y', 'z', 'w'], 'degree': 1, 'domain_label': '60.72.1.fo.1', 'domain_model_type': 8, 'dont_display': False, 'factored': False, '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: 1826755
    {'Elabel': None, 'ainvs': None, 'cardinality': 1, 'cm': 0, 'conductor_norm': None, 'coordinates': {'8': ['0,-1/5:0,0:1,0:0,0']}, 'curve_genus': 1, 'curve_index': 72, 'curve_label': '60.72.1.fo.1', 'curve_level': 60, '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': '2.2.60.1', 'upload_id': None}
  • id: 1826756
    {'Elabel': None, 'ainvs': None, 'cardinality': 1, 'cm': 0, 'conductor_norm': None, 'coordinates': {'8': ['0,0:0,0:0,1/3:1,0']}, 'curve_genus': 1, 'curve_index': 72, 'curve_label': '60.72.1.fo.1', 'curve_level': 60, '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}