Modular curve data - 24.192.1-24.da.1.4

Formats: - HTML - YAML - JSON - 2024-06-01T04:33:14.583441

• 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': '12V1', 'Glabel': '384.12578', 'RSZBlabel': '24.192.1.1734', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3], 'canonical_conjugator': [2, 3, 23, 22], 'canonical_generators': [[1, 0, 1, 17], [1, 0, 2, 1], [1, 0, 12, 1], [1, 12, 0, 1], [7, 0, 1, 19], [13, 0, 22, 13], [13, 12, 12, 13], [19, 12, 23, 1], [19, 12, 23, 19]], 'cm_discriminants': [], 'coarse_class': '24.96.1.da', 'coarse_class_num': 79, 'coarse_index': 96, 'coarse_label': '24.96.1.da.1', 'coarse_level': 24, 'coarse_num': 1, 'conductor': [[2, 6], [3, 2]], 'contains_negative_one': False, 'curve_label': None, 'cusp_orbits': [[1, 2], [2, 3], [4, 2]], 'cusp_widths': [[2, 4], [4, 4], [6, 4], [12, 4]], 'cusps': 16, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': [], 'fine_num': 4, 'generators': [[1, 6, 20, 1], [13, 9, 0, 23], [19, 0, 8, 23], [19, 3, 8, 11]], 'genus': 1, 'genus_minus_rank': 0, 'has_obstruction': -1, 'index': 192, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [3, 1, 1], [3, 3, 1], [4, 1, 2], [4, 4, 1], [6, 1, 1], [6, 2, 1], [6, 3, 1], [6, 6, 1], [8, 2, 2], [8, 8, 1], [12, 1, 2], [12, 3, 2], [12, 4, 1], [12, 12, 1], [24, 2, 2], [24, 6, 2], [24, 8, 1], [24, 24, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [3, 1, 1], [3, 3, 1], [4, 1, 2], [4, 4, 1], [6, 1, 1], [6, 2, 1], [6, 3, 1], [6, 6, 1], [8, 4, 2], [8, 16, 1], [12, 2, 2], [12, 4, 2], [12, 6, 2], [12, 24, 1], [24, 8, 2], [24, 16, 2], [24, 24, 2], [24, 96, 1]], 'label': '24.192.1-24.da.1.4', 'lattice_labels': None, 'lattice_x': None, 'level': 24, 'level_is_squarefree': False, 'level_radical': 6, 'log_conductor': {'__RealLiteral__': 0, 'data': '6.35610766069589123929', 'prec': 74}, 'models': None, 'mults': [1], 'name': None, 'newforms': None, 'nu2': 0, 'nu3': 0, 'num_bad_primes': 2, 'num_known_degree1_noncm_points': 1, 'num_known_degree1_noncusp_points': 1, 'num_known_degree1_points': 2, 'obstructions': None, 'orbits': [[2, 1, 1], [2, 2, 1], [3, 2, 1], [3, 3, 2], [4, 2, 2], [4, 8, 1], [6, 2, 1], [6, 3, 2], [6, 4, 1], [6, 6, 2], [8, 8, 2], [8, 32, 1], [12, 4, 2], [12, 6, 4], [12, 8, 2], [12, 24, 2], [24, 16, 2], [24, 24, 4], [24, 32, 2], [24, 96, 2]], 'parents': ['12.96.0-12.c.3.3', '24.96.0-12.c.3.10', '24.96.0-24.bu.4.7', '24.96.0-24.bu.4.24', '24.96.1-24.ik.1.2', '24.96.1-24.ik.1.12'], 'parents_conj': None, 'pointless': False, 'power': True, 'psl2index': 96, 'psl2label': '12.96.1.a.1', 'psl2level': 12, 'q_gonality': 2, 'q_gonality_bounds': [2, 2], 'qbar_gonality': 2, 'qbar_gonality_bounds': [2, 2], 'rank': 1, 'rational_cusps': 2, 'reductions': ['2.3.0.a.1', '3.8.0-3.a.1.1', '4.6.0.c.1', '6.24.0-6.a.1.2', '8.12.0-4.c.1.4', '12.96.0-12.c.3.3'], 'scalar_label': '12.4.1', 'simple': True, 'sl2label': '12.192.1-12.a.1.1', 'sl2level': 12, 'squarefree': True, 'trace_hash': 246910301975607220, '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': '12V1', 'Glabel': '768.1035912', 'RSZBlabel': '24.96.1.1623', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3], 'canonical_conjugator': [2, 3, 23, 22], 'canonical_generators': [[1, 0, 1, 17], [1, 0, 2, 1], [1, 0, 12, 1], [1, 12, 0, 1], [5, 12, 1, 5], [5, 12, 1, 23], [7, 0, 1, 19], [11, 0, 2, 11], [13, 12, 12, 13]], 'cm_discriminants': [], 'coarse_class': '24.96.1.da', 'coarse_class_num': 79, 'coarse_index': 96, 'coarse_label': '24.96.1.da.1', 'coarse_level': 24, 'coarse_num': 1, 'conductor': [[2, 6], [3, 2]], 'contains_negative_one': True, 'curve_label': '576.b5', 'cusp_orbits': [[1, 2], [2, 3], [4, 2]], 'cusp_widths': [[2, 4], [4, 4], [6, 4], [12, 4]], 'cusps': 16, 'determinant_label': '1.1.1', 'dims': [1], 'factorization': [], 'fine_num': 0, 'generators': [[1, 6, 0, 23], [11, 6, 0, 13], [19, 3, 20, 23], [19, 6, 8, 23], [19, 6, 12, 1]], 'genus': 1, 'genus_minus_rank': 0, 'has_obstruction': -1, 'index': 96, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [3, 1, 1], [3, 3, 1], [4, 1, 2], [4, 4, 1], [6, 1, 1], [6, 2, 1], [6, 3, 1], [6, 6, 1], [8, 2, 2], [8, 8, 1], [12, 1, 2], [12, 3, 2], [12, 4, 1], [12, 12, 1], [24, 2, 2], [24, 6, 2], [24, 8, 1], [24, 24, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [3, 1, 1], [3, 3, 1], [4, 1, 2], [4, 4, 1], [6, 1, 1], [6, 2, 1], [6, 3, 1], [6, 6, 1], [8, 4, 2], [8, 16, 1], [12, 2, 2], [12, 4, 2], [12, 6, 2], [12, 24, 1], [24, 8, 2], [24, 16, 2], [24, 24, 2], [24, 96, 1]], 'label': '24.96.1.da.1', 'lattice_labels': ['1.1.0.a.1', '2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '12.24.0.g.1', '12.48.0.c.3', '24.2.0.a.1', '24.6.0.a.1', '24.6.0.i.1', '24.8.0.c.1', '24.12.0.s.1', '24.24.0.ca.1', '24.24.1.eq.1', '24.48.0.bu.4', '24.48.1.ik.1', '24.96.1.da.1'], 'lattice_x': [7198, 4879, 9106, 1570, 5459, 1739, 2391, 7198, 6208, 3551, 8358, 2560, 6763, 4758, 652, 4130, 2391], '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.b'], 'nu2': 0, 'nu3': 0, 'num_bad_primes': 2, 'num_known_degree1_noncm_points': 1, 'num_known_degree1_noncusp_points': 1, 'num_known_degree1_points': 2, 'obstructions': [], 'orbits': [[2, 1, 1], [2, 2, 1], [3, 2, 1], [3, 6, 1], [4, 2, 2], [4, 8, 1], [6, 2, 1], [6, 4, 1], [6, 6, 1], [6, 12, 1], [8, 8, 2], [8, 32, 1], [12, 4, 2], [12, 8, 2], [12, 12, 2], [12, 48, 1], [24, 16, 2], [24, 32, 2], [24, 48, 2], [24, 192, 1]], 'parents': ['12.48.0.c.3', '24.48.0.bu.4', '24.48.1.ik.1'], 'parents_conj': [[9, 8, 14, 9], [1, 0, 0, 1], [21, 16, 2, 17]], 'pointless': False, 'power': True, 'psl2index': 96, 'psl2label': '12.96.1.a.1', 'psl2level': 12, 'q_gonality': 2, 'q_gonality_bounds': [2, 2], 'qbar_gonality': 2, 'qbar_gonality_bounds': [2, 2], 'rank': 1, 'rational_cusps': 2, 'reductions': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '4.6.0.c.1', '6.12.0.a.1', '12.48.0.c.3'], 'scalar_label': '12.2.1', 'simple': True, 'sl2label': '12.96.1.a.1', 'sl2level': 12, 'squarefree': True, 'trace_hash': 246910301975607220, 'traces': [0, 0, -2, 0, -4, 2, -2, -4, -8, 6, -8, -6, 6, 4, 0, -2, -4, 2, -4, 8, 10, 8, 4, 6, 2, -18, -16, 12, 2, -18, 8, 4, 6, -12, 14, 16, 2, 12, 24, 6, -12, -6, 0, 2, -18, -16, -20, 8, -12, -22, -10, -16, 18, -20, -2, -8, -10, -8, 26, -26, -28, -18, 12, -24, -6, 6, 20, 18, 12, -30, -2, -24, 8, 10, 20, 0, -2, -14, 30, -6, -12, 10, 32, -14, 0, -20, 14, -22, -26, -8, 36, -16, 32, 12, 12, 24, 6, -26, 4, 18, 44, -26, -28, -10, 36, 2, 44, 14, 24, -38, 40, -38, -42, -44, -16, 14, 12, 8, 6, -12, 10, 34, -2, -4, -4, 6, 10, -32, -48, -14, -4, -8, -24, -38, 22, 2, -18, 28, 22, -26, 4, 30, 16, 28, 50, -24, 10, -42, -12, -32, 18, -50, -4, 8, 4, 16, -16, -50, 42, 6, -12, 54, 16, -36, 30, -24, -40, 26]}
• 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+24*x*z^2+56*z^3'], 'modcurve': '24.96.1.da.1', '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': ['48*x^2*y^30+5692032*x^2*y^28*z^2+188620876800*x^2*y^26*z^4+865293713842176*x^2*y^24*z^6-18848487595015471104*x^2*y^22*z^8-40618300162102009528320*x^2*y^20*z^10+10067995772968125887152128*x^2*y^18*z^12+15473670617226567981289439232*x^2*y^16*z^14-794061797776012679744248086528*x^2*y^14*z^16-445561858290011775724810200416256*x^2*y^12*z^18+16553690172472716947879918926036992*x^2*y^10*z^20+1282889542337633135313051365274550272*x^2*y^8*z^22-22416156065344262934735628130838380544*x^2*y^6*z^24-207500837287607204438376295614426120192*x^2*y^4*z^26-29405065906854270953324094403897196544*x^2*y^2*z^28+454034544748725490855096936058918535168*x^2*z^30-96*x*y^30*z+44603136*x*y^28*z^3+4318642096128*x*y^26*z^5+95349934306934784*x*y^24*z^7+264834223411475644416*x*y^22*z^9-202168256505657135464448*x*y^20*z^11-326010707038073564713451520*x*y^18*z^13+28318858415885770964286308352*x*y^16*z^15+23314170523492828896304627187712*x*y^14*z^17-1254067647065260649666920870576128*x*y^12*z^19-175640356042420846165764222172004352*x*y^10*z^21+6280089793223554685578833408942931968*x*y^8*z^23+109078772270106141130118994521481019392*x*y^6*z^25-647561431005250698698444672932503355392*x*y^4*z^27-3060667747674787596117320625848536006656*x*y^2*z^29-908069089497450981710193872117837070336*x*z^31-y^32-176640*y^30*z^2-10764845568*y^28*z^4-235955358056448*y^26*z^6-903725526741073920*y^24*z^8+2161786961867009163264*y^22*z^10+3746998723354151425671168*y^20*z^12-546350747573344709011046400*y^18*z^14-490000357235068143306471899136*y^16*z^16+44766027472498693035127197401088*y^14*z^18+4906717146574462988126524211724288*y^12*z^20-456290103371475960071254237771726848*y^10*z^22+2046651966672012326530636387253747712*y^8*z^24+303155130874927691644962365807693660160*y^6*z^26-383483689011572341941729617474513534976*y^4*z^28-5925548112296553353585485694613464285184*y^2*z^30-3654728615697158484080862699595140956160*z^32', 'z^2*y^2*(y^2-216*z^2)^6*(36*x^2*y^14-150336*x^2*y^12*z^2+320806656*x^2*y^10*z^4-593535983616*x^2*y^8*z^6+129901662683136*x^2*y^6*z^8-10438106657587200*x^2*y^4*z^10+296148833645101056*x^2*y^2*z^12+252*x*y^14*z+1226016*x*y^12*z^3-2238928128*x*y^10*z^5-2081366710272*x*y^8*z^7+826245624840192*x*y^6*z^9-114858668772163584*x*y^4*z^11+7403720841127526400*x*y^2*z^13-191904444202025484288*x*z^15-y^16-11520*y^14*z^2+41824512*y^12*z^4-60089942016*y^10*z^6+1252375437312*y^8*z^8+2255216157130752*y^6*z^10-336140887693197312*y^4*z^12+18953525353286467584*y^2*z^14-383808888404050968576*z^16)'], 'degree': 96, 'domain_label': '24.96.1.da.1', 'domain_model_type': 5, 'dont_display': False, 'factored': True, 'leading_coefficients': ['1', '2^3*3^3'], '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: 1725749
    {'Elabel': None, 'ainvs': None, 'cardinality': 2, 'cm': 0, 'conductor_norm': None, 'coordinates': {'5': ['0:1:0', '-2:0:1']}, 'curve_genus': 1, 'curve_index': 96, 'curve_label': '24.96.1.da.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: 1725750
    {'Elabel': None, 'ainvs': None, 'cardinality': 1, 'cm': 0, 'conductor_norm': None, 'coordinates': {'5': ['4,0:0,-6:1,0']}, 'curve_genus': 1, 'curve_index': 96, 'curve_label': '24.96.1.da.1', '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: 1725751
    {'Elabel': None, 'ainvs': None, 'cardinality': 1, 'cm': 0, 'conductor_norm': None, 'coordinates': {'5': ['-8,0:0,18:1,0']}, 'curve_genus': 1, 'curve_index': 96, 'curve_label': '24.96.1.da.1', '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': '2.0.8.1', 'upload_id': None}
  • id: 1725752
    {'Elabel': None, 'ainvs': None, 'cardinality': 1, 'cm': 0, 'conductor_norm': None, 'coordinates': {'5': ['-2,6:0,0:1,0']}, 'curve_genus': 1, 'curve_index': 96, 'curve_label': '24.96.1.da.1', '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': '2.0.3.1', 'upload_id': None}
  • id: 1725753
    {'Elabel': None, 'ainvs': None, 'cardinality': 1, 'cm': 0, 'conductor_norm': None, 'coordinates': {'5': ['22,0,-6,0:0,-198,0,54:1,0,0,0']}, 'curve_genus': 1, 'curve_index': 96, 'curve_label': '24.96.1.da.1', 'curve_level': 24, 'curve_name': None, 'cusp': True, 'degree': 4, 'isolated': None, 'j_field': '1.1.1.1', 'j_height': 0.0, 'jinv': None, 'jorig': None, 'quo_info': None, 'residue_field': '4.4.2304.1', 'upload_id': None}
  • id: 1725754
    {'Elabel': None, 'ainvs': None, 'cardinality': 1, 'cm': 0, 'conductor_norm': None, 'coordinates': {'5': ['-2,0,2,0:0,-6,0,2:1,0,0,0']}, 'curve_genus': 1, 'curve_index': 96, 'curve_label': '24.96.1.da.1', 'curve_level': 24, 'curve_name': None, 'cusp': True, 'degree': 4, 'isolated': None, 'j_field': '1.1.1.1', 'j_height': 0.0, 'jinv': None, 'jorig': None, 'quo_info': None, 'residue_field': '4.0.2304.2', 'upload_id': None}
  • id: 917
    {'Elabel': '30.a2', 'ainvs': None, 'cardinality': None, 'cm': 0, 'conductor_norm': 30, 'coordinates': {'5': ['1:-9:1', '1:9:1', '10:-36:1', '10:36:1']}, 'curve_genus': 1, 'curve_index': 96, 'curve_label': '24.96.1.da.1', 'curve_level': 24, 'curve_name': None, 'cusp': False, 'degree': 1, 'isolated': 2, 'j_field': '1.1.1.1', 'j_height': 29.9647266552028, 'jinv': '10316097499609/5859375000', 'jorig': None, 'quo_info': None, 'residue_field': '1.1.1.1', 'upload_id': None}