Modular curve data - 60.60.4.cj.1

Formats: - HTML - YAML - JSON - 2024-06-11T16:54:52.029461

• 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': '20C4', 'Glabel': None, 'RSZBlabel': '60.60.4.46', 'RZBlabel': None, 'SZlabel': None, 'Slabel': None, 'all_degree1_points_known': None, 'bad_primes': [2, 3, 5], 'canonical_conjugator': [53, 53, 30, 41], 'canonical_generators': [[1, 0, 20, 1], [1, 20, 0, 1], [2, 7, 17, 18], [2, 7, 27, 38], [2, 7, 57, 38], [2, 13, 59, 14], [21, 20, 40, 41], [40, 3, 33, 16], [40, 21, 39, 16]], 'cm_discriminants': [-4], 'coarse_class': '60.60.4.cj', 'coarse_class_num': 62, 'coarse_index': 60, 'coarse_label': '60.60.4.cj.1', 'coarse_level': 60, 'coarse_num': 1, 'conductor': [[2, 9], [3, 4], [5, 8]], 'contains_negative_one': True, 'curve_label': None, 'cusp_orbits': [[1, 1], [2, 1]], 'cusp_widths': [[20, 3]], 'cusps': 3, 'determinant_label': '1.1.1', 'dims': [1, 1, 1, 1], 'factorization': [], 'fine_num': 0, 'generators': [[3, 44, 5, 9], [13, 14, 5, 59], [33, 28, 16, 25], [49, 6, 24, 55]], 'genus': 4, 'genus_minus_rank': 3, 'has_obstruction': -1, 'index': 60, 'isogeny_orbits': [[2, 1, 1], [2, 2, 1], [3, 4, 1], [4, 2, 1], [4, 4, 1], [5, 6, 1], [6, 4, 1], [6, 8, 1], [10, 6, 1], [10, 12, 1], [12, 8, 1], [12, 16, 1], [15, 24, 1], [20, 12, 1], [20, 24, 1], [30, 24, 1], [30, 48, 1], [60, 48, 1], [60, 96, 1]], 'kummer_orbits': [[2, 1, 1], [2, 2, 1], [3, 4, 1], [4, 2, 1], [4, 4, 1], [5, 12, 1], [6, 4, 1], [6, 8, 1], [10, 12, 1], [10, 24, 1], [12, 16, 1], [12, 32, 1], [15, 96, 1], [20, 48, 1], [20, 96, 1], [30, 96, 1], [30, 192, 1], [60, 384, 1], [60, 768, 1]], 'label': '60.60.4.cj.1', 'lattice_labels': ['1.1.0.a.1', '2.3.0.a.1', '4.6.0.e.1', '5.5.0.a.1', '10.15.1.a.1', '20.30.2.l.1', '60.12.0.bn.1', '60.60.4.cj.1'], 'lattice_x': [5114, 7898, 7898, 2386, 3807, 3807, 7898, 5853], 'level': 60, 'level_is_squarefree': False, 'level_radical': 30, 'log_conductor': {'__RealLiteral__': 0, 'data': '23.50827707918474954714', 'prec': 77}, 'models': 2, 'mults': [1, 1, 1, 1], 'name': None, 'newforms': ['50.2.a.b', '400.2.a.a', '450.2.a.g', '1800.2.a.r'], 'nu2': 2, 'nu3': 0, 'num_bad_primes': 3, 'num_known_degree1_noncm_points': 0, 'num_known_degree1_noncusp_points': 0, 'num_known_degree1_points': 1, 'obstructions': [], 'orbits': [[2, 1, 1], [2, 2, 1], [3, 8, 1], [4, 4, 1], [4, 8, 1], [5, 24, 1], [6, 8, 1], [6, 16, 1], [10, 24, 1], [10, 48, 1], [12, 32, 1], [12, 64, 1], [15, 192, 1], [20, 96, 1], [20, 192, 1], [30, 192, 1], [30, 384, 1], [60, 768, 1], [60, 1536, 1]], 'parents': ['20.30.2.l.1', '60.12.0.bn.1'], 'parents_conj': [[45, 26, 52, 23], [1, 0, 0, 1]], 'pointless': False, 'power': False, 'psl2index': 60, 'psl2label': '20.60.4.c.1', 'psl2level': 20, 'q_gonality': None, 'q_gonality_bounds': [2, 4], 'qbar_gonality': None, 'qbar_gonality_bounds': [2, 4], 'rank': 1, 'rational_cusps': 1, 'reductions': ['1.1.0.a.1', '2.3.0.a.1', '2.3.0.a.1', '4.6.0.e.1', '4.6.0.e.1', '5.5.0.a.1', '5.5.0.a.1', '10.15.1.a.1', '10.15.1.a.1', '20.30.2.l.1'], 'scalar_label': '1.1.1', 'simple': False, 'sl2label': '20.60.4.c.1', 'sl2level': 20, 'squarefree': True, 'trace_hash': 2238588706973193292, 'traces': [2, -4, 0, 4, -2, 0, -4, 10, -12, 0, 4, 0, 0, 8, -24, -24, -16, 24, -2, 24, 0, -20, 18, 0, 0, 0, 8, 6, 8, 36, -12, 24, -20, 10, 0, 4, 0, 14, -24, 32, 38, 8, 20, 0, 40, 40, -26, -8, -24, 48, -24, -48, 20, -30, -24, -12, 0, 4, 0, 0, -2, -8, 26, -28, 0, -48, 34, 0, 6, -56, 8, 36, 40, 0, -50, -12, 0, 0, 0, -12, 6, -80, 68, 0, -80, 18, 0, 0, 0, -72, -24, -44, -76, -72, 40, -72, 0, 0, -70, 0, -38, 32, 48, 0, -56, 0, 66, -60, -60, 60, 0, 0, 72, 40, 4, 0, -24, -24, 56, 42, 112, 0, 160, 78, 34, 0, -16, 28, 16, 0, 40, -12, 64, 0, 0, 36, 48, -104, -168, 0, -56, 0, 56, 66, 0, 32, 0, 12, 10, 48, 0, 0, 10, -24, 24, -56, -20, 0, 0, 0, 96, 156, 0, 62, -148, -12, -116, 0]}
• modcurve_models •

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

  
  
  • id: 91954
    {'dont_display': False, 'equation': ['90*x^2+15*x*y+15*y^2-x*z-y*z+2*z^2+x*w+y*w-2*z*w', '30*x^3-x^2*y-2*x*y^2-y^3-3*x^2*z+3*y^2*z+4*x*z^2-2*y*z^2+3*x^2*w+4*x*y*w+y^2*w-2*x*z*w-2*y*z*w-2*x*w^2'], 'modcurve': '60.60.4.cj.1', 'model_type': 0, 'number_variables': 4, 'smooth': True, 'upload_id': None}
  • id: 91955
    {'dont_display': False, 'equation': ['11310*x^6-8906*x^5*y-240*x^5*z+4111*x^4*y^2-137*x^4*y*z+240*x^4*z^2-3066*x^3*y^3-111*x^3*y^2*z-99*x^3*y*z^2+1081*x^2*y^4-231*x^2*y^3*z+222*x^2*y^2*z^2-8*x^2*y*z^3-206*x*y^5-47*x*y^4*z+21*x*y^3*z^2-8*x*y^2*z^3+4*x*y*z^4+120*y^6-30*y^5*z+30*y^4*z^2'], 'modcurve': '60.60.4.cj.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: 91293
    {'codomain_label': '1.1.0.a.1', 'codomain_model_type': 1, 'coordinates': ['17161113600821886843485419350*x*y*z^9+16187684328403919780088680325*x*y*z^8*w-43204352112996993868946354910*x*y*z^7*w^2-34592305609327169944385200080*x*y*z^6*w^3+22005900533638867294191933540*x*y*z^5*w^4-26664194908609532797416008625*x*y*z^4*w^5-27168818544938381446856157300*x*y*z^3*w^6+9637358052811019771677621860*x*y*z^2*w^7+6718961664097091673956938080*x*y*z*w^8+2169597862169073515627760*x*y*w^9-14171247504675097660132798330*x*z^10-9281540978288277041848801505*x*z^9*w+36965622198650940590523946773*x*z^8*w^2+6340506564358168204055842206*x*z^7*w^3-13994717762976059058048920616*x*z^6*w^4+29680539285752176910455262247*x*z^5*w^5+6521036262109340106566441865*x*z^4*w^6-27151794731279022274667085588*x*z^3*w^7-14675091756370927810156999596*x*z^2*w^8-848254336341994235198571824*x*z*w^9+511544232522819540651684368*x*w^10+2691162715769192515838868000*y^3*z^8+27270245025168104418814072125*y^3*z^7*w+41229135680571350542870644825*y^3*z^6*w^2+18415794346276118051607946425*y^3*z^5*w^3+33921550284683501154957773625*y^3*z^4*w^4+24829258352079968381402365500*y^3*z^3*w^5-1085441800678914490183599750*y^3*z^2*w^6-4336749007882765057944666450*y^3*z*w^7-625847604550262452185279300*y^3*w^8-11938561604252458980092258700*y^2*z^9-40592203176176859572679955275*y^2*z^8*w-24685064231167754210904142680*y^2*z^7*w^2-6043668262946650269718142940*y^2*z^6*w^3-10638830373672097618656639480*y^2*z^5*w^4+2256790146483735995166966375*y^2*z^4*w^5+22311971312576354144882839350*y^2*z^3*w^6+14955728805480969310393029780*y^2*z^2*w^7+1974591954577249763814206190*y^2*z*w^8-283629719368622155955902620*y^2*w^9+5597728564403308712773852070*y*z^10+18623306268702475048536716920*y*z^9*w-1514309007878872022957732292*y*z^8*w^2-19569249080613207275545360314*y*z^7*w^3-5106745003438984608815429706*y*z^6*w^4-19735934258657808089624660628*y*z^5*w^5-35030162508633599812104540210*y*z^4*w^6-15195317725760183550413220348*y*z^3*w^7-388679287496303764324814826*y*z^2*w^8+652207626163620665751240466*y*z*w^9+1543460624866378892698868*y*w^10+253656991935725650770144710*z^11-281272701044808573641593640*z^10*w-885514174834083236350582026*z^9*w^2+1027281821832868841876719548*z^8*w^3+640502106295046057776313652*z^7*w^4-1176735167447539745377190244*z^6*w^5+260738610584113309211676120*z^5*w^6+636698918357886071278247256*z^4*w^7-289554564230351480631243018*z^3*w^8-167773729376258923885688372*z^2*w^9-1307251144707702821491486*z*w^10-171789265971480805312500*w^11', '49215170596350083172973625550*x*y*z^9+51744778601640756143991732225*x*y*z^8*w-637649615313551724005818980*x*y*z^7*w^2+18801509940327867097518810135*x*y*z^6*w^3+15725865072629641016730693870*x*y*z^5*w^4-15535826701874950555288629000*x*y*z^4*w^5-13932223020018568238559224400*x*y*z^3*w^6-2535860261299277952635263920*x*y*z^2*w^7+266703690730164641902038240*x*y*z*w^8+83717624525958120075161280*x*y*w^9-52780434786152861206648081490*x*z^10-45701214971427545096184349765*x*z^9*w+18213388882550024383173559719*x*z^8*w^2+9399739451636527038117231543*x*z^7*w^3+5979872659228573355191682727*x*z^6*w^4+33035377728431845680671741466*x*z^5*w^5+26745991991392738210003275720*x*z^4*w^6+6255335892662016274877154336*x*z^3*w^7-561366287417490918069455088*x*z^2*w^8-377455110048048099182032672*x*z*w^9-34750437323018143788226496*x*w^10-20586873740563855200445652250*y^3*z^8-11106807808215553096430521125*y^3*z^7*w-14597382930341054127061493025*y^3*z^6*w^2-18904764914890956383982717600*y^3*z^5*w^3+281758793845213565833767750*y^3*z^4*w^4+8115549029779728877058934000*y^3*z^3*w^5+3300120620631174545469432000*y^3*z^2*w^6+445473406765401584974034400*y^3*z*w^7+26681437258690073692809600*y^3*w^8-35115260358946551502196729850*y^2*z^9-66644098388853070800785104575*y^2*z^8*w-49556853420340158936698263290*y^2*z^7*w^2-41800261235977166108544851445*y^2*z^6*w^3-46288278426593424955903799940*y^2*z^5*w^4-28624108487189128005432766500*y^2*z^4*w^5-7272755415237448459427083200*y^2*z^3*w^6-28134586745148847700414160*y^2*z^2*w^7+236607369281500368485344320*y^2*z*w^8+16429826212610412266168640*y^2*w^9+27287231760967776279202458460*y*z^10+73343763444505187397438170510*y*z^9*w+66802730610816501025915709274*y*z^8*w^2+50986703892903812854120746108*y*z^7*w^3+50982092379290105965336019082*y*z^6*w^4+29219208454060398377497969716*y*z^5*w^5+5406541261465397419296378870*y*z^4*w^6-996583841431608388037302944*y*z^3*w^7-452712091836703432003488528*y*z^2*w^8-42900680430890454920827552*y*z*w^9-284224317839207456770496*y*w^10+1118142448618872296239065880*z^11-270717553067652584522635420*z^10*w-1057720216286750857884760128*z^9*w^2-170289604975871986866556956*z^8*w^3-68059031028218961563853444*z^7*w^4-129325506256601252783736432*z^6*w^5+254824388693276733697051860*z^5*w^6+238779491805778765429493568*z^4*w^7+52841978491014666234139296*z^3*w^8+3028596940986813370750784*z^2*w^9+568448635678414913540992*z*w^10'], 'degree': 60, 'domain_label': '60.60.4.cj.1', 'domain_model_type': 0, 'dont_display': False, 'factored': True, 'leading_coefficients': ['-2^2*3^6', '1'], 'upload_id': None}
  • id: 91294
    {'codomain_label': '60.60.4.cj.1', 'codomain_model_type': 2, 'coordinates': ['x', 'y', 'w'], 'degree': 1, 'domain_label': '60.60.4.cj.1', 'domain_model_type': 0, '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: 1825997
    {'Elabel': None, 'ainvs': None, 'cardinality': 1, 'cm': 0, 'conductor_norm': None, 'coordinates': {'0': ['0:0:0:1']}, 'curve_genus': 4, 'curve_index': 60, 'curve_label': '60.60.4.cj.1', 'curve_level': 60, '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: 1825998
    {'Elabel': None, 'ainvs': None, 'cardinality': 1, 'cm': 0, 'conductor_norm': None, 'coordinates': {'0': ['0,0:1/4,-1/4:-3/4,-1/4:1,0']}, 'curve_genus': 4, 'curve_index': 60, 'curve_label': '60.60.4.cj.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': '2.0.15.1', 'upload_id': None}