Formats: - HTML - YAML - JSON - 2026-07-25T19:00:36.701036
  • nf_fields • Show schema
    {'class_group': [3], 'class_number': 3, 'cm': False, 'coeffs': [1259712000000, 0, 0, -933120000, 0, 0, 381715200, 0, 0, 529920, 0, 0, 35344, 0, 0, -8, 0, 0, 1], 'conductor': 0, 'degree': 18, 'disc_abs': 533384837621025615313834850942347141675200000000, 'disc_rad': 4110, 'disc_sign': -1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [36, 93, 36, 36], 'galois_label': '18T24', 'galt': 24, 'grd': 818.1932124074161, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 2, 'label': '18.0.533384837621025615313834850942347141675200000000.2', 'local_algs': ['2.2.3.4a1.2', '2.2.3.4a1.2', '2.2.3.4a1.2', '3.1.6.9a1.5', '3.1.6.9a1.5', '3.1.6.9a1.2', '5.2.3.4a1.1', '5.2.3.4a1.1', '5.6.1.0a1.1', '137.6.3.12a1.2'], 'maximal_cm_subfield': [1, -1, 1], 'maxp': 137, 'minimal_sibling': [1988184, -1596528, 182844, 127866, -11790, -15174, 4257, -345, -3, 1], 'monogenic': -1, 'narrow_class_group': [3], 'narrow_class_number': 3, 'num_ram': 4, 'r2': 9, 'ramps': [2, 3, 5, 137], 'rd': 448.231381711, 'regulator': 159078827156081020, 'subfield_mults': [1, 3, 1, 1], 'subfields': ['1.-1.1', '-548.0.0.1', '11163.0.-365.0.1.0.1', '-86400.-388800.-583200.-293040.-4320.-3240.-8.-12.0.1'], 'torsion_order': 6, 'unit_signature_rank': 0, 'used_grh': True}
  • nf_fields_extra • Show schema
    {'dirichlet_group': [], 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [[3, 6]]], [11, [[2, 9]]], [13, [[3, 6]]], [17, [[2, 9]]], [19, [[3, 6]]], [23, [[6, 3]]], [29, [[6, 3]]], [31, [[3, 6]]], [37, [[3, 6]]], [41, [[2, 9]]], [43, [[3, 4], [1, 6]]], [47, [[6, 3]]], [53, [[2, 9]]], [59, [[6, 3]]]], 'label': '18.0.533384837621025615313834850942347141675200000000.2', 'torsion_gen': '\\( -\\frac{4277}{164044362240000} a^{15} + \\frac{839}{3728280960000} a^{12} - \\frac{2597717}{2563193160000} a^{9} - \\frac{350929}{28479924000} a^{6} - \\frac{1400863}{86302800} a^{3} + \\frac{178009}{351604} \\)', 'units': ['\\( \\frac{52249790728879081}{7381996300800000} a^{17} + \\frac{33782398027018699}{492133086720000} a^{16} + \\frac{3750168275148893}{8202218112000} a^{15} + \\frac{396406838527861583}{167772643200000} a^{14} + \\frac{53226261313431541}{5592421440000} a^{13} + \\frac{8641692112299623}{372828096000} a^{12} + \\frac{90917856894772205029}{461374768800000} a^{11} + \\frac{1190257052301517613}{961197435000} a^{10} + \\frac{399104064295259839}{64079829000} a^{9} + \\frac{71464658377940603269}{2563193160000} a^{8} + \\frac{7537453336909026713}{85439772000} a^{7} + \\frac{58032010397134771}{1423996200} a^{6} + \\frac{1024118254305625417}{1941813000} a^{5} + \\frac{1037484280175901371}{258908400} a^{4} + \\frac{25205530903087903}{1078785} a^{3} + \\frac{810877830194282887}{7911090} a^{2} + \\frac{163474570074191131}{527406} a + \\frac{1945603286675903}{175802} \\)', '\\( \\frac{235604255129169271}{14763992601600000} a^{17} - \\frac{5388572618200711}{492133086720000} a^{16} - \\frac{3750168275148893}{8202218112000} a^{15} + \\frac{166922697935760653}{335545286400000} a^{14} + \\frac{145163109730161277}{11184842880000} a^{13} - \\frac{8641692112299623}{372828096000} a^{12} + \\frac{11634528640911058129}{57671846100000} a^{11} + \\frac{4079529861470126819}{7689579480000} a^{10} - \\frac{399104064295259839}{64079829000} a^{9} - \\frac{7212770404667210683}{2563193160000} a^{8} + \\frac{32050255010602601}{175081500} a^{7} - \\frac{58032010397134771}{1423996200} a^{6} + \\frac{100558418428972469}{127332000} a^{5} + \\frac{144863672145153991}{258908400} a^{4} - \\frac{25205530903087903}{1078785} a^{3} - \\frac{491176031615776009}{31644360} a^{2} + \\frac{728671019089870405}{1054812} a - \\frac{1945603286675903}{175802} \\)', '\\( \\frac{497698413049}{123033271680000} a^{17} - \\frac{43296279287}{1518929280000} a^{16} + \\frac{8054361909503}{164044362240000} a^{15} + \\frac{864239221249}{5592421440000} a^{14} - \\frac{22216992571}{207126720000} a^{13} - \\frac{570684862871}{3728280960000} a^{12} + \\frac{1656787247417987}{15379158960000} a^{11} - \\frac{482051879970323}{569598480000} a^{10} + \\frac{5058504392391413}{2563193160000} a^{9} + \\frac{607085579626069}{85439772000} a^{8} - \\frac{235642978793203}{7119981000} a^{7} + \\frac{827397615227881}{28479924000} a^{6} + \\frac{103390870279363}{129454200} a^{5} - \\frac{9341665726731}{1598200} a^{4} + \\frac{1878599098922857}{86302800} a^{3} - \\frac{143050883219683}{7911090} a^{2} - \\frac{49828164982919}{527406} a + \\frac{137559613014775}{351604} \\)', '\\( \\frac{39372547498039}{14763992601600000} a^{17} + \\frac{43296279287}{1518929280000} a^{16} + \\frac{102914948747}{8202218112000} a^{15} - \\frac{79143319104373}{335545286400000} a^{14} + \\frac{22216992571}{207126720000} a^{13} + \\frac{237151838417}{372828096000} a^{12} + \\frac{3466741605434161}{57671846100000} a^{11} + \\frac{482051879970323}{569598480000} a^{10} + \\frac{140538541413649}{256319316000} a^{9} - \\frac{10088227021969927}{2563193160000} a^{8} + \\frac{235642978793203}{7119981000} a^{7} + \\frac{49160519806217}{711998100} a^{6} - \\frac{833349784075999}{7767252000} a^{5} + \\frac{9341665726731}{1598200} a^{4} + \\frac{10176916719449}{2157570} a^{3} - \\frac{44257844167135}{703208} a^{2} + \\frac{49828164982919}{527406} a + \\frac{233612627406313}{175802} \\)', '\\( \\frac{148022266841455471871077}{164044362240000} a^{15} + \\frac{914584859176957277404661}{3728280960000} a^{12} + \\frac{2582629007665396173943717}{2563193160000} a^{9} + \\frac{258952343863233180100701389}{28479924000} a^{6} - \\frac{15950296771041200018841097}{86302800} a^{3} + \\frac{13158175847424184476941479}{351604} \\)', '\\( \\frac{496138322580199174825357}{164044362240000} a^{15} - \\frac{277311172551067809263299}{3728280960000} a^{12} + \\frac{201037032908152000404164347}{2563193160000} a^{9} + \\frac{79378647875950604863923749}{28479924000} a^{6} + \\frac{16494678112091550622528823}{86302800} a^{3} + \\frac{7332533323113752336085435}{351604} \\)', '\\( \\frac{917380104595263261494255767900143097}{1466864640000} a^{17} + \\frac{14053167665048891051933306524046046199}{3844789740000} a^{16} + \\frac{60871623366948509813650369179754909697}{3728280960000} a^{15} + \\frac{19596254274864162534573908263302495451}{366716160000} a^{14} + \\frac{1401682968178257718496781783229197721921}{11184842880000} a^{13} + \\frac{41437153183555564895511654705677568487}{1864140480000} a^{12} + \\frac{115556833714775798532680681875345545163}{5729940000} a^{11} + \\frac{1762651500822188378337443555126580439068499}{15379158960000} a^{10} + \\frac{479969722689237443163743418959178913517}{954990000} a^{9} + \\frac{177829089685482044171352156980871408517}{84888000} a^{8} + \\frac{549760598591053257665986184814354378342619}{85439772000} a^{7} + \\frac{7799749630940343433446435314818176050719}{647271000} a^{6} + \\frac{372221600887584973969528625695728085241}{1697760} a^{5} + \\frac{135937713698914904946897937872191389915859}{129454200} a^{4} + \\frac{86839817703300115940862775962651754176323}{21575700} a^{3} + \\frac{533762291435115766749802943668316629829}{47160} a^{2} + \\frac{17233157910077969439852280244386356160439}{1054812} a - \\frac{1119742097177781099930834374419884791923}{15982} \\)', '\\( \\frac{917380104595263261494255767900143097}{1466864640000} a^{17} - \\frac{10973406772759534350798873930572341151}{3417590880000} a^{16} - \\frac{66132146277071068823025066128376789569}{7456561920000} a^{15} + \\frac{19596254274864162534573908263302495451}{366716160000} a^{14} + \\frac{179732992618594727759885392337743823237}{1242760320000} a^{13} - \\frac{1807550898643441244875260181914759271637}{1864140480000} a^{12} + \\frac{115556833714775798532680681875345545163}{5729940000} a^{11} - \\frac{328829632547157175301329968857153724469619}{3417590880000} a^{10} - \\frac{135029793984672188432149767977679185043371}{466035120000} a^{9} + \\frac{177829089685482044171352156980871408517}{84888000} a^{8} + \\frac{128683023997909477039362037071071112777533}{56959848000} a^{7} - \\frac{93968578706882830226692600855403809138151}{2589084000} a^{6} + \\frac{372221600887584973969528625695728085241}{1697760} a^{5} - \\frac{5817091250928811768661666171043804483443}{9589200} a^{4} - \\frac{18188835627792883696257570900042321561037}{5393925} a^{3} + \\frac{533762291435115766749802943668316629829}{47160} a^{2} + \\frac{14114139286599896493846634500489272493901}{263703} a - \\frac{1735312457769335707447730941230641186195}{7991} \\)'], 'zk': ['1', 'a', '1/2*a^2', '1/4*a^3', '1/8*a^4 - 1/2*a', '1/8*a^5', '1/16*a^6', '1/32*a^7 - 1/2*a', '1/192*a^8 - 1/24*a^5 + 1/12*a^2', '1/1920*a^9 + 13/480*a^6 - 11/120*a^3 - 1/2', '1/11520*a^10 + 43/2880*a^7 - 41/720*a^4 - 1/4*a', '1/11520*a^11 - 1/1440*a^8 - 41/720*a^5', '1/21081600*a^12 + 853/5270400*a^9 - 10301/1317600*a^6 - 125/1464*a^3 + 2/61', '1/126489600*a^13 + 853/31622400*a^10 - 92651/7905600*a^7 + 241/8784*a^4 - 181/366*a', '1/3794688000*a^14 + 3881/118584000*a^11 - 7379/59292000*a^8 + 14297/658800*a^5 - 2741/21960*a^2', '1/164044362240000*a^15 - 82657/3728280960000*a^12 - 327853483/5126386320000*a^9 + 189704791/14239962000*a^6 + 3725849/86302800*a^3 + 151259/351604', '1/492133086720000*a^16 + 721/1398105360000*a^13 + 173984809/30758317920000*a^10 - 1243832201/170879544000*a^7 + 2707331/64727100*a^4 + 332825/1054812*a', '1/14763992601600000*a^17 + 721/41943160800000*a^14 + 4360486523/115343692200000*a^11 - 337389793/160199572500*a^8 + 13346489/7767252000*a^5 + 561967/15822180*a^2']}