-
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-108, 0, 796, 0, -2571, 0, 2277, 0, 708, 0, -386, 0, -126, 0, 12, 0, -3, 0, 1], 'conductor': 0, 'degree': 18, 'dirichlet_group': [], 'disc_abs': 2534788041928904776561145413632, 'disc_rad': 318, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[2, 9]]], [7, [[6, 3]]], [11, [[6, 2], [3, 2]]], [13, [[3, 6]]], [17, [[2, 9]]], [19, [[6, 3]]], [23, [[6, 2], [3, 2]]], [29, [[2, 9]]], [31, [[6, 3]]], [37, [[3, 6]]], [41, [[2, 9]]], [43, [[6, 3]]], [47, [[6, 2], [3, 2]]], [53, [0]], [59, [[6, 2], [3, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [36, 18, 24], 'galois_label': '18T11', 'galt': 11, 'grd': 48.877374517097394, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '18.6.2534788041928904776561145413632.1', 'local_algs': ['2.2.2.2', '2.2.2.2', '2.2.2.2', '2.4.4.1', '2.4.4.1', '2.4.4.1', '3.2.1.1', '3.2.1.1', '3.2.1.1', '3.4.2.1', '3.4.2.1', '3.4.2.1', '53.6.4.1', '53.6.4.1', '53.6.4.1'], 'minimal_sibling': [4, 12, 9, -6, -3, 0, 1], 'monogenic': -1, 'num_ram': 3, 'r2': 6, 'ramps': [2, 3, 53], 'rd': 48.8773745171, 'regulator': {'__RealLiteral__': 0, 'data': '11538528860.450172', 'prec': 60}, 'res': {'sib': ['4,12,9,-6,-3,0,1', '-36,66,62,-141,119,-50,5,4,-3,1', '108,-936,3658,-8268,11355,-9171,4167,-1806,2244,-2340,1678,-816,396,-294,210,-108,39,-9,1', '1296,0,8820,0,13888,0,-1115,0,369,0,686,0,-7,0,-54,0,1,0,1', '4,-4,26,-42,27,-38,65,-50,26,-20,15,-6,1']}, 'subfield_mults': [1, 3, 1, 1, 1, 3], 'subfields': ['-3.0.1', '51.-35.-1.1', '-53.0.0.1', '-108.0.-35.0.-1.0.1', '-32.136.257.-74.-70.-2.1', '-36.66.62.-141.119.-50.5.4.-3.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{68941301}{4875027360} a^{17} - \\frac{6226917}{1625009120} a^{16} - \\frac{7868629}{203126140} a^{15} + \\frac{1681657}{203126140} a^{14} + \\frac{64748001}{406252280} a^{13} - \\frac{14972099}{406252280} a^{12} - \\frac{202069349}{116072080} a^{11} + \\frac{363829129}{812504560} a^{10} - \\frac{128745809}{21763515} a^{9} + \\frac{381752407}{203126140} a^{8} + \\frac{492492977}{58036040} a^{7} - \\frac{80957991}{58036040} a^{6} + \\frac{56286964999}{1625009120} a^{5} - \\frac{17862486853}{1625009120} a^{4} - \\frac{193342727}{7254505} a^{3} + \\frac{144011253}{203126140} a^{2} + \\frac{971503247}{174108120} a + \\frac{79869527}{81250456} \\)', '\\( \\frac{30830113}{1950010944} a^{17} + \\frac{8392313}{650003648} a^{16} - \\frac{2274547}{58036040} a^{15} - \\frac{1570916}{50781535} a^{14} + \\frac{137706619}{812504560} a^{13} + \\frac{15840609}{116072080} a^{12} - \\frac{3096020703}{1625009120} a^{11} - \\frac{2515078481}{1625009120} a^{10} - \\frac{8641717967}{1218756840} a^{9} - \\frac{299896181}{50781535} a^{8} + \\frac{865944607}{116072080} a^{7} + \\frac{637442159}{116072080} a^{6} + \\frac{129784610927}{3250018240} a^{5} + \\frac{107357047949}{3250018240} a^{4} - \\frac{7881900021}{406252280} a^{3} - \\frac{722017521}{58036040} a^{2} + \\frac{6855102533}{2437513680} a + \\frac{1917963757}{812504560} \\)', '\\( \\frac{675481}{174108120} a^{17} - \\frac{68361}{5803604} a^{15} + \\frac{691507}{14509010} a^{13} - \\frac{2847967}{5803604} a^{11} - \\frac{12852823}{8705406} a^{9} + \\frac{3983074}{1450901} a^{7} + \\frac{477089787}{58036040} a^{5} - \\frac{60940909}{5803604} a^{3} + \\frac{112491908}{21763515} a + 2 \\)', '\\( \\frac{5992591}{650003648} a^{17} - \\frac{29371087}{3250018240} a^{16} - \\frac{4826371}{203126140} a^{15} + \\frac{8495849}{406252280} a^{14} + \\frac{82472617}{812504560} a^{13} - \\frac{76050411}{812504560} a^{12} - \\frac{1821759479}{1625009120} a^{11} + \\frac{1742937143}{1625009120} a^{10} - \\frac{817515371}{203126140} a^{9} + \\frac{1717348639}{406252280} a^{8} + \\frac{546726761}{116072080} a^{7} - \\frac{415120487}{116072080} a^{6} + \\frac{73341299131}{3250018240} a^{5} - \\frac{75583555559}{3250018240} a^{4} - \\frac{5611355713}{406252280} a^{3} + \\frac{3038067691}{406252280} a^{2} + \\frac{3188721163}{812504560} a - 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\\frac{7007087}{81250456} a^{8} + \\frac{171156941}{116072080} a^{7} - \\frac{3601173}{5803604} a^{6} + \\frac{13386213063}{3250018240} a^{5} - \\frac{68728981}{232144160} a^{4} - \\frac{1174497073}{406252280} a^{3} + \\frac{15540387}{20312614} a^{2} + \\frac{107726953}{487502736} a - \\frac{23724047}{406252280} \\)', '\\( \\frac{36986289}{3250018240} a^{17} + \\frac{17137059}{3250018240} a^{16} - \\frac{8546551}{203126140} a^{15} - \\frac{103062}{10156307} a^{14} + \\frac{127751051}{812504560} a^{13} + \\frac{39186009}{812504560} a^{12} - \\frac{2468865989}{1625009120} a^{11} - \\frac{27914733}{46428832} a^{10} - \\frac{696856151}{203126140} a^{9} - \\frac{110424333}{40625228} a^{8} + \\frac{1337342251}{116072080} a^{7} + \\frac{29779061}{23214416} a^{6} + \\frac{14029353677}{650003648} a^{5} + \\frac{49566472099}{3250018240} a^{4} - \\frac{20276577623}{406252280} a^{3} + \\frac{35500501}{81250456} a^{2} + \\frac{17599975537}{812504560} a - \\frac{5908840421}{812504560} \\)', '\\( \\frac{644108321}{9750054720} a^{17} - \\frac{142763493}{3250018240} a^{16} - \\frac{41370057}{203126140} a^{15} + \\frac{49423923}{406252280} a^{14} + \\frac{92594883}{116072080} a^{13} - \\frac{408050221}{812504560} a^{12} - \\frac{13592326303}{1625009120} a^{11} + \\frac{1260211443}{232144160} a^{10} - \\frac{3796031854}{152344605} a^{9} + \\frac{1054324929}{58036040} a^{8} + \\frac{5826346397}{116072080} a^{7} - \\frac{3078024289}{116072080} a^{6} + \\frac{494749023659}{3250018240} a^{5} - \\frac{340892787357}{3250018240} a^{4} - \\frac{10880239473}{58036040} a^{3} + \\frac{5015677381}{58036040} a^{2} + \\frac{88352873729}{2437513680} a - \\frac{425839439}{23214416} \\)', '\\( \\frac{175223353}{696432480} a^{17} - \\frac{59623073}{406252280} a^{16} - \\frac{276218753}{406252280} a^{15} + \\frac{165144199}{406252280} a^{14} + \\frac{142541372}{50781535} a^{13} - \\frac{675725759}{406252280} a^{12} - \\frac{25057691663}{812504560} a^{11} + \\frac{7351525137}{406252280} a^{10} - \\frac{129682197119}{1218756840} a^{9} + \\frac{24727545019}{406252280} a^{8} + \\frac{4284678771}{29018020} a^{7} - \\frac{5249215301}{58036040} a^{6} + \\frac{144193137407}{232144160} a^{5} - \\frac{72446680221}{203126140} a^{4} - \\frac{95091406311}{203126140} a^{3} + \\frac{15163041162}{50781535} a^{2} + \\frac{45823743739}{1218756840} a - \\frac{394930645}{10156307} \\)', '\\( \\frac{69643877}{4875027360} a^{17} + \\frac{21638097}{1625009120} a^{16} - \\frac{15894999}{406252280} a^{15} - \\frac{734131}{20312614} a^{14} + \\frac{16403339}{101563070} a^{13} + \\frac{61413567}{406252280} a^{12} - \\frac{1428603509}{812504560} a^{11} - \\frac{38055851}{23214416} a^{10} - \\frac{7280344957}{1218756840} a^{9} - \\frac{226933927}{40625228} a^{8} + \\frac{248530893}{29018020} a^{7} + \\frac{89665359}{11607208} a^{6} + \\frac{11247228199}{325001824} a^{5} + \\frac{51294387497}{1625009120} a^{4} - \\frac{5774643633}{203126140} a^{3} - \\frac{267825157}{10156307} a^{2} + \\frac{4017218861}{1218756840} a + \\frac{2010338917}{406252280} \\)', '\\( \\frac{4717115741}{9750054720} a^{17} + \\frac{497584709}{3250018240} a^{16} - \\frac{578096599}{406252280} a^{15} - \\frac{17841343}{40625228} a^{14} + \\frac{4636627291}{812504560} a^{13} + \\frac{1429673279}{812504560} a^{12} - \\frac{98484425623}{1625009120} a^{11} - \\frac{879415683}{46428832} a^{10} - \\frac{232028027627}{1218756840} a^{9} - \\frac{2525356587}{40625228} a^{8} + \\frac{38630277807}{116072080} a^{7} + \\frac{2415525859}{23214416} a^{6} + \\frac{3678609097239}{3250018240} a^{5} + \\frac{1169342813749}{3250018240} a^{4} - \\frac{481734770511}{406252280} a^{3} - \\frac{28573393715}{81250456} a^{2} + \\frac{623499309989}{2437513680} a + \\frac{53925472229}{812504560} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', '1/4*a^8 - 1/2*a^5 - 1/2*a^4 + 1/4*a^2 - 1/2*a - 1/2', '1/4*a^9 - 1/2*a^6 - 1/2*a^5 + 1/4*a^3 - 1/2*a^2 - 1/2*a', '1/4*a^10 - 1/2*a^7 - 1/2*a^6 + 1/4*a^4 - 1/2*a^3 - 1/2*a^2', '1/4*a^11 - 1/2*a^7 + 1/4*a^5 - 1/2*a^4 - 1/2*a^3 - 1/2*a^2', '1/28*a^12 - 1/14*a^10 - 3/28*a^8 - 1/4*a^6 - 1/2*a^4 - 1/2*a^3 + 1/4*a^2 - 1/2*a + 1/14', '1/56*a^13 + 5/56*a^11 - 3/56*a^9 - 3/8*a^7 - 1/8*a^5 - 1/8*a^3 - 1/2*a^2 - 13/28*a - 1/2', '1/280*a^14 - 3/280*a^12 + 13/280*a^10 + 31/280*a^8 - 9/40*a^6 + 7/40*a^4 - 1/2*a^3 + 57/140*a^2 - 1/2*a - 9/35', '1/280*a^15 + 1/140*a^13 - 4/35*a^11 + 2/35*a^9 - 1/10*a^7 - 1/5*a^5 - 61/280*a^3 - 1/2*a^2 + 39/140*a - 1/2', '1/3250018240*a^16 + 59993/50781535*a^14 - 1128733/812504560*a^12 - 75151357/1625009120*a^10 - 5469369/101563070*a^8 - 330397/116072080*a^6 - 1/2*a^5 - 1369349791/3250018240*a^4 - 8331999/406252280*a^2 - 1/2*a + 72038861/162500912', '1/9750054720*a^17 + 18389/11607208*a^15 + 6394627/812504560*a^13 - 7718439/325001824*a^11 - 4085315/243751368*a^9 - 11435781/23214416*a^7 - 1/2*a^6 + 1358143587/3250018240*a^5 - 9841233/81250456*a^3 - 1/2*a^2 + 1021805161/2437513680*a']}
Number field data - 18.6.2534788041928904776561145413632.1