-
nf_fields • Show schema
{'class_group': [4], 'class_number': 4, 'cm': True, 'coeffs': [4096, -12288, 18432, -16384, 7680, 512, -3968, 3520, -1888, 352, 824, -1392, 1249, -696, 206, 44, -118, 110, -62, 4, 30, -32, 18, -6, 1], 'conductor': 0, 'degree': 24, 'dirichlet_group': [], 'disc_abs': 3785323726785214561740247642669056, 'disc_rad': 10902, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[6, 4]]], [7, [[6, 4]]], [11, [[4, 4], [2, 4]]], [13, [[3, 8]]], [17, [[4, 4], [2, 4]]], [19, [[2, 12]]], [23, [0]], [29, [[4, 4], [2, 4]]], [31, [[2, 12]]], [37, [[2, 12]]], [41, [[4, 4], [2, 4]]], [43, [[2, 12]]], [47, [[6, 4]]], [53, [[4, 4], [2, 4]]], [59, [[6, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_label': '24T400', 'galt': 400, 'inessentialp': [2], 'is_galois': False, 'iso_number': 1, 'label': '24.0.3785323726785214561740247642669056.1', 'local_algs': ['2.4.4.1', '2.4.4.1', '2.4.4.1', '2.4.4.1', '2.4.4.1', '2.4.4.1', '3.12.6.2', '3.12.6.2', '23.4.0.1', '23.4.2.1', '23.4.0.1', '23.4.0.1', '23.4.2.1', '23.4.0.1', '79.2.0.1', '79.2.0.1', '79.2.0.1', '79.2.0.1', '79.4.2.1', '79.4.2.1', '79.4.2.1', '79.4.2.1'], 'monogenic': -1, 'num_ram': 4, 'r2': 12, 'ramps': [2, 3, 23, 79], 'rd': 25.0661495321, 'regulator': {'__RealLiteral__': 0, 'data': '42401055.974884115', 'prec': 60}, 'subfield_mults': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'subfields': ['1.0.1', '1.-1.1', '-3.0.1', '2.-4.-1.1', '1.0.-1.0.1', '8.-4.4.-2.2.-1.1', '8.-8.6.-6.3.-2.1', '4.-8.18.0.5.-1.1', '172.-152.64.-16.13.0.1', '2.14.15.-6.-9.0.1', '-8.-32.42.12.-13.-1.1', '-2.22.31.-4.-11.0.1', '1.-12.-27.100.146.-156.-219.64.106.-8.-19.0.1', '2.10.17.14.6.10.13.-28.39.-32.18.-6.1', '4.-28.166.-234.327.-162.175.-68.66.-12.9.0.1', '64.-32.-16.16.-8.0.8.0.-2.2.-1.-1.1', '64.0.1696.0.2740.0.1316.0.277.0.27.0.1', '64.-64.16.48.-36.-4.18.-2.-9.6.1.-2.1', '4.-16.117.-240.224.-104.239.-242.151.-64.24.-6.1'], 'torsion_gen': '\\( -\\frac{290201}{50980864} a^{23} + \\frac{163497}{4634624} a^{22} - \\frac{2171221}{25490432} a^{21} + \\frac{2715659}{25490432} a^{20} - \\frac{571313}{25490432} a^{19} - \\frac{3867623}{25490432} a^{18} + \\frac{7251851}{25490432} a^{17} - \\frac{4062931}{12745216} a^{16} + \\frac{1472277}{6372608} a^{15} + \\frac{4176357}{25490432} a^{14} - \\frac{3346569}{2317312} a^{13} + \\frac{7550321}{2317312} a^{12} - \\frac{205942813}{50980864} a^{11} + \\frac{128302637}{50980864} a^{10} + \\frac{14494175}{25490432} a^{9} - \\frac{23181691}{6372608} a^{8} + \\frac{26950403}{3186304} a^{7} - \\frac{3669117}{289664} a^{6} + \\frac{5971125}{796576} a^{5} + \\frac{12539553}{796576} a^{4} - \\frac{17844963}{398288} a^{3} + \\frac{5194591}{99572} a^{2} - \\frac{789966}{24893} a + \\frac{266757}{49786} \\)', 'torsion_order': 12, 'units': ['\\( \\frac{40555}{12745216} a^{23} - \\frac{194089}{4634624} a^{22} + \\frac{3607173}{25490432} a^{21} - \\frac{6490327}{25490432} a^{20} + \\frac{1331661}{6372608} a^{19} + \\frac{3178139}{25490432} a^{18} - \\frac{6992917}{12745216} a^{17} + \\frac{20594913}{25490432} a^{16} - \\frac{19040545}{25490432} a^{15} + \\frac{7047529}{25490432} a^{14} + \\frac{1854399}{1158656} a^{13} - \\frac{13116367}{2317312} a^{12} + \\frac{121459677}{12745216} a^{11} - \\frac{475431371}{50980864} a^{10} + \\frac{5046705}{1593152} a^{9} + \\frac{15123755}{3186304} a^{8} - \\frac{45993421}{3186304} a^{7} + \\frac{61003}{2263} a^{6} - \\frac{23637937}{796576} a^{5} - \\frac{1282907}{796576} a^{4} + \\frac{1822977}{24893} a^{3} - \\frac{12850479}{99572} a^{2} + \\frac{2920321}{24893} a - \\frac{40477}{803} \\)', '\\( \\frac{1183995}{101961728} a^{23} - \\frac{736389}{12745216} a^{22} + \\frac{6502739}{50980864} a^{21} - \\frac{3432733}{25490432} a^{20} - \\frac{710583}{50980864} a^{19} + \\frac{3380715}{12745216} a^{18} - \\frac{21172733}{50980864} a^{17} + \\frac{1827197}{4634624} a^{16} - \\frac{12706615}{50980864} a^{15} - \\frac{2756029}{6372608} a^{14} + \\frac{120877685}{50980864} a^{13} - \\frac{3969677}{822272} a^{12} + \\frac{537366099}{101961728} a^{11} - \\frac{118703131}{50980864} a^{10} - \\frac{51054143}{25490432} a^{9} + \\frac{38509689}{6372608} a^{8} - \\frac{79204525}{6372608} a^{7} + \\frac{27888699}{1593152} a^{6} - \\frac{881355}{144832} a^{5} - \\frac{24212777}{796576} a^{4} + \\frac{26848109}{398288} a^{3} - \\frac{6629661}{99572} a^{2} + \\frac{2896475}{99572} a + \\frac{49987}{24893} \\)', '\\( \\frac{1348585}{101961728} a^{23} - \\frac{2446053}{50980864} a^{22} + \\frac{328157}{4634624} a^{21} - \\frac{60867}{6372608} a^{20} - \\frac{7506013}{50980864} a^{19} + \\frac{6005075}{25490432} a^{18} - \\frac{8664083}{50980864} a^{17} + \\frac{499859}{50980864} a^{16} + \\frac{7208565}{50980864} a^{15} - \\frac{1685371}{2317312} a^{14} + \\frac{102714715}{50980864} a^{13} - \\frac{7805121}{3186304} a^{12} + \\frac{71380865}{101961728} a^{11} + \\frac{67525839}{25490432} a^{10} - \\frac{102588561}{25490432} a^{9} + \\frac{29325991}{6372608} a^{8} - \\frac{44216279}{6372608} a^{7} + \\frac{237007}{51392} a^{6} + \\frac{17589027}{1593152} a^{5} - \\frac{1798383}{49786} a^{4} + \\frac{14538257}{398288} a^{3} - \\frac{104279}{24893} a^{2} - \\frac{3165559}{99572} a + \\frac{739364}{24893} \\)', '\\( \\frac{232585}{101961728} a^{23} - \\frac{1292087}{50980864} a^{22} + \\frac{4067353}{50980864} a^{21} - \\frac{1702265}{12745216} a^{20} + \\frac{4257423}{50980864} a^{19} + \\frac{2735185}{25490432} a^{18} - \\frac{1427637}{4634624} a^{17} + \\frac{20088399}{50980864} a^{16} - \\frac{17115083}{50980864} a^{15} + \\frac{2180811}{25490432} a^{14} + \\frac{53476295}{50980864} a^{13} - \\frac{40795775}{12745216} a^{12} + \\frac{45822587}{9269248} a^{11} - \\frac{4787149}{1158656} a^{10} + \\frac{8701519}{12745216} a^{9} + \\frac{37999765}{12745216} a^{8} - \\frac{25547041}{3186304} a^{7} + \\frac{45418589}{3186304} a^{6} - \\frac{22703305}{1593152} a^{5} - \\frac{2618027}{398288} a^{4} + \\frac{1089147}{24893} a^{3} - \\frac{13044697}{199144} a^{2} + \\frac{116945}{2263} a - \\frac{851467}{49786} \\)', '\\( \\frac{19365}{4634624} a^{23} - \\frac{76957}{2317312} a^{22} + \\frac{117057}{1158656} a^{21} - \\frac{24043}{144832} a^{20} + \\frac{263637}{2317312} a^{19} + \\frac{124817}{1158656} a^{18} - \\frac{879949}{2317312} a^{17} + \\frac{1196407}{2317312} a^{16} - \\frac{1081097}{2317312} a^{15} + \\frac{47953}{579328} a^{14} + \\frac{3015721}{2317312} a^{13} - \\frac{1139815}{289664} a^{12} + \\frac{28950785}{4634624} a^{11} - \\frac{6472553}{1158656} a^{10} + \\frac{3734453}{2317312} a^{9} + \\frac{4267497}{1158656} a^{8} - \\frac{5878797}{579328} a^{7} + \\frac{40654}{2263} a^{6} - \\frac{1286975}{72416} a^{5} - \\frac{56615}{9052} a^{4} + \\frac{1852855}{36208} a^{3} - \\frac{1509913}{18104} a^{2} + \\frac{640699}{9052} a - \\frac{2094}{73} \\)', '\\( \\frac{280105}{50980864} a^{23} - \\frac{26529}{1158656} a^{22} + \\frac{39707}{796576} a^{21} - \\frac{607095}{12745216} a^{20} - \\frac{391463}{25490432} a^{19} + \\frac{617075}{6372608} a^{18} - \\frac{4016549}{25490432} a^{17} + \\frac{3647009}{25490432} a^{16} - \\frac{2370099}{25490432} a^{15} - \\frac{2648779}{12745216} a^{14} + \\frac{2260955}{2317312} a^{13} - \\frac{2069073}{1158656} a^{12} + \\frac{97468229}{50980864} a^{11} - \\frac{17545159}{25490432} a^{10} - \\frac{17302447}{25490432} a^{9} + \\frac{31680903}{12745216} a^{8} - \\frac{31497419}{6372608} a^{7} + \\frac{914577}{144832} a^{6} - \\frac{1135293}{796576} a^{5} - \\frac{5173177}{398288} a^{4} + \\frac{9610619}{398288} a^{3} - \\frac{4769203}{199144} a^{2} + \\frac{1007673}{99572} a + \\frac{1596}{803} \\)', '\\( \\frac{27641}{822272} a^{23} - \\frac{141289}{822272} a^{22} + \\frac{32183}{74752} a^{21} - \\frac{117829}{205568} a^{20} + \\frac{46019}{205568} a^{19} + \\frac{266221}{411136} a^{18} - \\frac{310417}{205568} a^{17} + \\frac{371527}{205568} a^{16} - \\frac{596139}{411136} a^{15} - \\frac{13235}{18688} a^{14} + \\frac{1416911}{205568} a^{13} - \\frac{6795015}{411136} a^{12} + \\frac{18355527}{822272} a^{11} - \\frac{13583083}{822272} a^{10} + \\frac{793049}{822272} a^{9} + \\frac{958475}{51392} a^{8} - \\frac{8910423}{205568} a^{7} + \\frac{6918189}{102784} a^{6} - \\frac{1196509}{25696} a^{5} - \\frac{202471}{3212} a^{4} + \\frac{2828743}{12848} a^{3} - \\frac{235871}{803} a^{2} + \\frac{683527}{3212} a - \\frac{113777}{1606} \\)', '\\( \\frac{2378969}{101961728} a^{23} - \\frac{5732669}{50980864} a^{22} + \\frac{13710447}{50980864} a^{21} - \\frac{2280053}{6372608} a^{20} + \\frac{7182291}{50980864} a^{19} + \\frac{10003179}{25490432} a^{18} - \\frac{47868835}{50980864} a^{17} + \\frac{60130451}{50980864} a^{16} - \\frac{4310625}{4634624} a^{15} - \\frac{12614801}{25490432} a^{14} + \\frac{225838571}{50980864} a^{13} - \\frac{8253467}{796576} a^{12} + \\frac{1433502129}{101961728} a^{11} - \\frac{274917653}{25490432} a^{10} + \\frac{29386871}{25490432} a^{9} + \\frac{74729483}{6372608} a^{8} - \\frac{179139903}{6372608} a^{7} + \\frac{67002473}{1593152} a^{6} - \\frac{45806791}{1593152} a^{5} - \\frac{15325435}{398288} a^{4} + \\frac{54302393}{398288} a^{3} - \\frac{18347093}{99572} a^{2} + \\frac{14071291}{99572} a - \\frac{1343283}{24893} \\)', '\\( \\frac{378493}{50980864} a^{23} - \\frac{708155}{50980864} a^{22} - \\frac{390581}{25490432} a^{21} + \\frac{2653055}{25490432} a^{20} - \\frac{4455371}{25490432} a^{19} + \\frac{2123571}{25490432} a^{18} + \\frac{3615957}{25490432} a^{17} - \\frac{4073257}{12745216} a^{16} + \\frac{209265}{579328} a^{15} - \\frac{14886389}{25490432} a^{14} + \\frac{14822391}{25490432} a^{13} + \\frac{22364553}{25490432} a^{12} - \\frac{186572791}{50980864} a^{11} + \\frac{269448027}{50980864} a^{10} - \\frac{83685341}{25490432} a^{9} + \\frac{8982729}{12745216} a^{8} + \\frac{1207689}{796576} a^{7} - \\frac{12793463}{1593152} a^{6} + \\frac{15992247}{796576} a^{5} - \\frac{16437583}{796576} a^{4} - \\frac{4159901}{398288} a^{3} + \\frac{10579645}{199144} a^{2} - \\frac{1640168}{24893} a + \\frac{774657}{24893} \\)', '\\( \\frac{106389}{25490432} a^{23} - \\frac{14793}{6372608} a^{22} - \\frac{708369}{25490432} a^{21} + \\frac{524097}{6372608} a^{20} - \\frac{762797}{6372608} a^{19} + \\frac{182803}{6372608} a^{18} + \\frac{9715}{72416} a^{17} - \\frac{3131175}{12745216} a^{16} + \\frac{1047901}{3186304} a^{15} - \\frac{134061}{411136} a^{14} + \\frac{864099}{6372608} a^{13} + \\frac{7679099}{6372608} a^{12} - \\frac{6985247}{2317312} a^{11} + \\frac{4462553}{1158656} a^{10} - \\frac{62497527}{25490432} a^{9} - \\frac{1997381}{12745216} a^{8} + \\frac{1768435}{796576} a^{7} - \\frac{6795073}{796576} a^{6} + \\frac{667031}{49786} a^{5} - \\frac{4257589}{398288} a^{4} - \\frac{5283199}{398288} a^{3} + \\frac{8720531}{199144} a^{2} - \\frac{103384}{2263} a + \\frac{741428}{24893} \\)', '\\( \\frac{70913}{6372608} a^{23} - \\frac{55139}{579328} a^{22} + \\frac{971233}{3186304} a^{21} - \\frac{6501467}{12745216} a^{20} + \\frac{284147}{796576} a^{19} + \\frac{2194959}{6372608} a^{18} - \\frac{938445}{796576} a^{17} + \\frac{9912043}{6372608} a^{16} - \\frac{2186161}{1593152} a^{15} + \\frac{1935499}{6372608} a^{14} + \\frac{2210717}{579328} a^{13} - \\frac{6984273}{579328} a^{12} + \\frac{122442217}{6372608} a^{11} - \\frac{27049067}{1593152} a^{10} + \\frac{828093}{199144} a^{9} + \\frac{144850641}{12745216} a^{8} - \\frac{192034719}{6372608} a^{7} + \\frac{15801233}{289664} a^{6} - \\frac{22248047}{398288} a^{5} - \\frac{452720}{24893} a^{4} + \\frac{31889207}{199144} a^{3} - \\frac{51292273}{199144} a^{2} + \\frac{21227917}{99572} a - \\frac{125519}{1606} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', '1/2*a^7 - 1/2*a', '1/2*a^8 - 1/2*a^2', '1/2*a^9 - 1/2*a^3', '1/2*a^10 - 1/2*a^4', '1/2*a^11 - 1/2*a^5', '1/2*a^12 - 1/2*a^6', '1/2*a^13 - 1/2*a', '1/4*a^14 - 1/4*a^2', '1/8*a^15 - 1/4*a^13 - 1/4*a^11 - 1/4*a^9 - 1/4*a^8 - 1/4*a^7 - 1/2*a^6 - 1/4*a^5 - 1/2*a^4 - 3/8*a^3 + 1/4*a^2', '1/16*a^16 - 1/8*a^14 - 1/4*a^13 - 1/8*a^12 + 1/8*a^10 + 1/8*a^9 - 1/8*a^8 + 3/8*a^6 + 1/4*a^5 - 7/16*a^4 - 1/8*a^3 - 1/2*a^2 - 1/2*a', '1/32*a^17 - 1/16*a^15 - 1/8*a^14 - 1/16*a^13 - 1/4*a^12 - 3/16*a^11 - 3/16*a^10 - 1/16*a^9 - 1/4*a^8 + 3/16*a^7 - 1/8*a^6 - 15/32*a^5 - 5/16*a^4 + 1/4*a^3 - 1/2*a^2 - 1/2*a', '1/128*a^18 - 1/64*a^17 + 1/64*a^16 - 1/16*a^15 + 7/64*a^14 - 1/32*a^13 + 1/64*a^12 + 11/64*a^11 + 9/64*a^10 + 1/32*a^9 + 7/64*a^8 - 1/4*a^7 - 15/128*a^6 - 11/32*a^5 - 1/2*a^4 - 1/2*a^2 - 1/2*a - 1/2', '1/256*a^19 - 1/128*a^17 - 1/64*a^16 - 1/128*a^15 + 3/32*a^14 + 29/128*a^13 + 13/128*a^12 + 31/128*a^11 - 3/32*a^10 + 11/128*a^9 + 15/64*a^8 - 15/256*a^7 + 27/128*a^6 - 3/32*a^5 - 1/4*a^4 + 1/4*a^3 + 1/4*a - 1/2', '1/512*a^20 - 1/256*a^18 - 1/128*a^17 - 1/256*a^16 + 3/64*a^15 + 29/256*a^14 + 13/256*a^13 + 31/256*a^12 - 3/64*a^11 - 53/256*a^10 - 17/128*a^9 + 113/512*a^8 + 27/256*a^7 + 29/64*a^6 - 1/8*a^5 - 1/8*a^4 + 1/4*a^3 + 3/8*a^2 - 1/4*a', '1/1024*a^21 - 1/512*a^19 - 1/256*a^18 - 1/512*a^17 + 3/128*a^16 + 29/512*a^15 + 13/512*a^14 - 97/512*a^13 - 3/128*a^12 - 53/512*a^11 + 47/256*a^10 - 143/1024*a^9 + 27/512*a^8 - 3/128*a^7 - 1/16*a^6 - 1/16*a^5 + 3/8*a^4 + 7/16*a^3 + 3/8*a^2 - 1/2*a', '1/698368*a^22 - 19/87296*a^21 - 149/349184*a^20 + 3/15872*a^19 - 457/349184*a^18 + 1303/87296*a^17 + 9909/349184*a^16 - 19427/349184*a^15 + 41407/349184*a^14 - 21185/87296*a^13 + 41291/349184*a^12 + 31567/174592*a^11 - 129119/698368*a^10 + 41255/349184*a^9 - 8379/43648*a^8 + 16749/87296*a^7 - 2307/43648*a^6 + 5309/10912*a^5 - 3533/10912*a^4 + 179/496*a^3 - 149/682*a^2 + 37/1364*a - 339/682', '1/101961728*a^23 - 19/50980864*a^22 - 20407/50980864*a^21 - 8663/12745216*a^20 + 5703/50980864*a^19 + 14749/25490432*a^18 - 49279/50980864*a^17 - 311089/50980864*a^16 - 2436523/50980864*a^15 + 2629503/25490432*a^14 - 8141857/50980864*a^13 + 279379/12745216*a^12 - 23858367/101961728*a^11 + 168327/3186304*a^10 + 29709/1158656*a^9 + 1579081/12745216*a^8 - 73361/796576*a^7 - 813111/3186304*a^6 - 451997/1593152*a^5 + 41535/199144*a^4 + 4910/24893*a^3 + 2309/18104*a^2 + 8456/24893*a - 9093/49786']}
Number field data - 24.0.3785323726785214561740247642669056.1