Number field search results

Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)

Results (1-50 of 8148 matches)

 

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
9.5.453771377.1	$x^{9} - x^{8} - 3 x^{7} + 3 x^{6} + 2 x^{5} - x^{4} - 3 x^{2} + 1$	$9$	[5,2]	$453771377$	$1$	$9.15947936661$	$21301.910172564338$			✓	$S_9$ (as 9T34)	trivial	$2$	$6$	$5.89844215304$
9.5.455809769.1	$x^{9} - x^{6} - 3 x^{5} + 4 x^{4} + x^{3} - 4 x^{2} + 1$	$9$	[5,2]	$109\cdot 4181741$	$2$	$9.16404197719$	$21349.701848035256$			✓	$S_9$ (as 9T34)	trivial	$2$	$6$	$5.9132753462$
9.5.460080721.1	$x^{9} - x^{8} - 2 x^{7} + 2 x^{5} + x^{4} - 5 x^{3} - x^{2} + 3 x + 1$	$9$	[5,2]	$41\cdot 11221481$	$2$	$9.17354329592$	$21449.492324994546$			?	$S_9$ (as 9T34)	trivial	$2$	$6$	$5.955048869306523$
9.5.467890073.1	$x^{9} - 2 x^{8} + x^{7} + 2 x^{6} - 5 x^{5} + 2 x^{4} + x^{3} - 3 x^{2} + x + 1$	$9$	[5,2]	$7^{6}\cdot 41\cdot 97$	$3$	$9.19071532866$	$230.76847964399414$			✓	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$6.00908707275$
9.5.507490937.1	$x^{9} - x^{8} - 5 x^{7} + 5 x^{6} + 7 x^{5} - 8 x^{4} - 2 x^{3} + 4 x^{2} - x - 1$	$9$	[5,2]	$507490937$	$1$	$9.2740580522$	$22527.559499422037$			✓	$S_9$ (as 9T34)	trivial	$2$	$6$	$6.32032258654$
9.5.672128737.1	$x^{9} - x^{8} - 4 x^{6} + 4 x^{5} + x^{4} - 5 x^{3} + 5 x^{2} + x - 1$	$9$	[5,2]	$7^{6}\cdot 29\cdot 197$	$3$	$9.56815168396$	$276.5863896330595$			?	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$7.55238207911$
9.5.678717521.1	$x^{9} - x^{8} - 2 x^{7} + 7 x^{6} - 5 x^{5} - 5 x^{4} + 9 x^{3} - x^{2} - 3 x + 1$	$9$	[5,2]	$678717521$	$1$	$9.57852825147$	$26052.20760319555$			✓	$S_9$ (as 9T34)	trivial	$2$	$6$	$7.569374672378502$
9.5.689278977.1	$x^{9} - 3 x^{8} + 9 x^{6} - 9 x^{5} - 6 x^{4} + 11 x^{3} - 3 x + 1$	$9$	[5,2]	$3^{12}\cdot 1297$	$2$	$9.59497599462$	$155.82303573761126$			✓	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$7.6705025888$
9.5.710045729.1	$x^{9} - 3 x^{7} - 2 x^{6} + 3 x^{5} + 3 x^{4} - x^{3} + x^{2} - 1$	$9$	[5,2]	$109\cdot 541\cdot 12041$	$3$	$9.62667383828$	$26646.683264526564$			✓	$S_9$ (as 9T34)	trivial	$2$	$6$	$7.85677083129401$
9.5.741306349.1	$x^{9} - 4 x^{8} + 6 x^{7} - 8 x^{6} + 11 x^{5} - 7 x^{4} + 4 x^{3} - 3 x^{2} - 2 x + 1$	$9$	[5,2]	$7^{6}\cdot 6301$	$2$	$9.67286891182$	$290.4714369409525$			✓	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$8.21022401044$
9.5.823660649.1	$x^{9} - x^{8} + 4 x^{6} - 6 x^{5} - 3 x^{4} + 8 x^{3} + 2 x^{2} - 3 x - 1$	$9$	[5,2]	$7^{6}\cdot 7001$	$2$	$9.78675467486$	$306.1813489978226$			✓	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$8.5381469526$
9.5.830248993.1	$x^{9} - x^{8} - 2 x^{7} + 3 x^{6} + x^{5} - 6 x^{4} - x^{3} + 5 x^{2} - 1$	$9$	[5,2]	$7^{6}\cdot 7057$	$2$	$9.79542200247$	$307.40346045185186$			✓	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$8.57688308628$
9.5.840423481.1	$x^{9} - 2 x^{8} - x^{7} + 2 x^{6} - x^{5} + 6 x^{4} - 4 x^{3} - x - 1$	$9$	[5,2]	$2293\cdot 366517$	$2$	$9.80868773281$	$28990.058313152804$			✓	$S_9$ (as 9T34)	trivial	$2$	$6$	$8.723677925848085$
9.5.865377817.1	$x^{9} - 2 x^{8} + 3 x^{6} - 5 x^{5} + 5 x^{3} + x^{2} - x - 1$	$9$	[5,2]	$865377817$	$1$	$9.8406290723$	$29417.304720181284$			✓	$S_9$ (as 9T34)	trivial	$2$	$6$	$9.131853525653796$
9.5.960133489.1	$x^{9} - 3 x^{8} + 2 x^{7} - x^{5} + 4 x^{4} - 4 x^{3} - 2 x^{2} + 3 x + 1$	$9$	[5,2]	$7^{6}\cdot 8161$	$2$	$9.95489873179$	$330.57528594593737$			?	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$9.71382080416$
9.5.1021310969.1	$x^{9} - x^{8} + 3 x^{7} - 6 x^{6} + 2 x^{5} - 4 x^{4} + x^{3} + 5 x^{2} - x - 1$	$9$	[5,2]	$7^{6}\cdot 8681$	$2$	$10.023457543$	$340.94440776104506$			✓	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$9.79641964427$
9.5.1058958649.1	$x^{9} + 2 x^{7} - 4 x^{6} - x^{5} - 3 x^{4} + 2 x^{3} + 6 x^{2} - 5 x + 1$	$9$	[5,2]	$7^{6}\cdot 9001$	$2$	$10.0638541356$	$347.17150665476555$			✓	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$10.4133226688$
9.5.1087194409.1	$x^{9} - x^{8} - 4 x^{7} - x^{6} + 8 x^{5} + 7 x^{4} - 3 x^{3} - 6 x^{2} - x + 1$	$9$	[5,2]	$7^{6}\cdot 9241$	$2$	$10.09332214$	$351.76949756907226$			✓	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$10.3008784678$
9.5.1091048373.1	$x^{9} - 3 x^{7} - x^{6} + 3 x^{5} - x^{3} + 3 x^{2} - 1$	$9$	[5,2]	$3^{12}\cdot 2053$	$2$	$10.0972913933$	$196.04517030146403$			✓	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$10.4179310363$
9.5.1149783677.1	$x^{9} - 2 x^{8} - 4 x^{7} + 8 x^{6} + 7 x^{5} - 9 x^{4} - 8 x^{3} + x^{2} + 4 x + 1$	$9$	[5,2]	$7^{6}\cdot 29\cdot 337$	$3$	$10.1562907818$	$361.75341759911805$			✓	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$10.6926461036$
9.5.1209078773.1	$x^{9} - 2 x^{8} + 3 x^{6} - 6 x^{5} + 4 x^{4} + 2 x^{3} - 4 x^{2} + 4 x - 1$	$9$	[5,2]	$7^{6}\cdot 43\cdot 239$	$3$	$10.2131949505$	$370.96409038808986$			✓	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$11.128579116$
9.5.1209078773.2	$x^{9} - 3 x^{8} + x^{7} + x^{6} + x^{5} + 4 x^{4} - 5 x^{3} - 3 x^{2} + 3 x + 1$	$9$	[5,2]	$7^{6}\cdot 43\cdot 239$	$3$	$10.2131949505$	$370.96409038808986$			✓	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$11.1353177196$
9.5.1215667117.1	$x^{9} - x^{8} - 4 x^{7} + 6 x^{6} + x^{5} - 7 x^{4} + 4 x^{3} + x^{2} - x + 1$	$9$	[5,2]	$7^{6}\cdot 10333$	$2$	$10.2193636177$	$371.97342026159566$			✓	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$11.1708382468$
9.5.1238726321.1	$x^{9} - 2 x^{8} - 2 x^{7} + 6 x^{6} - 5 x^{5} + 4 x^{3} + 2 x^{2} - 4 x + 1$	$9$	[5,2]	$7^{6}\cdot 10529$	$2$	$10.2407224594$	$375.4847093609451$			?	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$10.9623890042$
9.5.1263235257.1	$x^{9} - 2 x^{6} - 4 x^{3} + 3 x + 1$	$9$	[5,2]	$3^{12}\cdot 2377$	$2$	$10.2630401163$	$210.94841366208323$			✓	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$11.0427461597$
9.5.1274962213.1	$x^{9} - 2 x^{8} - 2 x^{7} + 8 x^{6} - 3 x^{5} - 9 x^{4} + 8 x^{3} + 3 x^{2} - 4 x - 1$	$9$	[5,2]	$7^{6}\cdot 10837$	$2$	$10.2735827583$	$380.937063822793$			✓	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$11.479403783$
9.5.1299958592.1	$x^{9} - 2 x^{8} - 3 x^{7} + 9 x^{6} - x^{5} - 14 x^{4} + 10 x^{3} + 7 x^{2} - 7 x + 1$	$9$	[5,2]	$2^{6}\cdot 37^{3}\cdot 401$	$3$	$10.2957700768$	$193.35691669702553$			✓	$S_3\wr S_3$ (as 9T31)	trivial	$2$	$6$	$11.6514404114$
9.5.1330963137.1	$x^{9} - 2 x^{8} + 2 x^{7} + x^{6} - 8 x^{5} + 14 x^{4} - 13 x^{3} + 2 x^{2} + 3 x - 1$	$9$	[5,2]	$3^{3}\cdot 7^{6}\cdot 419$	$3$	$10.3227693878$	$129.73774114425706$			?	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$11.4732826838$
9.5.1512142597.1	$x^{9} - 2 x^{8} + x^{7} - 2 x^{6} - 2 x^{5} + 5 x^{4} + 4 x^{3} - 3 x - 1$	$9$	[5,2]	$7^{6}\cdot 12853$	$2$	$10.4701945071$	$414.85941166281214$			?	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$12.8545958634$
9.5.1610967757.1	$x^{9} - 4 x^{8} + 5 x^{7} + x^{6} - 7 x^{5} + 6 x^{4} - x^{3} - 5 x^{2} + 2 x + 1$	$9$	[5,2]	$7^{6}\cdot 13693$	$2$	$10.544103246$	$428.20131573818907$			✓	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$13.3770802693$
9.5.1619909081.1	$x^{9} - x^{8} + 2 x^{7} - 7 x^{6} + 7 x^{3} + 3 x^{2} - 3 x - 1$	$9$	[5,2]	$7^{8}\cdot 281$	$2$	$10.5505897878$	$94.52602987072896$			?	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$13.3970481809$
9.5.1626740901.1	$x^{9} - 3 x^{7} - 4 x^{6} + 3 x^{5} + 9 x^{4} - 6 x^{2} + 1$	$9$	[5,2]	$3^{12}\cdot 3061$	$2$	$10.5555245628$	$239.38301786312434$			✓	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$13.2920242823$
9.5.1630732789.1	$x^{9} + x^{7} - x^{6} - 2 x^{5} - 3 x^{4} - 3 x^{3} + 3 x^{2} + 4 x + 1$	$9$	[5,2]	$7^{6}\cdot 83\cdot 167$	$3$	$10.5583994718$	$430.8201177647773$			✓	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$13.4684200729$
9.5.1653791993.1	$x^{9} - 2 x^{7} - 3 x^{6} - x^{5} + 4 x^{4} + 4 x^{3} + x^{2} - 2 x - 1$	$9$	[5,2]	$7^{6}\cdot 14057$	$2$	$10.5748850166$	$433.85540846417985$			✓	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$12.9974380833$
9.5.1669812553.1	$x^{9} - 4 x^{5} + 3 x - 1$	$9$	[5,2]	$37\cdot 757\cdot 59617$	$3$	$10.586218606$	$40863.339963835555$			✓	$S_9$ (as 9T34)	trivial	$2$	$6$	$12.99379870020899$
9.5.1684851329.1	$x^{9} - 3 x^{8} + 3 x^{7} - 2 x^{6} - 5 x^{5} + 13 x^{4} - 2 x^{3} - 5 x^{2} + 1$	$9$	[5,2]	$7^{6}\cdot 14321$	$2$	$10.59677003$	$437.9105071580079$			✓	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$13.7141696567$
9.5.1699910401.1	$x^{9} - 4 x^{8} + 4 x^{7} + x^{6} - 5 x^{5} + 4 x^{4} - x^{3} + 5 x^{2} - 5 x + 1$	$9$	[5,2]	$7^{6}\cdot 14449$	$2$	$10.6072521392$	$439.8631589700912$			?	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$13.3763049081$
9.5.1730969737.1	$x^{9} - x^{8} - 3 x^{7} + 5 x^{6} - 2 x^{5} - 3 x^{4} + 7 x^{3} - 4 x - 1$	$9$	[5,2]	$7^{6}\cdot 14713$	$2$	$10.6286133465$	$443.86337475050937$			?	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$13.7667614034$
9.5.1742734637.1	$x^{9} - x^{8} - x^{7} + 6 x^{6} - x^{5} - 4 x^{4} + 3 x^{3} - 3 x - 1$	$9$	[5,2]	$7^{6}\cdot 14813$	$2$	$10.6366158263$	$445.3692257810948$			✓	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$13.7796253945$
9.5.1783676489.1	$x^{9} - 2 x^{8} + 2 x^{7} - 2 x^{6} - 4 x^{5} + 9 x^{4} - 7 x^{3} + 5 x - 1$	$9$	[5,2]	$7^{6}\cdot 15161$	$2$	$10.6640951097$	$450.5703581396421$			?	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$14.3680714141$
9.5.1790264833.1	$x^{9} - 2 x^{8} + 2 x^{7} + 2 x^{6} - 7 x^{5} + 4 x^{4} - 2 x^{3} - 6 x^{2} + 6 x + 1$	$9$	[5,2]	$7^{6}\cdot 15217$	$2$	$10.6684645901$	$451.40172425205924$			?	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$14.1931912755$
9.5.1837191537.1	$x^{9} - 3 x^{8} + 7 x^{6} - 6 x^{5} + 5 x^{3} - 6 x^{2} + 1$	$9$	[5,2]	$3^{12}\cdot 3457$	$2$	$10.6991799724$	$254.39663517156413$			✓	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$13.6940072971$
9.5.1861324829.1	$x^{9} - x^{8} + 4 x^{7} - x^{6} + 2 x^{5} + 5 x^{4} - 12 x^{3} - x^{2} + 5 x - 1$	$9$	[5,2]	$7^{6}\cdot 13\cdot 1217$	$3$	$10.7147055611$	$460.2731685624242$			?	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$14.5686204324$
9.5.1890972377.1	$x^{9} - 2 x^{8} + x^{7} + x^{6} + x^{5} + x^{4} - 8 x^{3} - x^{2} + 4 x + 1$	$9$	[5,2]	$7^{6}\cdot 16073$	$2$	$10.7335355321$	$463.9243476095044$			?	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$14.4555866466$
9.5.1928620057.1	$x^{9} - 4 x^{8} + 6 x^{7} - 4 x^{6} - 2 x^{5} + 5 x^{4} - 4 x^{3} - x^{2} + 3 x + 1$	$9$	[5,2]	$7^{6}\cdot 13^{2}\cdot 97$	$3$	$10.7570719989$	$199.2569425075224$			✓	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$15.0276828703$
9.5.2096622829.1	$x^{9} - x^{8} + x^{7} - 2 x^{6} - 3 x^{5} - 5 x^{3} + 2 x^{2} + 5 x + 1$	$9$	[5,2]	$7^{6}\cdot 71\cdot 251$	$3$	$10.8573660213$	$488.5001804066271$			?	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$16.2490777372$
9.5.2116387861.1	$x^{9} - 4 x^{8} + 5 x^{7} + 3 x^{6} - 17 x^{5} + 20 x^{4} - 7 x^{3} - 5 x^{2} + 4 x + 1$	$9$	[5,2]	$7^{6}\cdot 17989$	$2$	$10.8686912379$	$490.7973444592458$			✓	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$16.1524193705$
9.5.2143301553.1	$x^{9} - 3 x^{7} + 3 x^{5} - 4 x^{3} + 3 x - 1$	$9$	[5,2]	$3^{12}\cdot 37\cdot 109$	$3$	$10.8839623542$	$274.77409362113264$			✓	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$14.9148673744$
9.5.2159425756.1	$x^{9} - x^{8} + 2 x^{6} - 4 x^{5} + 4 x^{4} - 7 x^{2} + 2 x + 2$	$9$	[5,2]	$2^{2}\cdot 539856439$	$2$	$10.8930299433$	$46469.621862029395$			?	$S_9$ (as 9T34)	trivial	$2$	$6$	$24.603917125$
9.5.2165800441.1	$x^{9} - x^{8} - 2 x^{6} - 2 x^{5} - 4 x^{3} - 2 x^{2} + 2 x + 1$	$9$	[5,2]	$7^{6}\cdot 41\cdot 449$	$3$	$10.8965982118$	$496.4937572674992$			✓	$S_3 \wr C_3 $ (as 9T28)	trivial	$2$	$6$	$16.1061671291$