Number field search results

Results (1-50 of 7457 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
10.0.1185762483.1	$x^{10} - 2 x^{9} + 2 x^{8} - 2 x^{7} + 2 x^{6} - x^{5} + 3 x^{4} - 4 x^{3} + x^{2} + 1$	$10$	[0,5]	$-\,3^{5}\cdot 47^{4}$	$2$	$8.07978436776$	$11.874342087037917$			?	$D_{10}$ (as 10T3)	trivial	$6$	$4$	$4.90180202318$
10.0.1403737447.1	$x^{10} - 3 x^{9} + 6 x^{8} - 7 x^{7} + 6 x^{6} - 4 x^{5} + 4 x^{3} - 2 x^{2} - x + 1$	$10$	[0,5]	$-\,7^{5}\cdot 17^{4}$	$2$	$8.21728951631$	$10.908712114635714$			?	$D_{10}$ (as 10T3)	trivial	$2$	$4$	$1.92131760167$
10.0.1917386883.1	$x^{10} - x^{9} + 3 x^{8} - 4 x^{7} + 2 x^{6} - 2 x^{5} + x^{4} + 6 x^{3} + 4 x^{2} + 6 x + 3$	$10$	[0,5]	$-\,3^{5}\cdot 53^{4}$	$2$	$8.47756201091$	$12.609520212918492$			?	$D_{10}$ (as 10T3)	trivial	$6$	$4$	$8.69258267025$
10.2.3409076657.1	$x^{10} - x^{9} + 2 x^{8} - 4 x^{7} + 5 x^{6} - 7 x^{5} + 9 x^{4} - 8 x^{3} + 5 x^{2} - 4 x + 1$	$10$	[2,4]	$7^{4}\cdot 17^{5}$	$2$	$8.97973823085$	$10.908712114635714$			?	$D_{10}$ (as 10T3)	trivial	$2$	$5$	$4.02460808748$
10.0.4599777611.1	$x^{10} - 5 x^{9} + 11 x^{8} - 14 x^{7} + 10 x^{6} - 2 x^{5} - 2 x^{4} + x^{3} + 3 x^{2} - 3 x + 1$	$10$	[0,5]	$-\,11^{5}\cdot 13^{4}$	$2$	$9.25281083468$	$11.958260743101398$			?	$D_{10}$ (as 10T3)	trivial	$2$	$4$	$4.35544165008$
10.0.4996793344.3	$x^{10} - 3 x^{4} + 2 x^{2} + 1$	$10$	[0,5]	$-\,2^{10}\cdot 47^{4}$	$2$	$9.32973135944$	$13.711309200802088$			?	$D_{10}$ (as 10T3)	trivial	$4$	$4$	$9.28816852276$
10.2.5436100813.1	$x^{10} - 3 x^{9} + 6 x^{8} - 6 x^{7} + 3 x^{6} + 3 x^{5} - 9 x^{4} + 13 x^{3} - 12 x^{2} + 6 x - 1$	$10$	[2,4]	$11^{4}\cdot 13^{5}$	$2$	$9.40868113275$	$11.958260743101398$			?	$D_{10}$ (as 10T3)	trivial	$2$	$5$	$5.20372147856$
10.0.9464869683.1	$x^{10} - x^{9} + 3 x^{7} - 4 x^{6} + 3 x^{5} - 4 x^{3} + 7 x^{2} - 3 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 79^{4}$	$2$	$9.94515288581$	$15.394804318340652$			?	$D_{10}$ (as 10T3)	trivial	$6$	$4$	$24.3676081141$
10.2.15249003125.1	$x^{10} - 2 x^{9} + 2 x^{8} - 2 x^{6} + 9 x^{5} + 13 x^{4} + 8 x^{3} + 3 x^{2} - 1$	$10$	[2,4]	$5^{5}\cdot 47^{4}$	$2$	$10.4309567658$	$15.329709716755891$			?	$D_{10}$ (as 10T3)	trivial	$2$	$5$	$10.8923254182$
10.0.25286677443.1	$x^{10} - 3 x^{8} - 2 x^{7} + 6 x^{6} - 8 x^{4} + 21 x^{3} + 12 x^{2} - 9 x + 9$	$10$	[0,5]	$-\,3^{5}\cdot 101^{4}$	$2$	$10.9720853405$	$17.406895185529212$			?	$D_{10}$ (as 10T3)	trivial	$6$	$4$	$43.2958545685$
10.0.27349864083.1	$x^{10} - 2 x^{9} + x^{8} + 2 x^{6} - 4 x^{5} + 8 x^{4} - 9 x^{3} + 4 x^{2} + x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 103^{4}$	$2$	$11.0584820476$	$17.578395831246947$			?	$D_{10}$ (as 10T3)	trivial	$6$	$4$	$37.7617251907$
10.2.33873834933.1	$x^{10} - 4 x^{9} + 4 x^{8} + 4 x^{7} - 6 x^{6} - 11 x^{5} + 18 x^{4} + 4 x^{3} - 13 x^{2} - 7 x - 1$	$10$	[2,4]	$3^{4}\cdot 53^{5}$	$2$	$11.2976063093$	$12.609520212918492$			?	$D_{10}$ (as 10T3)	trivial	$2$	$5$	$17.0871877064$
10.0.39884882944.4	$x^{10} - x^{8} + 3 x^{6} + 5 x^{2} + 1$	$10$	[0,5]	$-\,2^{10}\cdot 79^{4}$	$2$	$11.4836733915$	$17.776388834631177$				$D_{10}$ (as 10T3)	trivial	$4$	$4$	$27.9384031564$
10.0.48729742803.1	$x^{10} - x^{9} + x^{8} + 2 x^{7} - 4 x^{6} + 5 x^{5} - 3 x^{3} + 8 x^{2} - 3 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 7^{4}\cdot 17^{4}$	$3$	$11.7160013194$	$18.894443627691185$			?	$D_{10}$ (as 10T3)	trivial	$6$	$4$	$60.4066621154$
10.2.55730836701.1	$x^{10} - 4 x^{9} + 4 x^{8} - 4 x^{7} + 21 x^{6} - 28 x^{5} + 8 x^{4} - 26 x^{3} + 11 x^{2} - 13 x + 1$	$10$	[2,4]	$3^{5}\cdot 47^{5}$	$2$	$11.874342087$	$11.874342087037917$			?	$D_{10}$ (as 10T3)	trivial	$2$	$5$	$25.719737423$
10.0.59326171875.1	$x^{10} - 10 x^{7} + 3 x^{5} + 25 x^{4} - 15 x^{2} + 9$	$10$	[0,5]	$-\,3^{5}\cdot 5^{12}$	$2$	$11.9488093718$	$14.035297835467638$			?	$D_{10}$ (as 10T3)	trivial	$6$	$4$	$71.7417167728$
10.0.61412507648.1	$x^{10} - 2 x^{9} - 3 x^{8} + 4 x^{7} + 5 x^{6} - 2 x^{5} + 5 x^{4} + 4 x^{3} - 3 x^{2} - 2 x + 1$	$10$	[0,5]	$-\,2^{15}\cdot 37^{4}$	$2$	$11.990179454$	$17.204650534085253$				$D_{10}$ (as 10T3)	trivial	$2$	$4$	$35.3340443364$
10.0.63215147763.1	$x^{10} - x^{9} + 3 x^{8} + 2 x^{6} + 3 x^{5} + 6 x^{4} - x^{3} + 10 x^{2} - 3 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 127^{4}$	$2$	$12.0249177845$	$19.519221295943137$			?	$D_{10}$ (as 10T3)	trivial	$6$	$4$	$71.0037805603$
10.0.71563480803.1	$x^{10} - x^{9} - x^{8} + 2 x^{6} + 2 x^{5} + x^{4} - 9 x^{3} + 3 x^{2} + 2 x + 4$	$10$	[0,5]	$-\,3^{5}\cdot 131^{4}$	$2$	$12.1750049266$	$19.82422760159901$				$D_{10}$ (as 10T3)	trivial	$6$	$4$	$114.524734536$
10.0.82012798567.1	$x^{10} - 2 x^{9} + 2 x^{8} - 3 x^{7} + 4 x^{6} + 3 x^{5} + 4 x^{4} - 40 x^{3} + 24 x^{2} + 32$	$10$	[0,5]	$-\,7^{5}\cdot 47^{4}$	$2$	$12.3420744881$	$18.138357147217054$			?	$D_{10}$ (as 10T3)	trivial	$2$	$4$	$15.4493312646$
10.2.98876953125.1	$x^{10} - 5 x^{7} + 10 x^{6} + 9 x^{5} - 10 x^{4} - 5 x^{3} - 1$	$10$	[2,4]	$3^{4}\cdot 5^{13}$	$2$	$12.5750438321$	$14.035297835467638$			?	$D_{10}$ (as 10T3)	trivial	$2$	$5$	$34.5229624611$
10.0.101613269043.1	$x^{10} - x^{9} + 2 x^{8} + x^{7} - 2 x^{6} + 5 x^{5} + 2 x^{4} - 2 x^{3} + 9 x^{2} - 3 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 11^{4}\cdot 13^{4}$	$3$	$12.6094180173$	$20.71231517720798$			?	$D_{10}$ (as 10T3)	trivial	$6$	$4$	$60.2886012708$
10.2.112027271168.1	$x^{10} + 4 x^{8} - 4 x^{7} + 5 x^{6} - 8 x^{5} + 10 x^{4} - 8 x^{3} - x^{2} - 8 x + 2$	$10$	[2,4]	$2^{15}\cdot 43^{4}$	$2$	$12.7330479847$	$18.547236990991408$				$D_{10}$ (as 10T3)	trivial	$2$	$5$	$76.2777407076$
10.0.113908312331.3	$x^{10} - 2 x^{9} + x^{7} + 7 x^{6} - 16 x^{5} + 10 x^{4} + 6 x^{3} - 7 x^{2} - 2 x + 3$	$10$	[0,5]	$-\,11^{5}\cdot 29^{4}$	$2$	$12.7542680983$	$17.86057109949175$				$D_{10}$ (as 10T3)	trivial	$2$	$4$	$43.1448825671$
10.0.115252102144.4	$x^{10} - 2 x^{8} - x^{6} - x^{4} + 7 x^{2} + 1$	$10$	[0,5]	$-\,2^{10}\cdot 103^{4}$	$2$	$12.7692351741$	$20.29778313018444$				$D_{10}$ (as 10T3)	trivial	$4$	$4$	$65.1656313171$
10.2.121719003125.1	$x^{10} - x^{9} + 2 x^{8} - 7 x^{7} + 16 x^{6} - x^{5} - 2 x^{4} + 2 x^{3} + 3 x^{2} - 3 x - 1$	$10$	[2,4]	$5^{5}\cdot 79^{4}$	$2$	$12.8391371674$	$19.87460691435179$				$D_{10}$ (as 10T3)	trivial	$2$	$5$	$34.1406412527$
10.2.148307253125.1	$x^{10} + 6 x^{8} - 2 x^{7} + 14 x^{6} - 2 x^{5} + 11 x^{4} + 7 x^{3} + x^{2} + 10 x - 1$	$10$	[2,4]	$5^{5}\cdot 83^{4}$	$2$	$13.0953237304$	$20.37154878746336$				$D_{10}$ (as 10T3)	trivial	$2$	$5$	$46.1401263901$
10.0.159897387008.4	$x^{10} - 24 x^{4} + 32 x^{2} + 32$	$10$	[0,5]	$-\,2^{15}\cdot 47^{4}$	$2$	$13.1942326218$	$19.390719429665317$			?	$D_{10}$ (as 10T3)	trivial	$2$	$4$	$21.9874639076$
10.2.159897387008.2	$x^{10} + 24 x^{4} + 32 x^{2} - 32$	$10$	[2,4]	$2^{15}\cdot 47^{4}$	$2$	$13.1942326218$	$19.390719429665317$			?	$D_{10}$ (as 10T3)	trivial	$2$	$5$	$29.2311437627$
10.0.205346735104.4	$x^{10} + x^{8} + 4 x^{6} + 3 x^{4} + 7 x^{2} + 1$	$10$	[0,5]	$-\,2^{10}\cdot 7^{4}\cdot 17^{4}$	$3$	$13.5284730311$	$21.817424229271428$			?	$D_{10}$ (as 10T3)	trivial	$4$	$4$	$51.5509735712$
10.2.214296753125.1	$x^{10} - 2 x^{9} - 5 x^{8} + 8 x^{7} + 11 x^{6} - 15 x^{5} + 4 x^{4} - 6 x^{3} - x^{2} + 5 x + 5$	$10$	[2,4]	$5^{5}\cdot 7^{4}\cdot 13^{4}$	$3$	$13.5863112324$	$21.330729007701542$			?	$D_{10}$ (as 10T3)	trivial	$2$	$5$	$77.2259671327$
10.2.234849287168.5	$x^{10} - 2 x^{8} + 9 x^{6} - 8 x^{4} + 16 x^{2} - 47$	$10$	[2,4]	$2^{10}\cdot 47^{5}$	$2$	$13.7113092008$	$13.711309200802088$			?	$D_{10}$ (as 10T3)	trivial	$2$	$5$	$42.393427204$
10.0.249470040483.1	$x^{10} - x^{9} + x^{8} - 6 x^{7} + 4 x^{6} + 11 x^{4} - 3 x^{3} - 5 x^{2} - 2 x + 4$	$10$	[0,5]	$-\,3^{5}\cdot 179^{4}$	$2$	$13.7943690174$	$23.173260452512935$				$D_{10}$ (as 10T3)	trivial	$6$	$4$	$260.944400622$
10.0.250000000000.1	$x^{10} - 10 x^{7} - 8 x^{5} + 25 x^{4} + 40 x^{2} + 20$	$10$	[0,5]	$-\,2^{10}\cdot 5^{12}$	$2$	$13.7972966146$	$16.206565966927624$				$D_{10}$ (as 10T3)	trivial	$4$	$4$	$210.403548246$
10.0.266388112384.4	$x^{10} + 5 x^{8} + 12 x^{6} + 15 x^{4} + 11 x^{2} + 1$	$10$	[0,5]	$-\,2^{10}\cdot 127^{4}$	$2$	$13.8851790397$	$22.538855339169288$				$D_{10}$ (as 10T3)	trivial	$4$	$4$	$104.742875965$
10.2.284032847872.1	$x^{10} - 3 x^{9} + 2 x^{8} + 5 x^{7} - 13 x^{6} + 2 x^{5} + 17 x^{4} - 5 x^{3} - 4 x^{2} + x - 7$	$10$	[2,4]	$2^{12}\cdot 37^{5}$	$2$	$13.9745186248$	$17.204650534085253$				$D_{10}$ (as 10T3)	trivial	$2$	$5$	$88.0446597898$
10.0.300015454375.1	$x^{10} - 2 x^{9} + 4 x^{8} - x^{7} + x^{5} + 9 x^{4} - 8 x^{3} + 11 x^{2} - 3 x + 11$	$10$	[0,5]	$-\,5^{4}\cdot 7^{5}\cdot 13^{4}$	$3$	$14.0512306471$	$21.330729007701542$			?	$D_{10}$ (as 10T3)	trivial	$2$	$4$	$51.9091044987$
10.2.300303732509.1	$x^{10} - 5 x^{9} + 11 x^{8} - 14 x^{7} + 10 x^{6} - 2 x^{5} + x^{4} - 5 x^{3} + 9 x^{2} - 6 x - 1$	$10$	[2,4]	$11^{4}\cdot 29^{5}$	$2$	$14.052580215$	$17.86057109949175$				$D_{10}$ (as 10T3)	trivial	$2$	$5$	$71.069594371$
10.0.301567919104.3	$x^{10} - 3 x^{8} + 4 x^{6} - 7 x^{4} + 5 x^{2} + 4$	$10$	[0,5]	$-\,2^{10}\cdot 131^{4}$	$2$	$14.0584847435$	$22.891046284519195$				$D_{10}$ (as 10T3)	trivial	$4$	$4$	$160.508240124$
10.2.312500000000.1	$x^{10} - 5 x^{9} + 10 x^{8} - 5 x^{7} - 15 x^{6} + 32 x^{5} - 15 x^{4} - 5 x^{3} + 10 x^{2} - 5 x + 1$	$10$	[2,4]	$2^{8}\cdot 5^{13}$	$2$	$14.1086351316$	$16.206565966927624$				$D_{10}$ (as 10T3)	trivial	$2$	$5$	$101.24867545$
10.2.341108199621.1	$x^{10} - x^{9} - 3 x^{8} + 8 x^{7} - 9 x^{6} + x^{5} + 7 x^{4} + 17 x^{3} + 13 x^{2} + 2 x + 1$	$10$	[2,4]	$3^{5}\cdot 7^{5}\cdot 17^{4}$	$3$	$14.2327629428$	$18.894443627691185$			?	$D_{10}$ (as 10T3)	trivial	$2$	$5$	$50.7666511079$
10.2.351721503125.1	$x^{10} - 2 x^{9} + 5 x^{8} - 6 x^{7} - 2 x^{6} + 10 x^{5} + 14 x^{4} + 15 x^{3} + 10 x^{2} + x - 1$	$10$	[2,4]	$5^{5}\cdot 103^{4}$	$2$	$14.2764389349$	$22.693611435820433$				$D_{10}$ (as 10T3)	trivial	$2$	$5$	$78.0020419672$
10.0.428197479424.4	$x^{10} + 3 x^{8} + 7 x^{6} + 8 x^{4} + 9 x^{2} + 1$	$10$	[0,5]	$-\,2^{10}\cdot 11^{4}\cdot 13^{4}$	$3$	$14.5601017732$	$23.916521486202797$			?	$D_{10}$ (as 10T3)	trivial	$4$	$4$	$127.064748502$
10.0.429162451875.1	$x^{10} - x^{9} + 5 x^{8} - 13 x^{7} + 17 x^{6} - 7 x^{5} + 13 x^{4} - 54 x^{3} + 78 x^{2} - 45 x + 9$	$10$	[0,5]	$-\,3^{5}\cdot 5^{4}\cdot 41^{4}$	$3$	$14.5633796695$	$24.79919353527449$				$D_{10}$ (as 10T3)	trivial	$6$	$4$	$533.709602782$
10.0.453700517888.1	$x^{10} - 4 x^{9} + 10 x^{8} - 18 x^{7} + 32 x^{6} - 52 x^{5} + 59 x^{4} - 48 x^{3} + 26 x^{2} - 8 x + 4$	$10$	[0,5]	$-\,2^{15}\cdot 61^{4}$	$2$	$14.6445802251$	$22.090722034374522$				$D_{10}$ (as 10T3)	trivial	$2$	$4$	$114.246653574$
10.0.491300061184.2	$x^{10} - 5 x^{8} + 7 x^{6} - 7 x^{4} + 16 x^{2} + 4$	$10$	[0,5]	$-\,2^{18}\cdot 37^{4}$	$2$	$14.7616424498$	$24.331050121192877$				$D_{10}$ (as 10T3)	trivial	$4$	$4$	$452.423073696$
10.2.557171558125.1	$x^{10} - 2 x^{8} - 3 x^{7} - 12 x^{6} - 7 x^{5} + 12 x^{4} - 3 x^{3} + 2 x^{2} - 1$	$10$	[2,4]	$5^{4}\cdot 7^{4}\cdot 13^{5}$	$3$	$14.9485439931$	$21.330729007701542$			?	$D_{10}$ (as 10T3)	trivial	$2$	$5$	$66.5948329047$
10.0.602146582528.1	$x^{10} - x^{9} + 2 x^{8} - 7 x^{7} + 17 x^{6} - 16 x^{5} + 21 x^{4} - 37 x^{3} + 46 x^{2} - 35 x + 13$	$10$	[0,5]	$-\,2^{12}\cdot 43^{5}$	$2$	$15.0650376917$	$18.547236990991408$				$D_{10}$ (as 10T3)	trivial	$2$	$4$	$86.5441645075$
10.2.626668503125.1	$x^{10} - x^{9} - x^{8} - 4 x^{7} + 18 x^{6} + x^{5} - 8 x^{4} + 3 x^{3} + 6 x^{2} - 3 x - 1$	$10$	[2,4]	$5^{5}\cdot 7^{4}\cdot 17^{4}$	$3$	$15.1252926647$	$24.392621835300936$			?	$D_{10}$ (as 10T3)	trivial	$2$	$5$	$57.6899187766$
10.0.645222795363.1	$x^{10} + x^{8} - 4 x^{7} - 2 x^{6} - 6 x^{5} + 7 x^{4} - 2 x^{3} + 17 x^{2} - 12 x + 16$	$10$	[0,5]	$-\,3^{5}\cdot 227^{4}$	$2$	$15.1694896589$	$26.095976701399778$				$D_{10}$ (as 10T3)	trivial	$6$	$4$	$415.723378174$