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 |
$6$ |
$4$ |
$415.723378174$ |