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 |
9.1.362467097.1 |
$x^{9} + x^{7} - 2 x^{6} + 2 x^{5} + 2 x^{4} + 4 x^{3} + x^{2} - 1$ |
$9$ |
[1,4] |
$23^{3}\cdot 31^{3}$ |
$2$ |
$8.93366870848$ |
$26.70205984563738$ |
|
|
|
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$3.47323076099$ |
9.1.584277056.1 |
$x^{9} - 2 x^{8} + 2 x^{7} - x^{6} + 2 x^{5} - x^{3} + 2 x^{2} + 1$ |
$9$ |
[1,4] |
$2^{6}\cdot 11^{3}\cdot 19^{3}$ |
$3$ |
$9.42038731855$ |
$22.948790792894883$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$7.81055328458$ |
9.1.1036433728.1 |
$x^{9} - x^{8} + x^{7} - 4 x^{6} + x^{4} + 7 x^{3} + 3 x^{2} - 1$ |
$9$ |
[1,4] |
$2^{6}\cdot 11^{3}\cdot 23^{3}$ |
$3$ |
$10.0398410582$ |
$25.24915941663813$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$6.19432761349$ |
9.1.1067589632.1 |
$x^{9} - 4 x^{8} + 10 x^{7} - 18 x^{6} + 26 x^{5} - 32 x^{4} + 34 x^{3} - 28 x^{2} + 16 x - 4$ |
$9$ |
[1,4] |
$2^{13}\cdot 19^{4}$ |
$2$ |
$10.0729351651$ |
$15.533349925214662$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$15.7263694056$ |
9.1.1222181568.1 |
$x^{9} - x^{8} - 3 x^{6} + 3 x^{5} - x^{4} + 3 x^{3} - 6 x^{2} + 4 x - 1$ |
$9$ |
[1,4] |
$2^{6}\cdot 3^{3}\cdot 29^{4}$ |
$3$ |
$10.2254339491$ |
$18.65475810617763$ |
|
|
✓ |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$6.29153929567$ |
9.1.1676676672.1 |
$x^{9} - x^{6} + x^{3} + 1$ |
$9$ |
[1,4] |
$2^{6}\cdot 3^{9}\cdot 11^{3}$ |
$3$ |
$10.591045006$ |
$18.96812793558615$ |
|
|
✓ |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$14.7493781811$ |
9.1.2238728000.1 |
$x^{9} - 2 x^{8} + 5 x^{7} - 5 x^{6} + 7 x^{5} - 6 x^{4} + 12 x^{3} - 7 x^{2} - x + 1$ |
$9$ |
[1,4] |
$2^{6}\cdot 5^{3}\cdot 23^{4}$ |
$3$ |
$10.9367689367$ |
$17.0229798060099$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$11.2143678466$ |
9.1.2498846293.1 |
$x^{9} + 2 x^{7} - 2 x^{6} + 8 x^{5} + 4 x^{4} + 11 x^{3} + 4 x^{2} - 1$ |
$9$ |
[1,4] |
$23^{3}\cdot 59^{3}$ |
$2$ |
$11.0711639598$ |
$36.837480912787726$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$8.98120788555$ |
9.1.2537716544.1 |
$x^{9} - x^{7} - 5 x^{6} + 3 x^{5} + 4 x^{4} + 8 x^{3} + x^{2} + x - 1$ |
$9$ |
[1,4] |
$2^{6}\cdot 11^{3}\cdot 31^{3}$ |
$3$ |
$11.0901679568$ |
$29.31324199109173$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$9.1868051415$ |
9.1.2744000000.1 |
$x^{9} - 4 x^{8} + 8 x^{7} - 11 x^{6} + 9 x^{5} - 5 x^{4} + 7 x^{3} - 6 x^{2} + x - 1$ |
$9$ |
[1,4] |
$2^{9}\cdot 5^{6}\cdot 7^{3}$ |
$3$ |
$11.1868894208$ |
$21.881345138484406$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$13.0979097965$ |
9.1.3456000000.1 |
$x^{9} - x^{8} + 2 x^{6} + 2 x^{5} - 4 x^{4} + 6 x^{3} - 4 x^{2} + 3 x - 1$ |
$9$ |
[1,4] |
$2^{13}\cdot 3^{3}\cdot 5^{6}$ |
$3$ |
$11.4773473676$ |
$18.047994736019533$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$34.1858836091$ |
9.3.3539149227.1 |
$x^{9} - 2 x^{8} - 3 x^{7} + 9 x^{6} - 4 x^{5} - 6 x^{4} + 10 x^{3} - 4 x^{2} - x - 1$ |
$9$ |
[3,3] |
$-\,3^{3}\cdot 107^{4}$ |
$2$ |
$11.5077061568$ |
$17.916472867168917$ |
|
|
✓ |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$5$ |
$15.4338108409$ |
9.1.3652264000.1 |
$x^{9} - 2 x^{7} - x^{6} - 2 x^{4} + 3 x^{3} + 2 x^{2} + 2 x + 1$ |
$9$ |
[1,4] |
$2^{6}\cdot 5^{3}\cdot 7^{3}\cdot 11^{3}$ |
$4$ |
$11.5480035029$ |
$31.147057781097917$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$24.7447313885$ |
9.1.3779136000.1 |
$x^{9} - 3 x^{8} + 6 x^{7} - 11 x^{6} + 15 x^{5} - 9 x^{4} - 3 x^{3} + 6 x^{2} - 3$ |
$9$ |
[1,4] |
$2^{9}\cdot 3^{10}\cdot 5^{3}$ |
$3$ |
$11.5919026326$ |
$22.786176627742247$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$21.036675158$ |
9.1.4251528000.1 |
$x^{9} + 3 x^{7} - 3 x^{6} + 3 x^{5} + 3 x^{2} - 3 x + 1$ |
$9$ |
[1,4] |
$2^{6}\cdot 3^{12}\cdot 5^{3}$ |
$3$ |
$11.7446029235$ |
$16.324507030901437$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$20.8171614701$ |
9.3.4314825152.1 |
$x^{9} - 2 x^{8} + 2 x^{7} - 3 x^{6} - 6 x^{5} + 2 x^{4} - 7 x^{3} + 6 x^{2} - 2 x + 1$ |
$9$ |
[3,3] |
$-\,2^{6}\cdot 11^{3}\cdot 37^{3}$ |
$3$ |
$11.7639038669$ |
$32.024611388968125$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$5$ |
$33.5921152358$ |
9.1.4353564672.1 |
$x^{9} - 3 x^{7} + 9 x^{5} - 6 x^{4} - 3 x^{3} + 6 x - 2$ |
$9$ |
[1,4] |
$2^{13}\cdot 3^{12}$ |
$2$ |
$11.7755927582$ |
$16.3891614959171$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$45.8507333647$ |
9.1.4537258673.1 |
$x^{9} - 3 x^{8} + 5 x^{7} - 5 x^{6} + x^{5} + 3 x^{4} - x^{3} + 4 x^{2} - 12 x + 8$ |
$9$ |
[1,4] |
$17^{3}\cdot 31^{4}$ |
$2$ |
$11.8297906742$ |
$22.956480566497994$ |
|
|
|
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$13.9114005334$ |
9.1.4603598912.1 |
$x^{9} - x^{8} + 4 x^{7} - x^{6} + 8 x^{5} + 5 x^{4} + 11 x^{3} + 8 x^{2} + 6 x + 2$ |
$9$ |
[1,4] |
$2^{6}\cdot 11^{4}\cdot 17^{3}$ |
$3$ |
$11.8488853604$ |
$21.707382906759687$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$28.1234681478$ |
9.1.5341020992.1 |
$x^{9} - 2 x^{7} - 4 x^{6} + 8 x^{5} - 8 x^{4} + 4 x^{3} + 8 x^{2} - 8$ |
$9$ |
[1,4] |
$2^{6}\cdot 19^{3}\cdot 23^{3}$ |
$3$ |
$12.0461188237$ |
$33.1838966610029$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$12.3756975872$ |
9.3.5508110403.1 |
$x^{9} - 9 x^{7} - 3 x^{6} + 27 x^{5} + 18 x^{4} - 25 x^{3} - 27 x^{2} - 6 x + 1$ |
$9$ |
[3,3] |
$-\,3^{9}\cdot 23^{4}$ |
$2$ |
$12.0874203768$ |
$17.278473921432806$ |
|
|
✓ |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$5$ |
$19.8234627097$ |
9.1.6118445789.1 |
$x^{9} - 4 x^{7} - 3 x^{6} + 4 x^{5} + 2 x^{4} + 12 x^{3} + 2 x - 1$ |
$9$ |
[1,4] |
$31^{3}\cdot 59^{3}$ |
$2$ |
$12.2293836207$ |
$42.76680956068619$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$14.6316877154$ |
9.1.6204088832.1 |
$x^{9} - 3 x^{8} + 5 x^{7} - 6 x^{6} + 4 x^{5} + 6 x^{4} - 15 x^{3} + x^{2} + 7 x + 2$ |
$9$ |
[1,4] |
$2^{9}\cdot 59^{4}$ |
$2$ |
$12.2482864371$ |
$21.72556098240043$ |
|
|
|
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$59.2944846688$ |
9.1.6772724288.1 |
$x^{9} - x^{6} - 4 x^{5} + 6 x^{4} + 3 x^{3} - 4 x^{2} + 2 x - 1$ |
$9$ |
[1,4] |
$2^{6}\cdot 11^{3}\cdot 43^{3}$ |
$3$ |
$12.3682155105$ |
$34.52369205633357$ |
|
|
✓ |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$31.6414476341$ |
9.1.6956932429.1 |
$x^{9} - x^{8} + x^{7} + 2 x^{6} + 3 x^{5} - 2 x^{4} + 7 x^{3} + 6 x^{2} + 8$ |
$9$ |
[1,4] |
$23^{3}\cdot 83^{3}$ |
$2$ |
$12.4051487463$ |
$43.69210454990696$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$18.2573617812$ |
9.1.7388168000.1 |
$x^{9} - 2 x^{8} - x^{7} + x^{6} + x^{5} + 4 x^{4} + 10 x^{3} + 7 x^{2} + x + 1$ |
$9$ |
[1,4] |
$2^{6}\cdot 5^{3}\cdot 31^{4}$ |
$3$ |
$12.4883219027$ |
$19.762983718745776$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$17.4275915124$ |
9.1.8012006001.1 |
$x^{9} - x^{8} + 2 x^{7} - 7 x^{6} + 5 x^{5} + 3 x^{4} + 17 x^{3} + 6 x^{2} - 1$ |
$9$ |
[1,4] |
$3^{3}\cdot 23^{3}\cdot 29^{3}$ |
$3$ |
$12.6013100175$ |
$44.73253849269008$ |
|
|
|
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$21.8062883305$ |
9.1.8302761792.1 |
$x^{9} - 3 x^{7} - 3 x^{6} + 3 x^{5} + 6 x^{3} + 3 x^{2} + 3 x + 1$ |
$9$ |
[1,4] |
$2^{6}\cdot 3^{10}\cdot 13^{3}$ |
$3$ |
$12.6513200343$ |
$20.620529060204074$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$34.165717418$ |
9.1.8640364608.1 |
$x^{9} - x^{6} + 3 x^{3} - 1$ |
$9$ |
[1,4] |
$2^{6}\cdot 3^{9}\cdot 19^{3}$ |
$3$ |
$12.7074707528$ |
$24.929004046463465$ |
|
|
✓ |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$48.4532063405$ |
9.1.8677779264.1 |
$x^{9} - 2 x^{8} - x^{7} + 7 x^{6} + x^{5} - 4 x^{4} + 2 x^{3} - 7 x^{2} - 3 x - 1$ |
$9$ |
[1,4] |
$2^{6}\cdot 3^{3}\cdot 7^{3}\cdot 11^{4}$ |
$4$ |
$12.7135730302$ |
$24.126407213910475$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$21.6686883139$ |
9.1.9261000000.1 |
$x^{9} - x^{7} - 7 x^{6} - 3 x^{5} + 8 x^{4} + 10 x^{3} + 7 x^{2} - x + 1$ |
$9$ |
[1,4] |
$2^{6}\cdot 3^{3}\cdot 5^{6}\cdot 7^{3}$ |
$4$ |
$12.8057916499$ |
$21.270432174892346$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$40.4895429774$ |
9.1.10056646017.1 |
$x^{9} - 4 x^{8} + 2 x^{7} + 9 x^{6} - 3 x^{5} - 17 x^{4} - 7 x^{3} + 30 x^{2} + 7 x - 19$ |
$9$ |
[1,4] |
$3^{3}\cdot 11^{3}\cdot 23^{4}$ |
$3$ |
$12.9236052733$ |
$27.54995462791182$ |
|
|
|
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$24.1053231738$ |
9.1.11299742784.1 |
$x^{9} - 2 x^{8} + 2 x^{7} - 3 x^{6} + 10 x^{5} - 10 x^{4} + 5 x^{3} + 2 x^{2} + 2 x + 1$ |
$9$ |
[1,4] |
$2^{6}\cdot 3^{3}\cdot 11^{3}\cdot 17^{3}$ |
$4$ |
$13.0920488626$ |
$37.59829009385996$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$43.2543917046$ |
9.3.11666192832.1 |
$x^{9} - 3 x^{6} + 12 x^{5} - 6 x^{4} - 9 x^{3} + 12 x^{2} - 6 x + 1$ |
$9$ |
[3,3] |
$-\,2^{6}\cdot 3^{12}\cdot 7^{3}$ |
$3$ |
$13.1385574197$ |
$19.31541720291671$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$5$ |
$77.2180549808$ |
9.1.11666192832.1 |
$x^{9} + 6 x^{7} - 3 x^{6} + 9 x^{5} - 3 x^{4} + x^{3} - 3 x - 1$ |
$9$ |
[1,4] |
$2^{6}\cdot 3^{12}\cdot 7^{3}$ |
$3$ |
$13.1385574197$ |
$22.89500214913901$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$36.4093654633$ |
9.1.12005000000.1 |
$x^{9} - 4 x^{8} + 7 x^{7} - 7 x^{6} + 5 x^{5} - 5 x^{2} + 15 x - 5$ |
$9$ |
[1,4] |
$2^{6}\cdot 5^{7}\cdot 7^{4}$ |
$3$ |
$13.1804163554$ |
$16.05871118442657$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$33.4614240148$ |
9.1.12766754304.1 |
$x^{9} - 2 x^{8} + 4 x^{7} - x^{6} + 9 x^{5} - 7 x^{4} + 3 x^{3} - 4 x^{2} - 5 x - 1$ |
$9$ |
[1,4] |
$2^{9}\cdot 3^{3}\cdot 31^{4}$ |
$3$ |
$13.2708222846$ |
$27.27636339397171$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$45.3112340278$ |
9.1.13077534016.1 |
$x^{9} + 4 x^{7} - 6 x^{6} + 4 x^{5} - 4 x^{4} + 8 x^{3} - 8 x - 8$ |
$9$ |
[1,4] |
$2^{6}\cdot 19^{3}\cdot 31^{3}$ |
$3$ |
$13.3063342545$ |
$38.52514758928459$ |
|
|
|
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$36.8418002943$ |
9.1.13686220288.1 |
$x^{9} - x^{7} - 4 x^{6} + 2 x^{5} - 4 x^{4} + 11 x^{3} + 2 x^{2} - 8$ |
$9$ |
[1,4] |
$2^{9}\cdot 13^{3}\cdot 23^{3}$ |
$3$ |
$13.373766154$ |
$48.908077042549934$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$21.364503862$ |
9.1.14693280768.1 |
$x^{9} + 3 x^{7} + 9 x^{5} - 6 x^{4} + 9 x^{3} - 18 x^{2} + 12 x - 4$ |
$9$ |
[1,4] |
$2^{10}\cdot 3^{15}$ |
$2$ |
$13.4796887448$ |
$16.714067630295588$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$91.8904659113$ |
9.1.14905098181.1 |
$x^{9} - x^{8} + 3 x^{7} - 4 x^{6} + 17 x^{5} - 10 x^{4} + 21 x^{3} - 10 x^{2} + 8$ |
$9$ |
[1,4] |
$23^{3}\cdot 107^{3}$ |
$2$ |
$13.5011430216$ |
$49.60846701924985$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$27.5837340644$ |
9.1.14992384000.1 |
$x^{9} - 2 x^{8} - 3 x^{7} + 10 x^{6} - 3 x^{5} - 12 x^{4} + 9 x^{3} - 6 x^{2} + 6 x - 2$ |
$9$ |
[1,4] |
$2^{13}\cdot 5^{3}\cdot 11^{4}$ |
$3$ |
$13.5099051422$ |
$26.4283269025114$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$75.3532187485$ |
9.1.15326915904.1 |
$x^{9} - 4 x^{6} + 12 x^{3} - 8$ |
$9$ |
[1,4] |
$2^{6}\cdot 3^{9}\cdot 23^{3}$ |
$3$ |
$13.5430723064$ |
$27.427867679287534$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$26.5304162357$ |
9.1.17034106517.1 |
$x^{9} - x^{7} - 4 x^{6} - 3 x^{5} + 5 x^{4} + 11 x^{3} - 4 x^{2} + 4 x - 8$ |
$9$ |
[1,4] |
$31^{3}\cdot 83^{3}$ |
$2$ |
$13.7029244117$ |
$50.724747411889595$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$19.8755762682$ |
9.1.17495004736.1 |
$x^{9} - 2 x^{7} - 5 x^{6} + 12 x^{5} + 8 x^{4} + 15 x^{3} + 4 x^{2} + 2 x - 1$ |
$9$ |
[1,4] |
$2^{6}\cdot 11^{3}\cdot 59^{3}$ |
$3$ |
$13.7436334162$ |
$40.43980122062354$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$56.6928571146$ |
9.3.18177663843.1 |
$x^{9} - 9 x^{7} - 3 x^{6} + 27 x^{5} + 18 x^{4} - 23 x^{3} - 27 x^{2} - 12 x - 3$ |
$9$ |
[3,3] |
$-\,3^{9}\cdot 31^{4}$ |
$2$ |
$13.8022113764$ |
$20.05960194310363$ |
|
|
✓ |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$5$ |
$50.6124783308$ |
9.1.18324175168.1 |
$x^{9} - 4 x^{8} + 9 x^{7} - 13 x^{6} + 17 x^{5} - 26 x^{4} + 36 x^{3} - 35 x^{2} + 21 x - 9$ |
$9$ |
[1,4] |
$2^{6}\cdot 13^{3}\cdot 19^{4}$ |
$3$ |
$13.8145279143$ |
$24.947965821847426$ |
|
|
|
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$45.701942614$ |
9.1.18566895168.1 |
$x^{9} - 5 x^{6} + 11 x^{3} - 1$ |
$9$ |
[1,4] |
$2^{6}\cdot 3^{10}\cdot 17^{3}$ |
$3$ |
$13.8347409544$ |
$23.58047712423637$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$96.6319155891$ |
9.1.18821096000.1 |
$x^{9} + 2 x^{7} - x^{6} + 4 x^{5} + 4 x^{4} + 5 x^{3} + 2 x^{2} - 1$ |
$9$ |
[1,4] |
$2^{6}\cdot 5^{3}\cdot 7^{3}\cdot 19^{3}$ |
$4$ |
$13.8556598224$ |
$40.93525371070981$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$50.152847838$ |
9.1.18991421632.1 |
$x^{9} - x^{8} + 5 x^{6} + 2 x^{5} + 2 x^{4} + 12 x^{3} + 8 x^{2} + 8$ |
$9$ |
[1,4] |
$2^{6}\cdot 23^{3}\cdot 29^{3}$ |
$3$ |
$13.8695363062$ |
$51.65268628057983$ |
|
|
? |
$S_3^2$ (as 9T8) |
trivial |
$2$ |
$4$ |
$30.693091584$ |