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 |
7.3.3884841.1 |
$x^{7} - 2 x^{6} + 4 x^{4} - 5 x^{3} + 2 x - 1$ |
$7$ |
[3,2] |
$3^{6}\cdot 73^{2}$ |
$2$ |
$8.7365312664$ |
$80.3310880644573$ |
|
|
✓ |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$4.01514406526$ |
7.3.4959529.1 |
$x^{7} - x^{4} - x^{3} + 3 x^{2} - 1$ |
$7$ |
[3,2] |
$17^{2}\cdot 131^{2}$ |
$2$ |
$9.04672711714$ |
$106.35028493145434$ |
|
|
✓ |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$4.32969873501$ |
7.3.12313081.1 |
$x^{7} - x^{6} - 2 x^{5} - 2 x^{4} + 4 x^{3} + 2 x^{2} - 1$ |
$7$ |
[3,2] |
$11^{4}\cdot 29^{2}$ |
$2$ |
$10.30171507$ |
$69.62404259846498$ |
|
|
✓ |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$7.88485808894$ |
7.3.16711744.1 |
$x^{7} - 2 x^{6} + 2 x^{4} - 2 x^{3} - 2 x^{2} + 2 x + 2$ |
$7$ |
[3,2] |
$2^{6}\cdot 7^{2}\cdot 73^{2}$ |
$3$ |
$10.7611888622$ |
$83.71243421506693$ |
|
|
✓ |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$13.3010937939$ |
7.3.16769025.1 |
$x^{7} - x^{6} + x^{5} - 4 x^{4} - 7 x^{2} - 6 x + 1$ |
$7$ |
[3,2] |
$3^{4}\cdot 5^{2}\cdot 7^{2}\cdot 13^{2}$ |
$4$ |
$10.7664504152$ |
$92.90677310638101$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$11.478674046$ |
7.3.17774656.1 |
$x^{7} - x^{6} + 4 x^{5} - 2 x^{3} + 2 x^{2} - 3 x + 1$ |
$7$ |
[3,2] |
$2^{6}\cdot 17^{2}\cdot 31^{2}$ |
$3$ |
$10.8564012494$ |
$92.75844411611145$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$14.5866216451$ |
7.3.18429849.1 |
$x^{7} - 3 x^{6} + 3 x^{5} - x^{4} - 6 x^{3} + 6 x^{2} + 2 x - 3$ |
$7$ |
[3,2] |
$3^{8}\cdot 53^{2}$ |
$2$ |
$10.9126865871$ |
$51.32790030673677$ |
|
|
✓ |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$11.0339522683$ |
7.3.23580736.1 |
$x^{7} + x^{5} - 2 x^{4} - 9 x^{3} - 8 x^{2} - 6 x - 2$ |
$7$ |
[3,2] |
$2^{6}\cdot 607^{2}$ |
$2$ |
$11.3037483238$ |
$180.647707661056$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$18.6592806381$ |
7.3.23882769.1 |
$x^{7} - x^{6} - 3 x^{5} - x^{4} + 4 x^{3} + 6 x^{2} - 3$ |
$7$ |
[3,2] |
$3^{6}\cdot 181^{2}$ |
$2$ |
$11.3243190562$ |
$126.33410800303831$ |
|
|
✓ |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$15.9176612596$ |
7.3.24950025.1 |
$x^{7} - 2 x^{6} + 8 x^{4} - 16 x^{3} + 12 x^{2} - x - 1$ |
$7$ |
[3,2] |
$3^{6}\cdot 5^{2}\cdot 37^{2}$ |
$3$ |
$11.3952649259$ |
$149.31939728603265$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$14.0210509186$ |
7.3.27154521.1 |
$x^{7} - 3 x^{5} - 4 x^{4} - 3 x^{3} - 6 x^{2} - 3 x + 3$ |
$7$ |
[3,2] |
$3^{6}\cdot 193^{2}$ |
$2$ |
$11.5339336689$ |
$131.85798692016243$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$18.2321606839$ |
7.3.30382144.1 |
$x^{7} - 3 x^{6} - x^{5} + 5 x^{4} + 4 x^{3} - 4 x^{2} - 5 x - 1$ |
$7$ |
[3,2] |
$2^{6}\cdot 13^{2}\cdot 53^{2}$ |
$3$ |
$11.7204824325$ |
$220.64350176198943$ |
|
|
✓ |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$17.7656779146$ |
7.3.30647296.1 |
$x^{7} - 2 x^{6} - 2 x^{5} + 4 x^{4} + 3 x^{3} - 6 x^{2} + 4$ |
$7$ |
[3,2] |
$2^{10}\cdot 173^{2}$ |
$2$ |
$11.735040552$ |
$139.3998776837993$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$28.4103090898$ |
7.3.34105600.1 |
$x^{7} - x^{6} - 4 x^{3} + 4 x^{2} - 3 x + 1$ |
$7$ |
[3,2] |
$2^{8}\cdot 5^{2}\cdot 73^{2}$ |
$3$ |
$11.9156559861$ |
$182.00510450511496$ |
|
|
✓ |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$23.3513585749$ |
7.3.34386496.1 |
$x^{7} - 2 x^{6} - x^{4} - 7 x^{3} + x^{2} + 4$ |
$7$ |
[3,2] |
$2^{6}\cdot 733^{2}$ |
$2$ |
$11.929626485$ |
$229.93988505427012$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$31.5723561724$ |
7.3.35450116.1 |
$x^{7} - x^{6} - x^{5} + x^{4} + 3 x^{3} - 6 x^{2} + 2$ |
$7$ |
[3,2] |
$2^{2}\cdot 13^{2}\cdot 229^{2}$ |
$3$ |
$11.9816549534$ |
$214.2308420493291$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$21.4481519348$ |
7.3.35521600.1 |
$x^{7} - 2 x^{6} + 6 x^{4} - 10 x^{3} + 4 x^{2} + 8 x - 8$ |
$7$ |
[3,2] |
$2^{6}\cdot 5^{2}\cdot 149^{2}$ |
$3$ |
$11.9851034908$ |
$80.12624648824512$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$34.0080474072$ |
7.3.36096064.1 |
$x^{7} - x^{6} - 2 x^{5} + 5 x^{4} - 5 x^{3} + x^{2} - 1$ |
$7$ |
[3,2] |
$2^{6}\cdot 751^{2}$ |
$2$ |
$12.0126029078$ |
$233.6890078996337$ |
|
|
✓ |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$23.4730354611$ |
7.3.37258816.1 |
$x^{7} - x^{6} + 3 x^{5} - 5 x^{4} + x^{3} - x^{2} - 5 x - 1$ |
$7$ |
[3,2] |
$2^{6}\cdot 7^{2}\cdot 109^{2}$ |
$3$ |
$12.0671344052$ |
$135.52986744798835$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$33.5217248846$ |
7.3.37945600.1 |
$x^{7} - 3 x^{6} - x^{5} + 5 x^{4} + 2 x^{3} - 2 x^{2} + 4 x + 4$ |
$7$ |
[3,2] |
$2^{8}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}$ |
$4$ |
$12.0986620643$ |
$136.3575339661761$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$25.478790819$ |
7.3.44622400.1 |
$x^{7} - 2 x^{6} - 3 x^{5} + 2 x^{4} + 6 x^{3} - 6 x^{2} - x + 2$ |
$7$ |
[3,2] |
$2^{6}\cdot 5^{2}\cdot 167^{2}$ |
$3$ |
$12.382070573$ |
$250.80487693243262$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$26.2645623565$ |
7.3.44836416.1 |
$x^{7} - x^{6} - 3 x^{5} + 7 x^{4} + 11 x^{3} - 3 x^{2} - 7 x + 1$ |
$7$ |
[3,2] |
$2^{6}\cdot 3^{6}\cdot 31^{2}$ |
$3$ |
$12.3905369497$ |
$82.21200673110225$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$28.6541490478$ |
7.3.49420900.1 |
$x^{7} - x^{5} - 6 x^{4} - 2 x^{3} + x^{2} - 4 x + 1$ |
$7$ |
[3,2] |
$2^{2}\cdot 5^{2}\cdot 19^{2}\cdot 37^{2}$ |
$4$ |
$12.5640626369$ |
$201.03419227828425$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$25.334946873$ |
7.3.50808384.1 |
$x^{7} - 2 x^{6} + 2 x + 2$ |
$7$ |
[3,2] |
$2^{6}\cdot 3^{8}\cdot 11^{2}$ |
$3$ |
$12.6138572475$ |
$73.58171494182155$ |
|
|
✓ |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$38.0037816148$ |
7.3.52186176.1 |
$x^{7} - 3 x^{6} + x^{5} + 5 x^{4} - 9 x^{3} + 5 x^{2} - x - 1$ |
$7$ |
[3,2] |
$2^{6}\cdot 3^{2}\cdot 7^{2}\cdot 43^{2}$ |
$4$ |
$12.6621637304$ |
$75.28687295411977$ |
|
|
✓ |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$25.6809068539$ |
7.3.54597321.1 |
$x^{7} - x^{6} - 2 x^{5} - 3 x^{3} - 4 x^{2} - x + 1$ |
$7$ |
[3,2] |
$3^{4}\cdot 821^{2}$ |
$2$ |
$12.7441299263$ |
$123.97475294805197$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$17.2086678656$ |
7.3.56776225.1 |
$x^{7} - 3 x^{6} + 9 x^{5} - 13 x^{4} + 10 x^{3} - 5 x^{2} - x + 1$ |
$7$ |
[3,2] |
$5^{2}\cdot 11^{2}\cdot 137^{2}$ |
$3$ |
$12.8155743142$ |
$257.72510401565415$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$21.9216903043$ |
7.3.60264169.1 |
$x^{7} - 2 x^{6} + 2 x^{5} + x^{4} - 4 x^{3} + 2 x^{2} - 9 x - 7$ |
$7$ |
[3,2] |
$7^{2}\cdot 1109^{2}$ |
$2$ |
$12.9251926394$ |
$283.4675721744882$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$44.7982333893$ |
7.3.60886809.1 |
$x^{7} - 3 x^{6} + 6 x^{5} - 9 x^{4} + 6 x^{3} - 3 x^{2} - 2 x + 3$ |
$7$ |
[3,2] |
$3^{6}\cdot 17^{4}$ |
$2$ |
$12.9441859993$ |
$48.75762136781643$ |
|
|
✓ |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$21.6919361287$ |
7.3.61089856.1 |
$x^{7} - 3 x^{6} + 4 x^{5} + 2 x^{4} - 6 x^{3} + 2 x^{2} - 3 x - 1$ |
$7$ |
[3,2] |
$2^{6}\cdot 977^{2}$ |
$2$ |
$12.9503438649$ |
$248.10548755567996$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$34.3499783429$ |
7.3.64770304.1 |
$x^{7} - x^{5} - x^{4} - 4 x^{3} - 2 x^{2} - 2 x - 2$ |
$7$ |
[3,2] |
$2^{8}\cdot 503^{2}$ |
$2$ |
$13.0590278456$ |
$252.99114156051223$ |
|
|
✓ |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$30.5053739529$ |
7.3.66699889.1 |
$x^{7} - 3 x^{6} - x^{5} + 13 x^{4} - 10 x^{3} - 11 x^{2} + 13 x + 2$ |
$7$ |
[3,2] |
$8167^{2}$ |
$1$ |
$13.1139087902$ |
$90.37145567047152$ |
|
|
✓ |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$44.4308833354$ |
7.3.68145025.1 |
$x^{7} - x^{5} - 6 x^{4} + 10 x^{3} + 2 x^{2} - 7 x + 2$ |
$7$ |
[3,2] |
$5^{2}\cdot 13^{2}\cdot 127^{2}$ |
$3$ |
$13.1541267461$ |
$266.3713384984645$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$32.7519505657$ |
7.3.68823616.1 |
$x^{7} - 3 x^{6} + x^{5} + 5 x^{4} - 6 x^{3} - 2 x^{2} + 4 x + 2$ |
$7$ |
[3,2] |
$2^{6}\cdot 17^{2}\cdot 61^{2}$ |
$3$ |
$13.1727601371$ |
$143.4319861593566$ |
|
|
✓ |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$47.2533924852$ |
7.3.74097664.1 |
$x^{7} - 2 x^{6} + 2 x^{4} - 3 x^{3} + 2 x^{2} - 2$ |
$7$ |
[3,2] |
$2^{10}\cdot 269^{2}$ |
$2$ |
$13.3124438223$ |
$73.63898559015824$ |
|
|
✓ |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$52.397972037$ |
7.3.75186241.1 |
$x^{7} - x^{6} + x^{5} + 5 x^{4} + 6 x^{3} + 11 x^{2} - 3 x - 1$ |
$7$ |
[3,2] |
$13^{2}\cdot 23^{2}\cdot 29^{2}$ |
$3$ |
$13.3402087218$ |
$240.79444171443956$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$17.5170340912$ |
7.3.76370121.1 |
$x^{7} - 3 x^{5} - 3 x^{4} - 4 x^{3} + 6 x^{2} - 7 x + 2$ |
$7$ |
[3,2] |
$3^{4}\cdot 971^{2}$ |
$2$ |
$13.3700159551$ |
$134.82526665892632$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$61.9026285591$ |
7.3.77951241.1 |
$x^{7} - 2 x^{6} + 6 x^{5} - 2 x^{4} - 2 x^{3} + 18 x^{2} - 15 x + 3$ |
$7$ |
[3,2] |
$3^{8}\cdot 109^{2}$ |
$2$ |
$13.4092130338$ |
$187.39877034063932$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$32.099888582$ |
7.3.78730129.1 |
$x^{7} - 2 x^{5} - 4 x^{4} - 7 x^{3} + 6 x + 1$ |
$7$ |
[3,2] |
$19^{2}\cdot 467^{2}$ |
$2$ |
$13.4282722456$ |
$262.3743571527446$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$17.1930554148$ |
7.3.83612736.1 |
$x^{7} - 2 x^{6} + 6 x^{5} - 2 x^{4} - 3 x^{3} - 8 x + 2$ |
$7$ |
[3,2] |
$2^{6}\cdot 3^{4}\cdot 127^{2}$ |
$3$ |
$13.5441952229$ |
$109.46245773927733$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$64.9989106493$ |
7.3.84437721.1 |
$x^{7} - 3 x^{6} + 2 x^{5} + 6 x^{4} - 7 x^{3} - 4 x^{2} + 5 x - 1$ |
$7$ |
[3,2] |
$3^{4}\cdot 1021^{2}$ |
$2$ |
$13.5632059889$ |
$76.95022159569126$ |
|
|
✓ |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$25.6890288323$ |
7.3.85655025.1 |
$x^{7} - 2 x^{6} - 3 x^{5} + 2 x^{4} + 9 x^{3} + 2 x^{2} - 7 x - 5$ |
$7$ |
[3,2] |
$3^{2}\cdot 5^{2}\cdot 617^{2}$ |
$3$ |
$13.5909685217$ |
$280.6956865499805$ |
|
|
✓ |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$33.1488936884$ |
7.3.87011584.1 |
$x^{7} - 2 x^{6} - 3 x^{5} - 5 x^{3} - 10 x^{2} - 8 x - 2$ |
$7$ |
[3,2] |
$2^{8}\cdot 11^{2}\cdot 53^{2}$ |
$3$ |
$13.6215113437$ |
$248.6951763737097$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$37.592823915$ |
7.3.87778161.1 |
$x^{7} - 3 x^{5} - 2 x^{4} + 3 x^{2} - 3 x - 3$ |
$7$ |
[3,2] |
$3^{6}\cdot 347^{2}$ |
$2$ |
$13.6385907198$ |
$73.54722749388725$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$34.3658523325$ |
7.3.88811776.1 |
$x^{7} - 2 x^{6} + 4 x^{4} - 11 x^{3} + 4 x^{2} + 4 x - 2$ |
$7$ |
[3,2] |
$2^{8}\cdot 19^{2}\cdot 31^{2}$ |
$3$ |
$13.6614184359$ |
$125.86352973294812$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$57.9714977253$ |
7.3.91623184.1 |
$x^{7} - 4 x^{5} - x^{4} + 2 x^{3} + 13 x^{2} - 13 x + 3$ |
$7$ |
[3,2] |
$2^{4}\cdot 2393^{2}$ |
$2$ |
$13.7223767881$ |
$357.81493300787105$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$34.0352530806$ |
7.3.92294449.1 |
$x^{7} - 3 x^{6} - x^{5} + 4 x^{4} + 5 x^{3} - 9 x^{2} + x + 1$ |
$7$ |
[3,2] |
$13^{2}\cdot 739^{2}$ |
$2$ |
$13.7366940616$ |
$294.71436293345596$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$21.0685742123$ |
7.3.92833225.1 |
$x^{7} - 2 x^{6} - x^{5} - 4 x^{4} - 2 x^{3} + x^{2} + 3 x - 1$ |
$7$ |
[3,2] |
$5^{2}\cdot 41^{2}\cdot 47^{2}$ |
$3$ |
$13.7481210787$ |
$128.35738485272273$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$27.205000544$ |
7.3.94167616.1 |
$x^{7} - 2 x^{6} - 2 x^{5} - 5 x^{3} - 2 x^{2} - x - 2$ |
$7$ |
[3,2] |
$2^{6}\cdot 1213^{2}$ |
$2$ |
$13.7761796155$ |
$321.7008393885537$ |
|
|
✓ |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$38.256796704$ |
7.3.95531076.1 |
$x^{7} - 2 x^{6} + x^{4} + x^{3} - 4 x + 2$ |
$7$ |
[3,2] |
$2^{2}\cdot 3^{6}\cdot 181^{2}$ |
$3$ |
$13.8044995541$ |
$98.21874046652506$ |
|
|
✓ |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$48.7245231412$ |