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 |
10.4.3120654523.1 |
$x^{10} - 2 x^{9} + 2 x^{8} - 7 x^{7} + 8 x^{6} - 3 x^{5} + 8 x^{4} - 7 x^{3} + 2 x^{2} - 2 x + 1$ |
$10$ |
[4,3] |
$-\,7^{2}\cdot 43\cdot 1217^{2}$ |
$3$ |
$8.90070831902$ |
$605.2412742039327$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$6$ |
$4.82542435626$ |
10.4.3191230411.1 |
$x^{10} - x^{9} - 4 x^{6} - x^{5} - x^{4} + 3 x^{2} + 3 x + 1$ |
$10$ |
[4,3] |
$-\,3191230411$ |
$1$ |
$8.9206359493$ |
$56490.97636791207$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$4.892791489720255$ |
10.4.3196989667.1 |
$x^{10} - x^{9} - x^{8} - 2 x^{7} + x^{6} - 2 x^{4} + x^{3} + x^{2} + 2 x - 1$ |
$10$ |
[4,3] |
$-\,29\cdot 73^{2}\cdot 137\cdot 151$ |
$4$ |
$8.92224456239$ |
$13528.915874373493$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$4.898963260479714$ |
10.4.3202088651.1 |
$x^{10} - 2 x^{9} - x^{8} + 2 x^{7} + 2 x^{6} - 5 x^{4} + 3 x^{3} + 4 x^{2} - 2 x - 1$ |
$10$ |
[4,3] |
$-\,53^{2}\cdot 59\cdot 139^{2}$ |
$3$ |
$8.92366658022$ |
$659.2821854107693$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$6$ |
$4.90098937737$ |
10.4.3204506051.1 |
$x^{10} - x^{9} - 2 x^{8} + 2 x^{7} + 3 x^{6} - 4 x^{5} - 2 x^{4} + 2 x^{3} + x + 1$ |
$10$ |
[4,3] |
$-\,3204506051$ |
$1$ |
$8.92434003898$ |
$56608.35672407388$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$4.907691153330467$ |
10.4.3209183443.1 |
$x^{10} - 3 x^{9} + 2 x^{8} + 2 x^{7} - 3 x^{6} + x^{4} + x^{3} - 2 x^{2} + x + 1$ |
$10$ |
[4,3] |
$-\,53\cdot 6091\cdot 9941$ |
$3$ |
$8.92564180728$ |
$56649.6552769741$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$4.909191013338611$ |
10.4.3259151627.1 |
$x^{10} - x^{9} - 2 x^{8} + x^{7} + x^{6} - 2 x^{5} + 4 x^{4} + x^{3} - 5 x^{2} + 1$ |
$10$ |
[4,3] |
$-\,107\cdot 5519^{2}$ |
$2$ |
$8.93944293868$ |
$768.4614499114448$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$6$ |
$4.95867924374$ |
10.4.3295770139.1 |
$x^{10} - 2 x^{9} - x^{8} + 7 x^{7} - 7 x^{6} - x^{5} + 9 x^{4} - 6 x^{3} - x^{2} + 3 x - 1$ |
$10$ |
[4,3] |
$-\,11287\cdot 291997$ |
$2$ |
$8.9494365117$ |
$57408.79844588284$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$4.994678643135897$ |
10.4.3307392083.1 |
$x^{10} - x^{9} - 4 x^{8} + 2 x^{7} + 4 x^{6} - x^{4} - 4 x^{3} + 3 x - 1$ |
$10$ |
[4,3] |
$-\,30091\cdot 109913$ |
$2$ |
$8.95258737374$ |
$57509.93029903618$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.005481880274628$ |
10.4.3312142387.1 |
$x^{10} - 2 x^{9} - 3 x^{8} + 8 x^{7} - 8 x^{5} + 2 x^{4} + 3 x^{3} + 2 x^{2} - x - 1$ |
$10$ |
[4,3] |
$-\,67\cdot 79^{2}\cdot 89^{2}$ |
$3$ |
$8.95387237561$ |
$686.3504935526746$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$6$ |
$5.00702615919$ |
10.4.3316535227.1 |
$x^{10} - x^{7} + x^{6} + 3 x^{5} - 2 x^{3} - 3 x^{2} + x + 1$ |
$10$ |
[4,3] |
$-\,1483\cdot 2236369$ |
$2$ |
$8.95505920482$ |
$57589.36730855792$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.01675572386$ |
10.4.3338068347.1 |
$x^{10} - 2 x^{9} - 2 x^{8} + 5 x^{7} + x^{6} - 3 x^{5} - 2 x^{3} - x^{2} + 3 x + 1$ |
$10$ |
[4,3] |
$-\,3^{3}\cdot 11119^{2}$ |
$2$ |
$8.96085649825$ |
$182.6389881706532$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$6$ |
$5.03687290029$ |
10.4.3342094627.1 |
$x^{10} - 4 x^{9} + 8 x^{8} - 12 x^{7} + 12 x^{6} - 9 x^{5} + 5 x^{4} - x^{2} + 2 x - 1$ |
$10$ |
[4,3] |
$-\,151\cdot 22133077$ |
$2$ |
$8.96193674424$ |
$57810.85215597501$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.0362191642113645$ |
10.4.3343581827.1 |
$x^{10} - 2 x^{9} + 6 x^{7} - 6 x^{6} - x^{5} + 8 x^{4} - 5 x^{3} - x^{2} + 2 x - 1$ |
$10$ |
[4,3] |
$-\,3343581827$ |
$1$ |
$8.96233546198$ |
$57823.71336225303$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.037308830638455$ |
10.4.3351773171.1 |
$x^{10} - x^{9} - 2 x^{8} + x^{6} + 3 x^{5} + x^{4} - 3 x^{3} - 2 x^{2} + 2 x + 1$ |
$10$ |
[4,3] |
$-\,3351773171$ |
$1$ |
$8.96452870168$ |
$57894.50035193326$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.043929323872601$ |
10.4.3367690163.1 |
$x^{10} - 2 x^{9} + 3 x^{8} - 3 x^{7} - x^{6} + 3 x^{5} - 5 x^{4} + 3 x^{3} - x + 1$ |
$10$ |
[4,3] |
$-\,29\cdot 103\cdot 181\cdot 6229$ |
$4$ |
$8.96877673152$ |
$58031.803030752024$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.061587924899763$ |
10.4.3385346179.1 |
$x^{10} - 2 x^{9} + x^{8} + 3 x^{7} - 6 x^{6} + 3 x^{5} + 2 x^{4} - 5 x^{3} + 2 x^{2} + x - 1$ |
$10$ |
[4,3] |
$-\,41\cdot 101\cdot 817519$ |
$3$ |
$8.97346779573$ |
$58183.727785352494$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.080055721571213$ |
10.4.3385465123.1 |
$x^{10} - 4 x^{9} + 6 x^{8} - 2 x^{7} - 7 x^{6} + 11 x^{5} - 4 x^{4} - 4 x^{3} + 5 x^{2} - 1$ |
$10$ |
[4,3] |
$-\,3385465123$ |
$1$ |
$8.97349932348$ |
$58184.749917826404$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.079708376740111$ |
10.4.3393524187.1 |
$x^{10} - 4 x^{9} + 7 x^{8} - 4 x^{7} - 6 x^{6} + 13 x^{5} - 9 x^{4} - x^{3} + 5 x^{2} - 4 x + 1$ |
$10$ |
[4,3] |
$-\,3^{3}\cdot 1367\cdot 91943$ |
$3$ |
$8.9756331707$ |
$19417.987614580456$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.08516157966$ |
10.4.3398303207.1 |
$x^{10} - 3 x^{9} + 3 x^{8} + x^{7} - 5 x^{6} + 8 x^{5} - 15 x^{4} + 13 x^{3} - 5 x^{2} + 2 x + 1$ |
$10$ |
[4,3] |
$-\,13^{2}\cdot 167\cdot 347^{2}$ |
$3$ |
$8.9768963876$ |
$867.949883345807$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$6$ |
$5.08704229856$ |
10.4.3405971875.1 |
$x^{10} - 3 x^{9} + 5 x^{8} - 4 x^{7} - 2 x^{6} + 8 x^{5} - 8 x^{4} + x^{3} + 3 x^{2} - 3 x + 1$ |
$10$ |
[4,3] |
$-\,5^{5}\cdot 1039\cdot 1049$ |
$3$ |
$8.97892007494$ |
$2334.4281955116976$ |
|
|
✓ |
$S_5^2 \wr C_2$ (as 10T43) |
trivial |
$2$ |
$6$ |
$5.09688776432$ |
10.4.3406095083.1 |
$x^{10} - x^{9} - x^{8} + 2 x^{7} - 4 x^{6} - 2 x^{5} + 9 x^{4} - 6 x^{2} + 1$ |
$10$ |
[4,3] |
$-\,911\cdot 3738853$ |
$2$ |
$8.97895255485$ |
$58361.76045151483$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.094818911753069$ |
10.4.3408425011.1 |
$x^{10} - 3 x^{8} - x^{6} + 5 x^{4} - 4 x^{3} - x^{2} + 3 x - 1$ |
$10$ |
[4,3] |
$-\,1721\cdot 1980491$ |
$2$ |
$8.97956656813$ |
$58381.71812305629$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.098324537600664$ |
10.4.3409004107.1 |
$x^{10} - x^{8} - x^{7} - x^{6} - 3 x^{5} + 3 x^{4} + x^{3} + 3 x - 1$ |
$10$ |
[4,3] |
$-\,3409004107$ |
$1$ |
$8.97971912051$ |
$58386.67747868515$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.09993147188$ |
10.4.3410947967.1 |
$x^{10} - 2 x^{9} - 2 x^{8} + 7 x^{7} - x^{6} - 8 x^{5} + 2 x^{4} + 6 x^{3} - 3 x - 1$ |
$10$ |
[4,3] |
$-\,7^{2}\cdot 47\cdot 1217^{2}$ |
$3$ |
$8.98023102484$ |
$632.766149537094$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$6$ |
$5.10029615868$ |
10.4.3410962979.1 |
$x^{10} - 3 x^{9} + 5 x^{8} - 3 x^{7} - 3 x^{6} + 8 x^{5} - 5 x^{4} - x^{3} + 4 x^{2} - x - 1$ |
$10$ |
[4,3] |
$-\,41\cdot 619\cdot 134401$ |
$3$ |
$8.98023497714$ |
$58403.450060762676$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.101160460584068$ |
10.4.3412809931.1 |
$x^{10} - x^{9} - 2 x^{8} + 5 x^{7} + x^{6} - 8 x^{5} + x^{4} + 7 x^{3} - 3 x^{2} - 3 x + 1$ |
$10$ |
[4,3] |
$-\,89\cdot 103\cdot 372293$ |
$3$ |
$8.98072111618$ |
$58419.25993197791$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.099985297480563$ |
10.4.3419621875.1 |
$x^{10} - 3 x^{9} + x^{8} + 6 x^{7} - 9 x^{6} + 2 x^{5} + 6 x^{4} - 5 x^{3} + x^{2} + 1$ |
$10$ |
[4,3] |
$-\,5^{5}\cdot 61\cdot 17939$ |
$3$ |
$8.98251205361$ |
$2339.1013231581055$ |
|
|
✓ |
$S_5^2 \wr C_2$ (as 10T43) |
trivial |
$2$ |
$6$ |
$5.10886306524$ |
10.4.3428429131.1 |
$x^{10} - x^{9} - 3 x^{8} + 3 x^{7} + 2 x^{6} - x^{5} - x^{4} - 2 x^{3} + 2 x + 1$ |
$10$ |
[4,3] |
$-\,20323\cdot 168697$ |
$2$ |
$8.98482282794$ |
$58552.789267463595$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.11605477103885$ |
10.4.3434563283.1 |
$x^{10} - x^{9} - x^{8} + 2 x^{7} + x^{5} - 3 x^{4} - 2 x^{3} + 3 x^{2} - 1$ |
$10$ |
[4,3] |
$-\,59\cdot 58212937$ |
$2$ |
$8.98642910131$ |
$58605.147239811624$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.118713369156141$ |
10.4.3444638167.1 |
$x^{10} - 2 x^{9} + x^{8} + 2 x^{7} - 5 x^{6} + 4 x^{4} - 4 x^{3} - x^{2} + 4 x - 1$ |
$10$ |
[4,3] |
$-\,103\cdot 5783^{2}$ |
$2$ |
$8.98906169049$ |
$771.7830005901918$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$6$ |
$5.12709085999$ |
10.4.3445999883.1 |
$x^{10} - 3 x^{8} + x^{6} - 3 x^{5} + 6 x^{4} + 4 x^{3} - 5 x^{2} - x + 1$ |
$10$ |
[4,3] |
$-\,211\cdot 16331753$ |
$2$ |
$8.98941697809$ |
$58702.63948920866$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.130273182623558$ |
10.4.3451623299.1 |
$x^{10} - x^{9} - 3 x^{8} + 2 x^{6} + 2 x^{5} - 3 x^{3} + x^{2} + 3 x - 1$ |
$10$ |
[4,3] |
$-\,811\cdot 4256009$ |
$2$ |
$8.9908828559$ |
$58750.51743601923$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.137285709970331$ |
10.4.3476098739.1 |
$x^{10} - x^{9} - 2 x^{8} + 4 x^{7} - x^{6} - 3 x^{5} + x^{4} + x^{3} - 2 x + 1$ |
$10$ |
[4,3] |
$-\,3476098739$ |
$1$ |
$8.99723803275$ |
$58958.44925877885$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.163212113578441$ |
10.4.3479589887.1 |
$x^{10} - x^{9} + x^{7} + x^{6} - 3 x^{5} - 3 x^{4} + x^{3} + 2 x^{2} + x - 1$ |
$10$ |
[4,3] |
$-\,109\cdot 31922843$ |
$2$ |
$8.99814124365$ |
$58988.04867937233$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.167998094393576$ |
10.4.3485322811.1 |
$x^{10} - x^{9} - x^{8} - x^{7} + x^{6} + 5 x^{5} - 5 x^{4} - 3 x^{3} + 4 x^{2} - 1$ |
$10$ |
[4,3] |
$-\,97\cdot 233\cdot 154211$ |
$3$ |
$8.99962266689$ |
$59036.622625282354$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.166269404976212$ |
10.4.3505569499.1 |
$x^{10} - x^{9} + x^{8} - x^{7} - x^{6} + 5 x^{5} - 4 x^{4} - x^{3} + 4 x^{2} - x - 1$ |
$10$ |
[4,3] |
$-\,3505569499$ |
$1$ |
$9.00483704685$ |
$59207.849977853446$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.1900689938179765$ |
10.4.3510827191.1 |
$x^{10} - 3 x^{9} + 2 x^{8} + x^{7} - 2 x^{6} + 4 x^{5} - 2 x^{4} - 4 x^{3} + 3 x + 1$ |
$10$ |
[4,3] |
$-\,9043\cdot 388237$ |
$2$ |
$9.00618669165$ |
$59252.23363722249$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.195370125131124$ |
10.4.3514218623.1 |
$x^{10} - x^{9} + x^{8} - x^{7} - x^{6} - 5 x^{4} + x^{3} + 5 x^{2} - 1$ |
$10$ |
[4,3] |
$-\,47\cdot 8647^{2}$ |
$2$ |
$9.00705630439$ |
$637.5021568590964$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$6$ |
$5.1945142551$ |
10.4.3521646451.1 |
$x^{10} - 2 x^{9} - x^{8} + 3 x^{7} + x^{5} - 4 x^{4} - 3 x^{3} + 4 x^{2} + x - 1$ |
$10$ |
[4,3] |
$-\,3521646451$ |
$1$ |
$9.00895827245$ |
$59343.46173758319$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.2130653854923645$ |
10.4.3526725619.1 |
$x^{10} - x^{9} - x^{8} - 3 x^{6} + 6 x^{5} + x^{4} - 8 x^{3} + 3 x^{2} + 2 x - 1$ |
$10$ |
[4,3] |
$-\,349\cdot 2707\cdot 3733$ |
$3$ |
$9.01025676571$ |
$59386.24099065372$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.2072598116155815$ |
10.4.3528835307.1 |
$x^{10} - x^{9} + x^{8} - 2 x^{7} + x^{6} - 2 x^{5} + 2 x^{3} - 3 x^{2} + 3 x - 1$ |
$10$ |
[4,3] |
$-\,31\cdot 113833397$ |
$2$ |
$9.01079561442$ |
$59404.00076594168$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.213563571367157$ |
10.4.3531636739.1 |
$x^{10} - x^{9} + 5 x^{5} - x^{4} - x^{2} - 3 x + 1$ |
$10$ |
[4,3] |
$-\,7933\cdot 445183$ |
$2$ |
$9.01151069789$ |
$59427.57557733615$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.215653226165113$ |
10.4.3540851199.1 |
$x^{10} - x^{9} - 3 x^{8} + x^{7} + 4 x^{6} + x^{5} - 5 x^{4} + 3 x^{2} - x - 1$ |
$10$ |
[4,3] |
$-\,3^{3}\cdot 3779\cdot 34703$ |
$3$ |
$9.01385915212$ |
$19835.017292656943$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.219912631781355$ |
10.4.3547219843.1 |
$x^{10} - x^{9} - 2 x^{8} + 5 x^{5} + 2 x^{4} - 4 x^{3} - x - 1$ |
$10$ |
[4,3] |
$-\,79\cdot 499\cdot 89983$ |
$3$ |
$9.01547909169$ |
$59558.54131021007$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.22374257856556$ |
10.4.3548877539.1 |
$x^{10} - 2 x^{9} + x^{8} - x^{7} + 3 x^{6} - x^{5} - 3 x^{4} - x^{2} + 3 x - 1$ |
$10$ |
[4,3] |
$-\,173\cdot 4373\cdot 4691$ |
$3$ |
$9.01590031683$ |
$59572.45621090337$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.223664969842654$ |
10.4.3550900883.1 |
$x^{10} - x^{9} + 2 x^{8} - 2 x^{6} + 3 x^{5} - 4 x^{4} + x^{2} - 2 x + 1$ |
$10$ |
[4,3] |
$-\,3550900883$ |
$1$ |
$9.01641421422$ |
$59589.43600169413$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.231642653765012$ |
10.4.3554861923.1 |
$x^{10} - 2 x^{9} - 2 x^{8} + 7 x^{7} - 3 x^{6} - 9 x^{5} + 11 x^{4} - x^{3} - 7 x^{2} + 5 x - 1$ |
$10$ |
[4,3] |
$-\,59\cdot 6577\cdot 9161$ |
$3$ |
$9.01741949326$ |
$59622.662830504305$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.230120826627221$ |
10.4.3574437551.1 |
$x^{10} - 3 x^{8} - 2 x^{7} + 3 x^{6} + 3 x^{5} - x^{4} + 2 x^{2} - x - 1$ |
$10$ |
[4,3] |
$-\,647\cdot 5524633$ |
$2$ |
$9.02237287114$ |
$59786.60009567361$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.247975599876225$ |
10.4.3576073931.1 |
$x^{10} - x^{9} + 2 x^{8} + 2 x^{7} - x^{6} + 3 x^{5} - x^{4} - x^{3} - 2 x - 1$ |
$10$ |
[4,3] |
$-\,52121\cdot 68611$ |
$2$ |
$9.02278583093$ |
$59800.28370334041$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$6$ |
$5.251051946288137$ |