| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Narrow class group |
Unit group torsion |
Unit group rank |
Regulator |
| 10.0.24626397184.1 |
$x^{10} - x^{8} - 4 x^{6} + 4 x^{4} + 3 x^{2} + 1$ |
$10$ |
(0, 5) |
$-\,2^{16}\cdot 613^{2}$ |
$2$ |
$10.9430929464$ |
$125.13760884231425$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$4$ |
$16.8080874668$ |
| 10.4.61790027776.2 |
$x^{10} - x^{8} - 4 x^{4} - x^{2} + 1$ |
$10$ |
(4, 3) |
$-\,2^{16}\cdot 971^{2}$ |
$2$ |
$11.9975298475$ |
$157.49516646828823$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$6$ |
$48.497121865$ |
| 10.0.76017106944.1 |
$x^{10} - 2 x^{8} + 4$ |
$10$ |
(0, 5) |
$-\,2^{16}\cdot 3^{2}\cdot 359^{2}$ |
$3$ |
$12.2487320355$ |
$165.86909171812445$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$4$ |
$48.1156635945$ |
| 10.0.80601481216.3 |
$x^{10} + 2 x^{8} - 4 x^{4} + 4$ |
$10$ |
(0, 5) |
$-\,2^{16}\cdot 1109^{2}$ |
$2$ |
$12.3206693424$ |
$168.31521955849624$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$4$ |
$54.7758516585$ |
| 10.4.129001652224.2 |
$x^{10} - 2 x^{8} + 8 x^{6} - 16 x^{4} + 4$ |
$10$ |
(4, 3) |
$-\,2^{16}\cdot 23^{2}\cdot 61^{2}$ |
$3$ |
$12.9139626878$ |
$189.31562099802582$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$6$ |
$88.9510586273$ |
| 10.2.155883864064.1 |
$x^{10} - 5 x^{8} + 8 x^{6} - 4 x^{4} + 27 x^{2} - 31$ |
$10$ |
(2, 4) |
$2^{16}\cdot 31\cdot 277^{2}$ |
$3$ |
$13.1607341469$ |
$468.3584351718518$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$5$ |
$51.7552736763$ |
| 10.0.158875582464.1 |
$x^{10} + 3 x^{8} + 8 x^{6} + 8 x^{4} + 15 x^{2} + 1$ |
$10$ |
(0, 5) |
$-\,2^{16}\cdot 3^{4}\cdot 173^{2}$ |
$3$ |
$13.185776665$ |
$115.14399506970062$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$4$ |
$47.2024081868$ |
| 10.0.165473222656.1 |
$x^{10} + 3 x^{8} + 4 x^{6} + 3 x^{2} + 1$ |
$10$ |
(0, 5) |
$-\,2^{16}\cdot 7^{2}\cdot 227^{2}$ |
$3$ |
$13.2395362334$ |
$201.47425728728456$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$4$ |
$87.7231098272$ |
| 10.4.176911089664.2 |
$x^{10} - 2 x^{8} - 4 x^{6} + 12 x^{4} - 12 x^{2} + 4$ |
$10$ |
(4, 3) |
$-\,2^{16}\cdot 31^{2}\cdot 53^{2}$ |
$3$ |
$13.3283229024$ |
$204.86907028901953$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$6$ |
$87.0331857249$ |
| 10.2.183594057728.1 |
$x^{10} - 5 x^{8} + 8 x^{6} - 12 x^{4} + 27 x^{2} - 23$ |
$10$ |
(2, 4) |
$2^{16}\cdot 23\cdot 349^{2}$ |
$3$ |
$13.3778358293$ |
$452.82901487549856$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$5$ |
$55.1159477014$ |
| 10.4.214939795456.1 |
$x^{10} - x^{8} + 4 x^{6} + 4 x^{4} - 5 x^{2} + 1$ |
$10$ |
(4, 3) |
$-\,2^{16}\cdot 1811^{2}$ |
$2$ |
$13.5903825953$ |
$215.08832624329145$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$6$ |
$92.1337326807$ |
| 10.0.220674457600.1 |
$x^{10} + 5 x^{8} + 2 x^{6} - 6 x^{4} + 5 x^{2} + 1$ |
$10$ |
(0, 5) |
$-\,2^{16}\cdot 5^{2}\cdot 367^{2}$ |
$3$ |
$13.6262140476$ |
$216.50884796437876$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$4$ |
$45.9906440931$ |
| 10.2.236340051968.1 |
$x^{10} + 5 x^{8} + 2 x^{6} - 30 x^{4} - 67 x^{2} - 47$ |
$10$ |
(2, 4) |
$2^{16}\cdot 47\cdot 277^{2}$ |
$3$ |
$13.7199880363$ |
$576.6953217629489$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$5$ |
$77.1530176137$ |
| 10.0.277838626816.1 |
$x^{10} + 6 x^{8} + 8 x^{6} + 4$ |
$10$ |
(0, 5) |
$-\,2^{16}\cdot 29^{2}\cdot 71^{2}$ |
$3$ |
$13.9437395576$ |
$229.34315791029596$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$4$ |
$66.6616282796$ |
| 10.0.280543952896.1 |
$x^{10} + 2 x^{8} + 8 x^{4} - 12 x^{2} + 4$ |
$10$ |
(0, 5) |
$-\,2^{16}\cdot 2069^{2}$ |
$2$ |
$13.9572575079$ |
$229.8994118389629$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$4$ |
$128.956026575$ |
| 10.0.327276363776.1 |
$x^{10} + 7 x^{8} + 24 x^{6} + 60 x^{4} + 55 x^{2} + 41$ |
$10$ |
(0, 5) |
$-\,2^{16}\cdot 41\cdot 349^{2}$ |
$3$ |
$14.1739685284$ |
$604.591805710327$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$4$ |
$54.8578162821$ |
| 10.4.329714827264.2 |
$x^{10} - 6 x^{8} + 8 x^{6} + 4 x^{4} - 12 x^{2} + 4$ |
$10$ |
(4, 3) |
$-\,2^{16}\cdot 2243^{2}$ |
$2$ |
$14.1844939952$ |
$239.3713954906369$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$6$ |
$152.029520602$ |
| 10.2.375170465792.1 |
$x^{10} + 6 x^{8} - 6 x^{7} + 8 x^{6} - 20 x^{5} - 38 x^{4} + 20 x^{3} - 24 x^{2} - 40 x + 2$ |
$10$ |
(2, 4) |
$2^{16}\cdot 47\cdot 349^{2}$ |
$3$ |
$14.368878227$ |
$647.32034558251$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$5$ |
$109.03653909$ |
| 10.0.391775846400.1 |
$x^{10} - x^{8} + 8 x^{4} - 5 x^{2} + 1$ |
$10$ |
(0, 5) |
$-\,2^{16}\cdot 3^{2}\cdot 5^{2}\cdot 163^{2}$ |
$4$ |
$14.431243869$ |
$249.91771795641918$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$4$ |
$73.1488181944$ |
| 10.0.397079543808.1 |
$x^{10} - 7 x^{8} + 18 x^{6} - 18 x^{4} - 3 x^{2} + 17$ |
$10$ |
(0, 5) |
$-\,2^{16}\cdot 3^{2}\cdot 17\cdot 199^{2}$ |
$4$ |
$14.4506622792$ |
$509.1775430439529$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$4$ |
$64.5742474644$ |
| 10.0.428490686464.1 |
$x^{10} + 5 x^{8} + 14 x^{6} + 26 x^{4} + 9 x^{2} + 1$ |
$10$ |
(0, 5) |
$-\,2^{16}\cdot 2557^{2}$ |
$2$ |
$14.5610984651$ |
$255.57771257534668$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$4$ |
$81.5841894161$ |
| 10.2.431761063936.1 |
$x^{10} - 9 x^{8} + 32 x^{6} - 60 x^{4} + 63 x^{2} - 31$ |
$10$ |
(2, 4) |
$2^{16}\cdot 31\cdot 461^{2}$ |
$3$ |
$14.5721739732$ |
$604.2114130513692$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$5$ |
$80.8829433458$ |
| 10.0.447464669184.1 |
$x^{10} - 3 x^{8} + 2 x^{6} - 6 x^{4} + 13 x^{2} + 1$ |
$10$ |
(0, 5) |
$-\,2^{16}\cdot 3^{2}\cdot 13^{2}\cdot 67^{2}$ |
$4$ |
$14.6243265179$ |
$258.36121588504267$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$4$ |
$75.1346630598$ |
| 10.0.447537545216.1 |
$x^{10} - 4 x^{9} + 5 x^{8} + 6 x^{7} - 8 x^{6} - 42 x^{5} + 98 x^{4} - 26 x^{3} - 79 x^{2} + 22 x + 61$ |
$10$ |
(0, 5) |
$-\,2^{16}\cdot 89\cdot 277^{2}$ |
$3$ |
$14.6245646786$ |
$793.5832683488329$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$4$ |
$63.2310292687$ |
| 10.2.456003616768.2 |
$x^{10} + 3 x^{8} - 4 x^{6} - 8 x^{4} + 11 x^{2} - 7$ |
$10$ |
(2, 4) |
$2^{16}\cdot 7\cdot 997^{2}$ |
$3$ |
$14.6519972583$ |
$422.23498437275174$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$5$ |
$144.395930766$ |
| 10.0.486645760000.1 |
$x^{10} - 3 x^{8} + 2 x^{6} + 10 x^{4} - 3 x^{2} + 1$ |
$10$ |
(0, 5) |
$-\,2^{16}\cdot 5^{4}\cdot 109^{2}$ |
$3$ |
$14.7475981216$ |
$154.29464967757525$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$4$ |
$80.8094689763$ |
| 10.0.487765639168.1 |
$x^{10} + 3 x^{8} + 4 x^{6} - 4 x^{4} - x^{2} + 97$ |
$10$ |
(0, 5) |
$-\,2^{16}\cdot 97\cdot 277^{2}$ |
$3$ |
$14.7509883598$ |
$828.4825520048919$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$4$ |
$63.8938363636$ |
| 10.0.568221827072.1 |
$x^{10} + 7 x^{8} + 12 x^{6} - 8 x^{4} - 49 x^{2} + 113$ |
$10$ |
(0, 5) |
$-\,2^{16}\cdot 113\cdot 277^{2}$ |
$3$ |
$14.9779298159$ |
$894.2042324453536$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$4$ |
$90.0956021358$ |
| 10.0.571038826496.1 |
$x^{10} - 5 x^{8} + 4 x^{6} + 28 x^{4} - 65 x^{2} + 41$ |
$10$ |
(0, 5) |
$-\,2^{16}\cdot 41\cdot 461^{2}$ |
$3$ |
$14.9853387157$ |
$694.8643102195315$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$4$ |
$93.0422102263$ |
| 10.0.582711574528.1 |
$x^{10} + 3 x^{8} - 2 x^{7} + 14 x^{6} - 22 x^{5} - 22 x^{4} - 50 x^{3} + 61 x^{2} + 62 x + 13$ |
$10$ |
(0, 5) |
$-\,2^{16}\cdot 73\cdot 349^{2}$ |
$3$ |
$15.0156924479$ |
$806.7365962039083$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$4$ |
$102.475015655$ |
| 10.0.604462710784.1 |
$x^{10} + 3 x^{8} + 8 x^{6} + 4 x^{4} - 5 x^{2} + 1$ |
$10$ |
(0, 5) |
$-\,2^{16}\cdot 3037^{2}$ |
$2$ |
$15.0708223813$ |
$278.5351510665838$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$4$ |
$167.604575029$ |
| 10.4.651520180224.1 |
$x^{10} + 5 x^{8} + 6 x^{6} - 14 x^{4} - 15 x^{2} + 9$ |
$10$ |
(4, 3) |
$-\,2^{16}\cdot 3^{2}\cdot 1051^{2}$ |
$3$ |
$15.1842304787$ |
$283.8047110071299$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$6$ |
$180.860416199$ |
| 10.4.675710304256.2 |
$x^{10} + 2 x^{8} - 4 x^{6} - 8 x^{4} + 4 x^{2} + 4$ |
$10$ |
(4, 3) |
$-\,2^{16}\cdot 13^{4}\cdot 19^{2}$ |
$3$ |
$15.2396872396$ |
$121.80449537674691$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$6$ |
$176.903182922$ |
| 10.0.750926233600.1 |
$x^{10} - 3 x^{8} + 6 x^{6} - 6 x^{4} - 15 x^{2} + 25$ |
$10$ |
(0, 5) |
$-\,2^{16}\cdot 5^{2}\cdot 677^{2}$ |
$3$ |
$15.4013832369$ |
$294.0606760689914$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$4$ |
$88.753626116$ |
| 10.2.759305273344.1 |
$x^{10} - 5 x^{8} + 16 x^{6} - 40 x^{4} + 103 x^{2} - 151$ |
$10$ |
(2, 4) |
$2^{16}\cdot 151\cdot 277^{2}$ |
$3$ |
$15.4184828342$ |
$1033.6796657555315$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$5$ |
$139.566056863$ |
| 10.4.802357313536.1 |
$x^{10} + 3 x^{8} + 4 x^{6} - 13 x^{2} + 1$ |
$10$ |
(4, 3) |
$-\,2^{16}\cdot 3499^{2}$ |
$2$ |
$15.5037508872$ |
$298.9713593700597$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$6$ |
$221.92394132$ |
| 10.2.877449904128.1 |
$x^{10} + 3 x^{8} - 4 x^{6} - 16 x^{4} + 75 x^{2} - 63$ |
$10$ |
(2, 4) |
$2^{16}\cdot 3^{2}\cdot 7\cdot 461^{2}$ |
$4$ |
$15.6430788027$ |
$497.29915916498317$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$5$ |
$171.976168573$ |
| 10.0.897672871936.1 |
$x^{10} + 2 x^{8} + 4 x^{6} + 8 x^{4} + 4 x^{2} + 4$ |
$10$ |
(0, 5) |
$-\,2^{16}\cdot 3701^{2}$ |
$2$ |
$15.678763531$ |
$307.4802017902791$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$4$ |
$156.637805582$ |
| 10.2.931148529664.2 |
$x^{10} - 5 x^{8} + 16 x^{6} - 32 x^{4} + 39 x^{2} - 31$ |
$10$ |
(2, 4) |
$2^{16}\cdot 31\cdot 677^{2}$ |
$3$ |
$15.7362735387$ |
$732.2051785551263$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$5$ |
$281.576368141$ |
| 10.4.939875958784.1 |
$x^{10} + 5 x^{8} + 10 x^{6} + 2 x^{4} - 11 x^{2} + 1$ |
$10$ |
(4, 3) |
$-\,2^{16}\cdot 7^{2}\cdot 541^{2}$ |
$3$ |
$15.7509609243$ |
$311.0321392593445$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$6$ |
$240.487434566$ |
| 10.0.949829566464.1 |
$x^{10} + 3 x^{8} - 4 x^{4} + 3 x^{2} + 9$ |
$10$ |
(0, 5) |
$-\,2^{16}\cdot 3^{8}\cdot 47^{2}$ |
$3$ |
$15.7675627645$ |
$124.83834647903213$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$4$ |
$235.966631456$ |
| 10.2.957468311552.1 |
$x^{10} - 3 x^{8} - 14 x^{6} - 14 x^{4} - 19 x^{2} - 23$ |
$10$ |
(2, 4) |
$2^{16}\cdot 23\cdot 797^{2}$ |
$3$ |
$15.7801977377$ |
$684.3065446491945$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$5$ |
$166.148374844$ |
| 10.2.960445743104.1 |
$x^{10} - x^{8} - 36 x^{4} - 161 x^{2} - 191$ |
$10$ |
(2, 4) |
$2^{16}\cdot 191\cdot 277^{2}$ |
$3$ |
$15.7850980398$ |
$1162.5568060370558$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$5$ |
$163.776187694$ |
| 10.0.981018935296.1 |
$x^{10} + 2 x^{8} + 12 x^{6} + 16 x^{4} - 16 x^{2} + 4$ |
$10$ |
(0, 5) |
$-\,2^{16}\cdot 53^{2}\cdot 73^{2}$ |
$3$ |
$15.8185888793$ |
$314.38149853012044$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$4$ |
$199.311660088$ |
| 10.2.988872114176.1 |
$x^{10} - 2 x^{9} + 5 x^{8} - 6 x^{7} - 6 x^{6} + 54 x^{5} - 134 x^{4} + 210 x^{3} - 193 x^{2} + 92 x - 7$ |
$10$ |
(2, 4) |
$2^{16}\cdot 71\cdot 461^{2}$ |
$3$ |
$15.831206471$ |
$914.4021781923227$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$5$ |
$211.810258584$ |
| 10.4.4066320646144.2 |
$x^{10} + 5 x^{8} - 2 x^{6} - 22 x^{4} + 9 x^{2} + 1$ |
$10$ |
(4, 3) |
$-\,2^{16}\cdot 7877^{2}$ |
$2$ |
$18.2356044014$ |
$448.578069524807$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$6$ |
$457.777245875$ |
| 10.4.6025964486656.4 |
$x^{10} + 2 x^{8} - 8 x^{6} - 8 x^{4} + 16 x^{2} + 4$ |
$10$ |
(4, 3) |
$-\,2^{16}\cdot 43^{2}\cdot 223^{2}$ |
$3$ |
$18.9671752431$ |
$494.93056407617956$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$6$ |
$726.797541433$ |
| 10.0.6718464000000.2 |
$x^{10} - 5 x^{8} + 20 x^{6} - 40 x^{4} + 35 x^{2} + 1$ |
$10$ |
(0, 5) |
$-\,2^{16}\cdot 3^{8}\cdot 5^{6}$ |
$3$ |
$19.1746303103$ |
$83.61694406953937$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$4$ |
$1157.79207661$ |
| 10.8.8204695699456.1 |
$x^{10} - 7 x^{8} + 10 x^{6} + 14 x^{4} - 27 x^{2} + 1$ |
$10$ |
(8, 1) |
$-\,2^{16}\cdot 67^{2}\cdot 167^{2}$ |
$3$ |
$19.5616843969$ |
$534.629909973456$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$8$ |
$1468.7675929$ |
| 10.2.100776960000000.3 |
$x^{10} + 3 x^{8} + 135 x^{2} - 135$ |
$10$ |
(2, 4) |
$2^{16}\cdot 3^{9}\cdot 5^{7}$ |
$3$ |
$25.1383127664$ |
$55.547625380156134$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
trivial |
$[2]$ |
$2$ |
$5$ |
$2345.57971388$ |
