| 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 |
| 10.2.799486935040.1 |
$x^{10} - 8 x^{8} + 12 x^{6} + 16 x^{4} + 32 x^{2} - 160$ |
$10$ |
[2,4] |
$2^{15}\cdot 5\cdot 47^{4}$ |
$3$ |
$15.4981955771$ |
$83.04137766739619$ |
|
|
? |
$C_2\times (C_2^4 : D_5)$ (as 10T23) |
trivial |
$2$ |
$5$ |
$80.5164124851$ |
| 10.2.799486935040.2 |
$x^{10} - 8 x^{8} + 20 x^{6} - 32 x^{4} + 96 x^{2} - 160$ |
$10$ |
[2,4] |
$2^{15}\cdot 5\cdot 47^{4}$ |
$3$ |
$15.4981955771$ |
$83.04137766739619$ |
|
|
? |
$C_2\times (C_2^4 : D_5)$ (as 10T23) |
trivial |
$2$ |
$5$ |
$82.7067987281$ |
| 10.0.933156978688.3 |
$x^{10} - 2 x^{8} + 12 x^{6} + 40 x^{4} - 96 x^{2} + 352$ |
$10$ |
[0,5] |
$-\,2^{15}\cdot 11\cdot 1609^{2}$ |
$3$ |
$15.7396644981$ |
$720.6675696475756$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$46.8628202943$ |
| 10.0.933156978688.8 |
$x^{10} + 14 x^{8} + 84 x^{6} + 272 x^{4} + 464 x^{2} + 352$ |
$10$ |
[0,5] |
$-\,2^{15}\cdot 11\cdot 1609^{2}$ |
$3$ |
$15.7396644981$ |
$720.6675696475756$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$54.5985995536$ |
| 10.0.938009001984.4 |
$x^{10} + 6 x^{8} + 28 x^{6} + 72 x^{4} + 128 x^{2} + 96$ |
$10$ |
[0,5] |
$-\,2^{15}\cdot 3\cdot 3089^{2}$ |
$3$ |
$15.7478293746$ |
$521.4710413705501$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$85.1753741764$ |
| 10.0.980130562048.5 |
$x^{10} + 16 x^{8} + 108 x^{6} + 368 x^{4} + 608 x^{2} + 352$ |
$10$ |
[0,5] |
$-\,2^{15}\cdot 11\cdot 17^{2}\cdot 97^{2}$ |
$4$ |
$15.8171558243$ |
$729.5705331700733$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$54.8786337311$ |
| 10.4.77265229938688.2 |
$x^{10} - 44 x^{6} + 352 x^{2} + 352$ |
$10$ |
[4,3] |
$-\,2^{15}\cdot 11^{9}$ |
$2$ |
$24.4792670483$ |
$46.88285286909621$ |
|
|
? |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
trivial |
$2$ |
$6$ |
$990.277238912$ |
| 10.0.192198386221056.2 |
$x^{10} + 4 x^{8} + 32 x^{6} - 136 x^{4} + 64 x^{2} + 96$ |
$10$ |
[0,5] |
$-\,2^{15}\cdot 3^{5}\cdot 17^{6}$ |
$3$ |
$26.8148254127$ |
$78.55212404345382$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$[2]$ |
$2$ |
$4$ |
$554.57345454$ |
| 10.0.192198386221056.4 |
$x^{10} - 2 x^{8} + 36 x^{6} + 160 x^{4} + 208 x^{2} + 96$ |
$10$ |
[0,5] |
$-\,2^{15}\cdot 3^{5}\cdot 17^{6}$ |
$3$ |
$26.8148254127$ |
$78.55212404345382$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$[2]$ |
$2$ |
$4$ |
$571.524332935$ |
| 10.0.1944000000000000.7 |
$x^{10} - 20 x^{6} + 120 x^{4} - 80 x^{2} + 96$ |
$10$ |
[0,5] |
$-\,2^{15}\cdot 3^{5}\cdot 5^{12}$ |
$3$ |
$33.7963365356$ |
$76.02951978637364$ |
|
|
? |
$C_2\times (C_2^4 : D_5)$ (as 10T23) |
$[2]$ |
$2$ |
$4$ |
$5001.60427195$ |
| 10.0.1944000000000000.8 |
$x^{10} + 40 x^{4} + 96$ |
$10$ |
[0,5] |
$-\,2^{15}\cdot 3^{5}\cdot 5^{12}$ |
$3$ |
$33.7963365356$ |
$100.0604752081037$ |
|
|
? |
$C_2\times (C_2^4 : D_5)$ (as 10T23) |
trivial |
$2$ |
$4$ |
$4953.24801936$ |
| 10.0.1944000000000000.17 |
$x^{10} + 20 x^{8} + 160 x^{6} + 600 x^{4} + 960 x^{2} + 864$ |
$10$ |
[0,5] |
$-\,2^{15}\cdot 3^{5}\cdot 5^{12}$ |
$3$ |
$33.7963365356$ |
$100.0604752081037$ |
|
|
? |
$C_2\times (C_2^4 : D_5)$ (as 10T23) |
trivial |
$2$ |
$4$ |
$7946.76730103$ |
| 10.2.3240000000000000.6 |
$x^{10} - 20 x^{6} - 120 x^{4} + 400 x^{2} - 1440$ |
$10$ |
[2,4] |
$2^{15}\cdot 3^{4}\cdot 5^{13}$ |
$3$ |
$35.5675950695$ |
$76.02951978637364$ |
|
|
|
$C_2\times (C_2^4 : D_5)$ (as 10T23) |
$[2]$ |
$2$ |
$5$ |
$16949.6742512$ |
| 10.0.3267372565757952.1 |
$x^{10} - 6 x^{8} + 56 x^{6} + 216 x^{4} - 1424 x^{2} + 1632$ |
$10$ |
[0,5] |
$-\,2^{15}\cdot 3^{5}\cdot 17^{7}$ |
$3$ |
$35.597530092$ |
$78.55212404345382$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$[2, 2]$ |
$2$ |
$4$ |
$2643.56956023$ |
| 10.0.3267372565757952.4 |
$x^{10} + 16 x^{8} + 164 x^{6} + 800 x^{4} + 1888 x^{2} + 1632$ |
$10$ |
[0,5] |
$-\,2^{15}\cdot 3^{5}\cdot 17^{7}$ |
$3$ |
$35.597530092$ |
$78.55212404345382$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$[2, 2]$ |
$2$ |
$4$ |
$1958.6695641$ |
| 10.0.17496000000000000.23 |
$x^{10} + 30 x^{8} + 300 x^{6} + 1080 x^{4} + 1440 x^{2} + 864$ |
$10$ |
[0,5] |
$-\,2^{15}\cdot 3^{7}\cdot 5^{12}$ |
$3$ |
$42.1011420681$ |
$100.0604752081037$ |
|
|
? |
$C_2\times (C_2^4 : D_5)$ (as 10T23) |
$[2]$ |
$2$ |
$4$ |
$22776.768269$ |
| 10.0.17496000000000000.29 |
$x^{10} - 30 x^{8} + 420 x^{6} - 2880 x^{4} + 6480 x^{2} + 7776$ |
$10$ |
[0,5] |
$-\,2^{15}\cdot 3^{7}\cdot 5^{12}$ |
$3$ |
$42.1011420681$ |
$100.0604752081037$ |
|
|
? |
$C_2\times (C_2^4 : D_5)$ (as 10T23) |
$[2]$ |
$2$ |
$4$ |
$19036.7048217$ |
| 10.6.25000000000000000.2 |
$x^{10} + 10 x^{8} - 100 x^{6} - 800 x^{4} + 1200 x^{2} - 160$ |
$10$ |
[6,2] |
$2^{15}\cdot 5^{17}$ |
$2$ |
$43.6308828551$ |
$83.56215312364702$ |
|
|
|
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$[2]$ |
$2$ |
$7$ |
$43165.3920089$ |
| 10.2.29160000000000000.16 |
$x^{10} - 10 x^{8} - 80 x^{6} - 1320 x^{4} - 1200 x^{2} - 1440$ |
$10$ |
[2,4] |
$2^{15}\cdot 3^{6}\cdot 5^{13}$ |
$3$ |
$44.3076536258$ |
$100.0604752081037$ |
|
|
? |
$C_2\times (C_2^4 : D_5)$ (as 10T23) |
$[2]$ |
$2$ |
$5$ |
$13737.9926118$ |
| 10.2.29160000000000000.18 |
$x^{10} + 20 x^{8} + 100 x^{6} - 120 x^{4} - 1200 x^{2} - 1440$ |
$10$ |
[2,4] |
$2^{15}\cdot 3^{6}\cdot 5^{13}$ |
$3$ |
$44.3076536258$ |
$100.0604752081037$ |
|
|
? |
$C_2\times (C_2^4 : D_5)$ (as 10T23) |
$[2]$ |
$2$ |
$5$ |
$23566.6942937$ |
| 10.2.29160000000000000.19 |
$x^{10} - 10 x^{8} + 60 x^{6} - 120 x^{4} - 1440$ |
$10$ |
[2,4] |
$2^{15}\cdot 3^{6}\cdot 5^{13}$ |
$3$ |
$44.3076536258$ |
$100.0604752081037$ |
|
|
|
$C_2\times (C_2^4 : D_5)$ (as 10T23) |
$[2]$ |
$2$ |
$5$ |
$36608.0361501$ |
| 10.2.29160000000000000.24 |
$x^{10} - 10 x^{8} + 120 x^{6} + 1680 x^{4} + 3600 x^{2} - 1440$ |
$10$ |
[2,4] |
$2^{15}\cdot 3^{6}\cdot 5^{13}$ |
$3$ |
$44.3076536258$ |
$100.0604752081037$ |
|
|
|
$C_2\times (C_2^4 : D_5)$ (as 10T23) |
$[2]$ |
$2$ |
$5$ |
$27761.4792113$ |
| 10.4.56687040000000000.9 |
$x^{10} - 20 x^{8} + 80 x^{6} + 120 x^{4} - 960 x^{2} + 96$ |
$10$ |
[4,3] |
$-\,2^{15}\cdot 3^{11}\cdot 5^{10}$ |
$3$ |
$47.3530958999$ |
$258.4035166490914$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$6$ |
$76527.4874471$ |
| 10.4.56687040000000000.12 |
$x^{10} - 20 x^{8} + 20 x^{6} + 120 x^{4} - 240 x^{2} + 96$ |
$10$ |
[4,3] |
$-\,2^{15}\cdot 3^{11}\cdot 5^{10}$ |
$3$ |
$47.3530958999$ |
$258.4035166490914$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$6$ |
$91977.7656769$ |
| 10.4.56687040000000000.13 |
$x^{10} - 10 x^{8} + 40 x^{6} + 120 x^{4} - 240 x^{2} + 96$ |
$10$ |
[4,3] |
$-\,2^{15}\cdot 3^{11}\cdot 5^{10}$ |
$3$ |
$47.3530958999$ |
$179.16699160049947$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$6$ |
$90693.7973174$ |
| 10.0.56687040000000000.16 |
$x^{10} + 10 x^{8} + 40 x^{6} + 120 x^{4} + 240 x^{2} + 96$ |
$10$ |
[0,5] |
$-\,2^{15}\cdot 3^{11}\cdot 5^{10}$ |
$3$ |
$47.3530958999$ |
$179.16699160049947$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$2$ |
$4$ |
$41914.0807138$ |
| 10.4.56687040000000000.16 |
$x^{10} + 40 x^{6} - 120 x^{4} + 96$ |
$10$ |
[4,3] |
$-\,2^{15}\cdot 3^{11}\cdot 5^{10}$ |
$3$ |
$47.3530958999$ |
$258.4035166490914$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$6$ |
$120719.035124$ |
| 10.4.56687040000000000.27 |
$x^{10} - 180 x^{6} - 840 x^{4} - 3600 x^{2} + 864$ |
$10$ |
[4,3] |
$-\,2^{15}\cdot 3^{11}\cdot 5^{10}$ |
$3$ |
$47.3530958999$ |
$179.16699160049947$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$6$ |
$69336.6105565$ |
| 10.4.56687040000000000.31 |
$x^{10} - 180 x^{6} + 1400 x^{4} - 3600 x^{2} + 2400$ |
$10$ |
[4,3] |
$-\,2^{15}\cdot 3^{11}\cdot 5^{10}$ |
$3$ |
$47.3530958999$ |
$196.34421324784506$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$6$ |
$196320.804474$ |
| 10.4.56687040000000000.32 |
$x^{10} - 10 x^{8} - 20 x^{6} + 600 x^{4} - 2400 x^{2} + 2400$ |
$10$ |
[4,3] |
$-\,2^{15}\cdot 3^{11}\cdot 5^{10}$ |
$3$ |
$47.3530958999$ |
$258.4035166490914$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$6$ |
$75431.3640494$ |
| 10.4.56687040000000000.34 |
$x^{10} + 120 x^{6} - 1080 x^{4} + 7776$ |
$10$ |
[4,3] |
$-\,2^{15}\cdot 3^{11}\cdot 5^{10}$ |
$3$ |
$47.3530958999$ |
$196.34421324784506$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$6$ |
$125313.008852$ |
| 10.6.94478400000000000.4 |
$x^{10} - 40 x^{8} + 520 x^{6} - 2200 x^{4} + 2560 x^{2} - 160$ |
$10$ |
[6,2] |
$2^{15}\cdot 3^{10}\cdot 5^{11}$ |
$3$ |
$49.8348611981$ |
$179.16699160049947$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$2$ |
$7$ |
$104842.16064$ |
| 10.2.94478400000000000.7 |
$x^{10} + 10 x^{8} - 20 x^{6} - 640 x^{4} - 4240 x^{2} - 160$ |
$10$ |
[2,4] |
$2^{15}\cdot 3^{10}\cdot 5^{11}$ |
$3$ |
$49.8348611981$ |
$179.16699160049947$ |
|
|
|
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$2$ |
$5$ |
$75884.9373954$ |
| 10.2.94478400000000000.8 |
$x^{10} - 20 x^{8} + 100 x^{6} + 200 x^{4} - 1840 x^{2} - 160$ |
$10$ |
[2,4] |
$2^{15}\cdot 3^{10}\cdot 5^{11}$ |
$3$ |
$49.8348611981$ |
$179.16699160049947$ |
|
|
|
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$2$ |
$5$ |
$93332.3340315$ |
| 10.2.94478400000000000.15 |
$x^{10} + 30 x^{8} - 80 x^{6} - 40 x^{4} + 240 x^{2} - 160$ |
$10$ |
[2,4] |
$2^{15}\cdot 3^{10}\cdot 5^{11}$ |
$3$ |
$49.8348611981$ |
$258.4035166490914$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$2$ |
$5$ |
$40025.9785662$ |
| 10.4.510...000.43 |
$x^{10} - 120 x^{4} + 864$ |
$10$ |
[4,3] |
$-\,2^{15}\cdot 3^{13}\cdot 5^{10}$ |
$3$ |
$58.9892166491$ |
$258.4035166490914$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$6$ |
$184719.200709$ |
| 10.2.850...000.38 |
$x^{10} - 180 x^{6} - 3600 x^{4} - 12960 x^{2} - 12960$ |
$10$ |
[2,4] |
$2^{15}\cdot 3^{12}\cdot 5^{11}$ |
$3$ |
$62.0808284659$ |
$258.4035166490914$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$2$ |
$5$ |
$83773.0735612$ |
| 10.2.850...000.39 |
$x^{10} + 30 x^{8} + 180 x^{6} - 720 x^{4} - 2160 x^{2} - 12960$ |
$10$ |
[2,4] |
$2^{15}\cdot 3^{12}\cdot 5^{11}$ |
$3$ |
$62.0808284659$ |
$258.4035166490914$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$2$ |
$5$ |
$54342.7257115$ |
| 10.2.850...000.40 |
$x^{10} + 30 x^{8} + 180 x^{6} + 1440 x^{4} - 2160 x^{2} - 12960$ |
$10$ |
[2,4] |
$2^{15}\cdot 3^{12}\cdot 5^{11}$ |
$3$ |
$62.0808284659$ |
$258.4035166490914$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$2$ |
$5$ |
$61936.4043879$ |
| 10.2.850...000.63 |
$x^{10} - 240 x^{6} - 1560 x^{4} - 1440 x^{2} - 1440$ |
$10$ |
[2,4] |
$2^{15}\cdot 3^{12}\cdot 5^{11}$ |
$3$ |
$62.0808284659$ |
$196.34421324784506$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$2$ |
$5$ |
$89174.6036403$ |
| 10.2.850...000.64 |
$x^{10} - 60 x^{6} - 480 x^{4} - 1440 x^{2} - 1440$ |
$10$ |
[2,4] |
$2^{15}\cdot 3^{12}\cdot 5^{11}$ |
$3$ |
$62.0808284659$ |
$196.34421324784506$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$2$ |
$5$ |
$105534.81666$ |
| 10.2.850...000.67 |
$x^{10} + 30 x^{8} - 420 x^{6} + 200 x^{4} - 960 x^{2} - 1440$ |
$10$ |
[2,4] |
$2^{15}\cdot 3^{12}\cdot 5^{11}$ |
$3$ |
$62.0808284659$ |
$258.4035166490914$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$2$ |
$5$ |
$103644.535372$ |
| 10.4.121...000.10 |
$x^{10} + 30 x^{8} - 540 x^{6} - 3240 x^{4} + 38880 x^{2} + 7776$ |
$10$ |
[4,3] |
$-\,2^{15}\cdot 3^{5}\cdot 5^{16}$ |
$3$ |
$64.3365291602$ |
$123.21774278516936$ |
|
|
? |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
trivial |
$2$ |
$6$ |
$186433.688145$ |
| 10.0.127...000.4 |
$x^{10} + 10 x^{8} + 100 x^{6} + 240 x^{4} + 240 x^{2} + 96$ |
$10$ |
[0,5] |
$-\,2^{15}\cdot 3^{13}\cdot 5^{12}$ |
$3$ |
$81.3891719172$ |
$328.96062672772797$ |
|
|
? |
$C_2 \wr A_5$ (as 10T36) |
$[2]$ |
$2$ |
$4$ |
$344080.806617$ |
| 10.0.127...000.64 |
$x^{10} + 10 x^{8} + 280 x^{6} + 2040 x^{4} + 20400 x^{2} + 92256$ |
$10$ |
[0,5] |
$-\,2^{15}\cdot 3^{13}\cdot 5^{12}$ |
$3$ |
$81.3891719172$ |
$328.96062672772797$ |
|
|
? |
$C_2 \wr A_5$ (as 10T36) |
$[2]$ |
$2$ |
$4$ |
$374359.78826$ |
| 10.0.127...000.65 |
$x^{10} + 30 x^{8} + 420 x^{6} + 3920 x^{4} + 34320 x^{2} + 92256$ |
$10$ |
[0,5] |
$-\,2^{15}\cdot 3^{13}\cdot 5^{12}$ |
$3$ |
$81.3891719172$ |
$360.4989672896519$ |
|
|
? |
$C_2 \wr A_5$ (as 10T36) |
trivial |
$2$ |
$4$ |
$633116.475685$ |
| 10.2.212...000.13 |
$x^{10} - 10 x^{8} + 280 x^{6} + 80 x^{4} + 400 x^{2} - 160$ |
$10$ |
[2,4] |
$2^{15}\cdot 3^{12}\cdot 5^{13}$ |
$3$ |
$85.6547604424$ |
$328.96062672772797$ |
|
|
? |
$C_2 \wr A_5$ (as 10T36) |
$[2]$ |
$2$ |
$5$ |
$491758.019822$ |
| 10.2.212...000.122 |
$x^{10} - 240 x^{6} - 5080 x^{4} + 2400 x^{2} - 1440$ |
$10$ |
[2,4] |
$2^{15}\cdot 3^{12}\cdot 5^{13}$ |
$3$ |
$85.6547604424$ |
$328.96062672772797$ |
|
|
? |
$C_2 \wr A_5$ (as 10T36) |
$[2]$ |
$2$ |
$5$ |
$455731.014032$ |
| 10.0.984...000.2 |
$x^{10} - 10 x^{8} + 100 x^{6} - 480 x^{4} + 720 x^{2} + 96$ |
$10$ |
[0,5] |
$-\,2^{15}\cdot 3^{9}\cdot 5^{16}$ |
$3$ |
$99.8403580184$ |
$256.3032334804013$ |
|
|
? |
$C_2 \wr A_5$ (as 10T36) |
$[2]$ |
$2$ |
$4$ |
$707014.307932$ |
| 10.0.984...000.7 |
$x^{10} - 10 x^{8} - 20 x^{6} + 360 x^{4} + 864$ |
$10$ |
[0,5] |
$-\,2^{15}\cdot 3^{9}\cdot 5^{16}$ |
$3$ |
$99.8403580184$ |
$256.3032334804013$ |
|
|
? |
$C_2 \wr A_5$ (as 10T36) |
$[2]$ |
$2$ |
$4$ |
$1177547.47107$ |
