| 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 |
| 10.0.5865429267.1 |
$x^{10} - 2 x^{8} - x^{6} + 5 x^{4} - 5 x^{2} + 3$ |
$10$ |
[0,5] |
$-\,3^{5}\cdot 17^{6}$ |
$2$ |
$9.48047244284$ |
$14.500978825806921$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$6$ |
$4$ |
$17.4279690081$ |
| 10.0.78732000000.1 |
$x^{10} - 3 x^{9} + 9 x^{8} - 24 x^{7} + 45 x^{6} - 75 x^{5} + 99 x^{4} - 102 x^{3} + 87 x^{2} - 45 x + 21$ |
$10$ |
[0,5] |
$-\,2^{8}\cdot 3^{9}\cdot 5^{6}$ |
$3$ |
$12.2917899001$ |
$15.648064552551654$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$6$ |
$4$ |
$94.6039648024$ |
| 10.0.79082438656.1 |
$x^{10} - 2 x^{7} + 2 x^{5} + 2 x^{4} + 4 x^{2} + 4 x + 2$ |
$10$ |
[0,5] |
$-\,2^{14}\cdot 13^{6}$ |
$2$ |
$12.2972500875$ |
$18.067560105343954$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$4$ |
$4$ |
$80.222639086$ |
| 10.0.82556485632.1 |
$x^{10} - 2 x^{9} + 3 x^{8} - 3 x^{6} + 6 x^{5} - 3 x^{4} - 24 x^{3} + 3 x^{2} + 22 x + 13$ |
$10$ |
[0,5] |
$-\,2^{22}\cdot 3^{9}$ |
$2$ |
$12.3502321076$ |
$18.081798170312066$ |
|
|
|
$F_{5}\times C_2$ (as 10T5) |
trivial |
$6$ |
$4$ |
$99.4440010381$ |
| 10.0.99712297539.1 |
$x^{10} - 5 x^{9} + 13 x^{8} - 22 x^{7} + 24 x^{6} - 16 x^{5} + 6 x^{4} - x^{3} - x^{2} + x + 1$ |
$10$ |
[0,5] |
$-\,3^{5}\cdot 17^{7}$ |
$2$ |
$12.5856274608$ |
$14.500978825806921$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
$[2]$ |
$2$ |
$4$ |
$17.4279690081$ |
| 10.0.160000000000.1 |
$x^{10} - 2 x^{5} + 2$ |
$10$ |
[0,5] |
$-\,2^{14}\cdot 5^{10}$ |
$2$ |
$13.1950791077$ |
$16.797996982738532$ |
|
|
✓ |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$4$ |
$4$ |
$117.792601679$ |
| 10.0.192216796875.1 |
$x^{10} - 3 x^{5} + 3$ |
$10$ |
[0,5] |
$-\,3^{9}\cdot 5^{10}$ |
$2$ |
$13.4393768976$ |
$17.10900031237617$ |
|
|
✓ |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$6$ |
$4$ |
$160.063051808$ |
| 10.0.300266134272.1 |
$x^{10} - x^{9} - x^{8} + 6 x^{7} - x^{6} - 7 x^{5} + 13 x^{4} - 3 x^{2} - x + 1$ |
$10$ |
[0,5] |
$-\,2^{8}\cdot 3^{5}\cdot 13^{6}$ |
$3$ |
$14.0524042658$ |
$20.646295463608727$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$6$ |
$4$ |
$149.754310475$ |
| 10.2.320000000000.1 |
$x^{10} - 2 x^{5} - 1$ |
$10$ |
[2,4] |
$2^{15}\cdot 5^{10}$ |
$2$ |
$14.1421356237$ |
$18.00364738986388$ |
|
|
✓ |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$2$ |
$5$ |
$105.547172322$ |
| 10.2.327680000000.1 |
$x^{10} - 3 x^{9} + 3 x^{8} + 10 x^{7} - 33 x^{6} + 49 x^{5} - 33 x^{4} + 10 x^{3} + 3 x^{2} - 3 x + 1$ |
$10$ |
[2,4] |
$2^{22}\cdot 5^{7}$ |
$2$ |
$14.1757156617$ |
$22.493653007613965$ |
|
|
|
$F_{5}\times C_2$ (as 10T5) |
trivial |
$2$ |
$5$ |
$86.6702492881$ |
| 10.0.393660000000.1 |
$x^{10} + 3 x^{8} - 6 x^{6} - 18 x^{4} + 21 x^{2} + 15$ |
$10$ |
[0,5] |
$-\,2^{8}\cdot 3^{9}\cdot 5^{7}$ |
$3$ |
$14.4381692611$ |
$15.648064552551654$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
$[2]$ |
$2$ |
$4$ |
$94.6039648024$ |
| 10.0.440301256704.1 |
$x^{10} - 2 x^{9} + 2 x^{8} - 8 x^{7} + 6 x^{6} + 4 x^{5} + 12 x^{4} - 8 x^{3} + x^{2} - 2 x + 2$ |
$10$ |
[0,5] |
$-\,2^{26}\cdot 3^{8}$ |
$2$ |
$14.6007442054$ |
$19.265797482245535$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$4$ |
$4$ |
$355.187442296$ |
| 10.2.524288000000.1 |
$x^{10} - 2 x^{9} + x^{8} + x^{6} - 10 x^{5} - x^{4} - x^{2} - 2 x - 1$ |
$10$ |
[2,4] |
$2^{25}\cdot 5^{6}$ |
$2$ |
$14.8578849718$ |
$22.493653007613965$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$2$ |
$5$ |
$158.742708564$ |
| 10.0.607500000000.1 |
$x^{10} + 10 x^{8} + 35 x^{6} - 2 x^{5} + 50 x^{4} - 10 x^{3} + 25 x^{2} - 10 x + 4$ |
$10$ |
[0,5] |
$-\,2^{8}\cdot 3^{5}\cdot 5^{10}$ |
$3$ |
$15.0783780619$ |
$22.049874807078353$ |
|
|
|
$F_{5}\times C_2$ (as 10T5) |
trivial |
$6$ |
$4$ |
$422.340044745$ |
| 10.0.607500000000.2 |
$x^{10} - 2 x^{5} + 4$ |
$10$ |
[0,5] |
$-\,2^{8}\cdot 3^{5}\cdot 5^{10}$ |
$3$ |
$15.0783780619$ |
$19.19553093391108$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$6$ |
$4$ |
$272.480106347$ |
| 10.0.630525109375.1 |
$x^{10} + 7$ |
$10$ |
[0,5] |
$-\,5^{6}\cdot 7^{9}$ |
$2$ |
$15.1345753048$ |
$19.267072840509627$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$2$ |
$4$ |
$178.853966027$ |
| 10.0.637009920000.1 |
$x^{10} - x^{9} + 3 x^{8} - 6 x^{7} + 3 x^{6} + 11 x^{5} - 13 x^{4} - 10 x^{3} + 25 x^{2} - 15 x + 3$ |
$10$ |
[0,5] |
$-\,2^{22}\cdot 3^{5}\cdot 5^{4}$ |
$3$ |
$15.1500693051$ |
$26.054222497305222$ |
|
|
|
$F_{5}\times C_2$ (as 10T5) |
trivial |
$6$ |
$4$ |
$295.358928554$ |
| 10.0.660451885056.1 |
$x^{10} - 2 x^{9} + 3 x^{8} + 3 x^{6} - 6 x^{5} + 3 x^{4} + 3 x^{2} - 2 x + 1$ |
$10$ |
[0,5] |
$-\,2^{25}\cdot 3^{9}$ |
$2$ |
$15.2049192628$ |
$18.081798170312066$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
$[2]$ |
$2$ |
$4$ |
$99.4440010381$ |
| 10.0.675496853504.1 |
$x^{10} - 5 x^{9} + 13 x^{8} - 16 x^{7} + 8 x^{6} + 12 x^{4} - 20 x^{3} + 19 x^{2} - 11 x + 3$ |
$10$ |
[0,5] |
$-\,2^{22}\cdot 11^{5}$ |
$2$ |
$15.2392057633$ |
$22.311503175611666$ |
|
|
|
$F_{5}\times C_2$ (as 10T5) |
trivial |
$2$ |
$4$ |
$182.098636898$ |
| 10.0.800000000000.1 |
$x^{10} + 5 x^{8} + 10 x^{6} + 10 x^{4} + 5 x^{2} + 5$ |
$10$ |
[0,5] |
$-\,2^{14}\cdot 5^{11}$ |
$2$ |
$15.4991898755$ |
$16.797996982738532$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
$[2]$ |
$2$ |
$4$ |
$117.792601679$ |
| 10.0.810000000000.1 |
$x^{10} + 15 x^{6} - 4 x^{5} + 10 x^{3} + 25 x^{2} + 20 x + 5$ |
$10$ |
[0,5] |
$-\,2^{10}\cdot 3^{4}\cdot 5^{10}$ |
$3$ |
$15.5184557392$ |
$22.049874807078353$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$4$ |
$4$ |
$330.571562571$ |
| 10.0.880602513408.1 |
$x^{10} - 2 x^{8} + 10 x^{6} + 8 x^{4} - 7 x^{2} + 2$ |
$10$ |
[0,5] |
$-\,2^{27}\cdot 3^{8}$ |
$2$ |
$15.6486901727$ |
$19.265797482245535$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$2$ |
$4$ |
$355.187442296$ |
| 10.0.961083984375.1 |
$x^{10} - 5 x^{9} + 15 x^{8} - 30 x^{7} + 45 x^{6} - 48 x^{5} + 45 x^{4} - 30 x^{3} + 15 x^{2} - 5 x + 1$ |
$10$ |
[0,5] |
$-\,3^{9}\cdot 5^{11}$ |
$2$ |
$15.7861466872$ |
$17.10900031237617$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
$[2]$ |
$2$ |
$4$ |
$160.063051808$ |
| 10.0.982540877824.1 |
$x^{10} - 4 x^{8} + 2 x^{6} + 20 x^{4} - 31 x^{2} + 16$ |
$10$ |
[0,5] |
$-\,2^{26}\cdot 11^{4}$ |
$2$ |
$15.8210412471$ |
$26.5329983228432$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$4$ |
$4$ |
$570.36325308$ |
| 10.0.1028071702528.2 |
$x^{10} - 3 x^{8} + 18 x^{6} - 22 x^{4} + 61 x^{2} + 13$ |
$10$ |
[0,5] |
$-\,2^{14}\cdot 13^{7}$ |
$2$ |
$15.8928703501$ |
$18.067560105343954$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
$[2]$ |
$2$ |
$4$ |
$80.222639086$ |
| 10.0.1048576000000.1 |
$x^{10} - 2 x^{9} - 2 x^{8} + 14 x^{6} - 4 x^{5} - 8 x^{4} - 16 x^{3} + 34 x^{2} - 20 x + 4$ |
$10$ |
[0,5] |
$-\,2^{26}\cdot 5^{6}$ |
$2$ |
$15.9242868221$ |
$26.74961219905688$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$4$ |
$4$ |
$702.178581232$ |
| 10.2.1061683200000.1 |
$x^{10} - 5 x^{9} + 19 x^{8} - 46 x^{7} + 93 x^{6} - 139 x^{5} + 177 x^{4} - 166 x^{3} + 125 x^{2} - 59 x + 11$ |
$10$ |
[2,4] |
$2^{22}\cdot 3^{4}\cdot 5^{5}$ |
$3$ |
$15.9440810915$ |
$26.054222497305222$ |
|
|
|
$F_{5}\times C_2$ (as 10T5) |
trivial |
$2$ |
$5$ |
$194.586521033$ |
| 10.0.1062521296875.1 |
$x^{10} + 10 x^{8} + 35 x^{6} + 50 x^{4} + 25 x^{2} + 27$ |
$10$ |
[0,5] |
$-\,3^{5}\cdot 5^{6}\cdot 23^{4}$ |
$3$ |
$15.9453392766$ |
$27.77487087706129$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$6$ |
$4$ |
$389.530844965$ |
| 10.0.1075648000000.1 |
$x^{10} - 3 x^{9} + 5 x^{8} - 7 x^{7} + 27 x^{6} - 39 x^{5} + 30 x^{4} - 28 x^{3} + 28 x^{2} - 20 x + 8$ |
$10$ |
[0,5] |
$-\,2^{12}\cdot 5^{6}\cdot 7^{5}$ |
$3$ |
$15.9649299536$ |
$25.021971019484877$ |
|
|
|
$F_{5}\times C_2$ (as 10T5) |
trivial |
$2$ |
$4$ |
$341.631976705$ |
| 10.2.1083499328125.1 |
$x^{10} - 2 x^{9} - 4 x^{8} + 9 x^{7} + 3 x^{6} - 13 x^{5} + 9 x^{4} + 21 x^{3} + 2 x^{2} - 2 x + 3$ |
$10$ |
[2,4] |
$5^{6}\cdot 37^{5}$ |
$2$ |
$15.9765449134$ |
$20.33894234805392$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$2$ |
$5$ |
$241.390810504$ |
| 10.0.1229312000000.1 |
$x^{10} + 10 x^{6} - 14 x^{5} + 10 x^{4} + 1$ |
$10$ |
[0,5] |
$-\,2^{15}\cdot 5^{6}\cdot 7^{4}$ |
$3$ |
$16.1795415671$ |
$25.021971019484877$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$2$ |
$4$ |
$215.119638342$ |
| 10.0.1259712000000.2 |
$x^{10} - 2 x^{9} + 3 x^{8} - 6 x^{7} + 6 x^{6} - 6 x^{5} - 3 x^{4} + 6 x^{3} + 9 x^{2} + 4 x + 16$ |
$10$ |
[0,5] |
$-\,2^{12}\cdot 3^{9}\cdot 5^{6}$ |
$3$ |
$16.2191140107$ |
$25.42035586229429$ |
|
|
|
$F_{5}\times C_2$ (as 10T5) |
trivial |
$6$ |
$4$ |
$623.840265196$ |
| 10.2.1320903770112.1 |
$x^{10} - 2 x^{9} - 3 x^{8} + 12 x^{6} + 24 x^{5} - 24 x^{4} - 48 x^{3} + 12 x^{2} + 40 x + 4$ |
$10$ |
[2,4] |
$2^{26}\cdot 3^{9}$ |
$2$ |
$16.2962289658$ |
$21.503003036178292$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$2$ |
$5$ |
$476.695060266$ |
| 10.0.1483154296875.1 |
$x^{10} - 5 x^{8} + 20 x^{6} - x^{5} - 25 x^{4} + 10 x^{3} + 25 x^{2} - 5 x + 1$ |
$10$ |
[0,5] |
$-\,3^{5}\cdot 5^{14}$ |
$2$ |
$16.4861267094$ |
$20.987665512343366$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$6$ |
$4$ |
$467.264758091$ |
| 10.2.1485172000000.1 |
$x^{10} - x^{8} - 2 x^{6} + 6 x^{4} - 3 x^{2} - 13$ |
$10$ |
[2,4] |
$2^{8}\cdot 5^{6}\cdot 13^{5}$ |
$3$ |
$16.4883681325$ |
$20.99051895628543$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$2$ |
$5$ |
$254.082176401$ |
| 10.2.1557315715072.1 |
$x^{10} + 5 x^{8} - 12 x^{7} + 3 x^{6} + 12 x^{5} - 3 x^{4} - 12 x^{3} - 5 x^{2} - 1$ |
$10$ |
[2,4] |
$2^{22}\cdot 13^{5}$ |
$2$ |
$16.5667632759$ |
$24.255161140409015$ |
|
|
|
$F_{5}\times C_2$ (as 10T5) |
trivial |
$2$ |
$5$ |
$298.012422213$ |
| 10.2.1600000000000.1 |
$x^{10} - 5 x^{6} - 6 x^{5} + 10 x^{4} - 30 x^{3} + 25 x^{2} - 30 x + 9$ |
$10$ |
[2,4] |
$2^{15}\cdot 5^{11}$ |
$2$ |
$16.6116203994$ |
$18.00364738986388$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
$[2]$ |
$2$ |
$5$ |
$217.764503745$ |
| 10.0.1679616000000.3 |
$x^{10} - 6 x^{5} + 18$ |
$10$ |
[0,5] |
$-\,2^{14}\cdot 3^{8}\cdot 5^{6}$ |
$3$ |
$16.6924852176$ |
$21.250370235038396$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$4$ |
$4$ |
$573.778122237$ |
| 10.2.1885747578125.1 |
$x^{10} + 2 x^{8} - x^{6} - 22 x^{4} - 39 x^{2} - 20$ |
$10$ |
[2,4] |
$5^{7}\cdot 17^{6}$ |
$2$ |
$16.8868387297$ |
$27.99395075493803$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$2$ |
$5$ |
$185.322365483$ |
| 10.0.1916696264704.1 |
$x^{10} + 8 x^{8} + 2 x^{6} + 4 x^{4} + x^{2} + 4$ |
$10$ |
[0,5] |
$-\,2^{26}\cdot 13^{4}$ |
$2$ |
$16.9143506491$ |
$28.844410203711913$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$4$ |
$4$ |
$778.00085364$ |
| 10.0.1965081755648.1 |
$x^{10} - 2 x^{9} - 3 x^{8} + 8 x^{7} + 4 x^{6} - 8 x^{5} - 16 x^{4} + 28 x^{2} + 8 x + 4$ |
$10$ |
[0,5] |
$-\,2^{27}\cdot 11^{4}$ |
$2$ |
$16.9565721583$ |
$26.5329983228432$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$2$ |
$4$ |
$570.36325308$ |
| 10.0.2002066523136.2 |
$x^{10} + x^{8} + 8 x^{6} - x^{4} + 7 x^{2} + 1$ |
$10$ |
[0,5] |
$-\,2^{10}\cdot 3^{4}\cdot 17^{6}$ |
$3$ |
$16.9882189769$ |
$29.001957651613843$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$4$ |
$4$ |
$272.459251919$ |
| 10.0.2097152000000.1 |
$x^{10} - 2 x^{9} - 3 x^{8} + 8 x^{6} + 8 x^{5} + 8 x^{4} - 3 x^{2} - 2 x + 1$ |
$10$ |
[0,5] |
$-\,2^{27}\cdot 5^{6}$ |
$2$ |
$17.0672280258$ |
$26.74961219905688$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$2$ |
$4$ |
$299.679926875$ |
| 10.0.2333772000000.1 |
$x^{10} - 2 x^{9} + 2 x^{8} - 20 x^{7} + 28 x^{6} - 12 x^{5} + 88 x^{4} - 80 x^{3} + 32 x^{2} - 32 x + 16$ |
$10$ |
[0,5] |
$-\,2^{8}\cdot 3^{5}\cdot 5^{6}\cdot 7^{4}$ |
$4$ |
$17.2506650415$ |
$26.67848399443575$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$6$ |
$4$ |
$555.393280234$ |
| 10.2.2430000000000.1 |
$x^{10} - 4 x^{5} + 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 3^{5}\cdot 5^{10}$ |
$3$ |
$17.3205080757$ |
$22.049874807078353$ |
|
|
✓ |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$2$ |
$5$ |
$345.407215079$ |
| 10.0.2530638036992.1 |
$x^{10} - 4 x^{8} + 8 x^{6} - 6 x^{4} + 2$ |
$10$ |
[0,5] |
$-\,2^{19}\cdot 13^{6}$ |
$2$ |
$17.3909378536$ |
$25.551388539968485$ |
|
|
✓ |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$2$ |
$4$ |
$162.481555916$ |
| 10.2.2530638036992.1 |
$x^{10} + 4 x^{8} + 8 x^{6} + 6 x^{4} - 2$ |
$10$ |
[2,4] |
$2^{19}\cdot 13^{6}$ |
$2$ |
$17.3909378536$ |
$25.551388539968485$ |
|
|
✓ |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$2$ |
$5$ |
$283.378428972$ |
| 10.0.2560000000000.4 |
$x^{10} - 10 x^{8} + 35 x^{6} - 50 x^{4} + 25 x^{2} + 4$ |
$10$ |
[0,5] |
$-\,2^{18}\cdot 5^{10}$ |
$2$ |
$17.4110112659$ |
$25.46100231092847$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$4$ |
$4$ |
$625.054130289$ |
| 10.2.2641807540224.1 |
$x^{10} - 4 x^{9} + 6 x^{8} - 12 x^{6} + 24 x^{4} - 15 x^{2} - 4 x - 2$ |
$10$ |
[2,4] |
$2^{27}\cdot 3^{9}$ |
$2$ |
$17.465865745$ |
$21.503003036178292$ |
|
|
? |
$F_{5}\times C_2$ (as 10T5) |
trivial |
$2$ |
$5$ |
$829.784198439$ |
| 10.0.3037500000000.1 |
$x^{10} + 5 x^{8} + 5 x^{6} - 5 x^{4} - 5 x^{2} + 15$ |
$10$ |
[0,5] |
$-\,2^{8}\cdot 3^{5}\cdot 5^{11}$ |
$3$ |
$17.7113485025$ |
$22.049874807078353$ |
|
|
|
$F_{5}\times C_2$ (as 10T5) |
$[2]$ |
$2$ |
$4$ |
$422.340044745$ |
