| 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 |
| 10.2.316329754624.1 |
$x^{10} - 2 x^{8} - 4 x^{6} + 8 x^{2} - 4$ |
$10$ |
[2,4] |
$2^{16}\cdot 13^{6}$ |
$2$ |
$14.1258309465$ |
$33.71525930972029$ |
|
|
? |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$82.4454675434$ |
| 10.2.640000000000.1 |
$x^{10} - 5 x^{8} + 10 x^{6} - 10 x^{4} + 5 x^{2} - 9$ |
$10$ |
[2,4] |
$2^{16}\cdot 5^{10}$ |
$2$ |
$15.1571656651$ |
$31.346170753261593$ |
|
|
? |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$202.301290674$ |
| 10.2.1265319018496.1 |
$x^{10} - x^{8} + 2 x^{6} - 4 x^{4} + x^{2} - 1$ |
$10$ |
[2,4] |
$2^{18}\cdot 13^{6}$ |
$2$ |
$16.2263187712$ |
$43.72328186816097$ |
|
|
✓ |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$249.985409032$ |
| 10.2.1265319018496.2 |
$x^{10} - 2 x^{8} + 2 x^{6} - 4 x^{4} - 4$ |
$10$ |
[2,4] |
$2^{18}\cdot 13^{6}$ |
$2$ |
$16.2263187712$ |
$43.72328186816097$ |
|
|
? |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$243.116982705$ |
| 10.2.1562500000000.1 |
$x^{10} + 5 x^{6} + 5 x^{2} - 4$ |
$10$ |
[2,4] |
$2^{8}\cdot 5^{14}$ |
$2$ |
$16.5722700867$ |
$40.757355654353084$ |
|
|
? |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$228.712485895$ |
| 10.2.1761205026816.1 |
$x^{10} + 4 x^{8} - 2 x^{6} - 28 x^{4} - 31 x^{2} - 16$ |
$10$ |
[2,4] |
$2^{28}\cdot 3^{8}$ |
$2$ |
$16.7718508505$ |
$33.8355984495082$ |
|
|
|
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$1164.15609174$ |
| 10.2.2002066523136.1 |
$x^{10} + x^{8} - x^{4} + 3 x^{2} - 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 3^{4}\cdot 17^{6}$ |
$3$ |
$16.9882189769$ |
$53.18982485476109$ |
|
|
✓ |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$370.470216022$ |
| 10.2.2002066523136.2 |
$x^{10} + 3 x^{8} - 5 x^{6} - 15 x^{4} + 8 x^{2} - 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 3^{4}\cdot 17^{6}$ |
$3$ |
$16.9882189769$ |
$53.18982485476109$ |
|
|
✓ |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$226.543972403$ |
| 10.2.2002066523136.3 |
$x^{10} + 3 x^{8} - 7 x^{6} - 12 x^{4} + 25 x^{2} - 9$ |
$10$ |
[2,4] |
$2^{10}\cdot 3^{4}\cdot 17^{6}$ |
$3$ |
$16.9882189769$ |
$53.18982485476109$ |
|
|
? |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$294.72378008$ |
| 10.2.2560000000000.1 |
$x^{10} - 5 x^{8} + 10 x^{6} - 20 x^{4} + 5 x^{2} - 1$ |
$10$ |
[2,4] |
$2^{18}\cdot 5^{10}$ |
$2$ |
$17.4110112659$ |
$40.65095411967427$ |
|
|
? |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$366.278895855$ |
| 10.2.2560000000000.2 |
$x^{10} + 5 x^{8} + 10 x^{6} + 10 x^{4} + 5 x^{2} - 1$ |
$10$ |
[2,4] |
$2^{18}\cdot 5^{10}$ |
$2$ |
$17.4110112659$ |
$40.65095411967427$ |
|
|
✓ |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$595.354285334$ |
| 10.2.3240000000000.1 |
$x^{10} - 5 x^{8} - 10 x^{7} + 30 x^{6} + 14 x^{5} - 40 x^{4} - 20 x^{3} + 15 x^{2} + 20 x + 5$ |
$10$ |
[2,4] |
$2^{12}\cdot 3^{4}\cdot 5^{10}$ |
$3$ |
$17.8260245797$ |
$32.28290630243523$ |
|
|
? |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$446.459525886$ |
| 10.2.3341233033216.1 |
$x^{10} + 2 x^{8} - 14 x^{7} + 2 x^{6} - 8 x^{5} + 24 x^{4} + 12 x^{3} - 32 x^{2} + 16 x - 4$ |
$10$ |
[2,4] |
$2^{12}\cdot 13^{8}$ |
$2$ |
$17.8809536176$ |
$27.624659049073333$ |
|
|
? |
$(C_2^4 : C_5):C_4$ (as 10T24) |
$[2]$ |
$2$ |
$5$ |
$179.259480357$ |
| 10.2.3930163511296.1 |
$x^{10} - x^{8} - 4 x^{6} - 12 x^{4} + 4 x^{2} - 4$ |
$10$ |
[2,4] |
$2^{28}\cdot 11^{4}$ |
$2$ |
$18.1736040549$ |
$46.5986356256745$ |
|
|
|
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$1197.35917999$ |
| 10.2.4194304000000.1 |
$x^{10} - x^{8} + 12 x^{6} - 4 x^{4} - 12 x^{2} - 4$ |
$10$ |
[2,4] |
$2^{28}\cdot 5^{6}$ |
$2$ |
$18.2922020771$ |
$46.979064213741616$ |
|
|
|
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$1449.53175272$ |
| 10.2.5345344000000.1 |
$x^{10} + 7 x^{8} + 26 x^{6} + 38 x^{4} + 29 x^{2} - 1$ |
$10$ |
[2,4] |
$2^{12}\cdot 5^{6}\cdot 17^{4}$ |
$3$ |
$18.7412073624$ |
$40.369043297108284$ |
|
|
? |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$536.346422978$ |
| 10.2.6250000000000.1 |
$x^{10} + 5 x^{6} + 5 x^{2} - 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 5^{14}$ |
$2$ |
$19.0365393872$ |
$44.446211504060095$ |
|
|
✓ |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$647.126372794$ |
| 10.2.6250000000000.2 |
$x^{10} - 5 x^{8} + 5 x^{6} + 5 x^{4} - 5 x^{2} - 4$ |
$10$ |
[2,4] |
$2^{10}\cdot 5^{14}$ |
$2$ |
$19.0365393872$ |
$44.446211504060095$ |
|
|
? |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$1006.90748526$ |
| 10.2.6718464000000.3 |
$x^{10} + 3 x^{8} + 6 x^{6} - 18 x^{4} + 9 x^{2} - 9$ |
$10$ |
[2,4] |
$2^{16}\cdot 3^{8}\cdot 5^{6}$ |
$3$ |
$19.1746303103$ |
$39.654593023325205$ |
|
|
? |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$1071.65046772$ |
| 10.2.7496644000000.1 |
$x^{10} - 8 x^{8} + 16 x^{6} - 2 x^{4} + 14 x^{2} - 1$ |
$10$ |
[2,4] |
$2^{8}\cdot 5^{6}\cdot 37^{4}$ |
$3$ |
$19.3859321665$ |
$68.41177484212203$ |
|
|
? |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$431.252905994$ |
| 10.2.7666785058816.3 |
$x^{10} + 3 x^{8} + 6 x^{6} - 14 x^{4} - 43 x^{2} - 81$ |
$10$ |
[2,4] |
$2^{28}\cdot 13^{4}$ |
$2$ |
$19.4294867665$ |
$50.658057734962696$ |
|
|
|
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$1752.62816229$ |
| 10.2.8745694265344.1 |
$x^{10} + 7 x^{8} + 12 x^{6} - 4 x^{4} + 52 x^{2} - 4$ |
$10$ |
[2,4] |
$2^{26}\cdot 19^{4}$ |
$2$ |
$19.6869949145$ |
$45.22234051768035$ |
|
|
|
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$1675.84043171$ |
| 10.2.10240000000000.1 |
$x^{10} + 10 x^{6} - 15 x^{2} - 16$ |
$10$ |
[2,4] |
$2^{20}\cdot 5^{10}$ |
$2$ |
$20.0$ |
$46.69568412632977$ |
|
|
? |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$1604.43411928$ |
| 10.2.10497600000000.1 |
$x^{10} - 5 x^{8} + 10 x^{6} - 24 x^{5} - 10 x^{4} + 5 x^{2} - 1$ |
$10$ |
[2,4] |
$2^{12}\cdot 3^{8}\cdot 5^{8}$ |
$3$ |
$20.0497518587$ |
$28.83316059082836$ |
|
|
? |
$(C_2^4 : C_5):C_4$ (as 10T24) |
$[2]$ |
$2$ |
$5$ |
$818.836752536$ |
| 10.2.12356631040000.1 |
$x^{10} - 2 x^{9} - 6 x^{8} + 6 x^{7} + 18 x^{6} + 26 x^{5} - 62 x^{4} - 22 x^{3} + 28 x^{2} + 16 x + 2$ |
$10$ |
[2,4] |
$2^{12}\cdot 5^{4}\cdot 13^{6}$ |
$3$ |
$20.3793349774$ |
$44.82693131283043$ |
|
|
? |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$812.064487551$ |
| 10.2.13589544960000.1 |
$x^{10} - 3 x^{9} + 4 x^{8} - 4 x^{7} - 14 x^{6} + 18 x^{5} - 12 x^{4} - 36 x^{3} + 7 x^{2} + 19 x - 16$ |
$10$ |
[2,4] |
$2^{28}\cdot 3^{4}\cdot 5^{4}$ |
$3$ |
$20.574083187$ |
$54.41548295093269$ |
|
|
|
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$4746.07692507$ |
| 10.2.16402500000000.6 |
$x^{10} - 5 x^{8} + 10 x^{6} - 10 x^{4} + 5 x^{2} - 4$ |
$10$ |
[2,4] |
$2^{8}\cdot 3^{8}\cdot 5^{10}$ |
$3$ |
$20.9648135631$ |
$51.560248424032004$ |
|
|
? |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$1328.32128466$ |
| 10.2.17909824000000.1 |
$x^{10} - 2 x^{8} + 11 x^{6} - 58 x^{4} + 29 x^{2} - 4$ |
$10$ |
[2,4] |
$2^{12}\cdot 5^{6}\cdot 23^{4}$ |
$3$ |
$21.1499396171$ |
$53.937885084186505$ |
|
|
|
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$844.569642212$ |
| 10.2.18018598708224.1 |
$x^{10} - 8 x^{8} + 9 x^{6} - 30 x^{4} - 36 x^{2} - 9$ |
$10$ |
[2,4] |
$2^{10}\cdot 3^{6}\cdot 17^{6}$ |
$3$ |
$21.1627499885$ |
$70.00174624484565$ |
|
|
? |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$440.001292906$ |
| 10.2.18018598708224.2 |
$x^{10} - 5 x^{8} + 21 x^{6} - 33 x^{4} - 18 x^{2} - 9$ |
$10$ |
[2,4] |
$2^{10}\cdot 3^{6}\cdot 17^{6}$ |
$3$ |
$21.1627499885$ |
$70.00174624484565$ |
|
|
? |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$487.43558864$ |
| 10.2.18018598708224.3 |
$x^{10} + x^{8} + 3 x^{6} - 3 x^{4} - 9$ |
$10$ |
[2,4] |
$2^{10}\cdot 3^{6}\cdot 17^{6}$ |
$3$ |
$21.1627499885$ |
$70.00174624484565$ |
|
|
? |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$763.306151702$ |
| 10.2.18018598708224.4 |
$x^{10} - 5 x^{8} + 15 x^{6} - 24 x^{4} + 27 x^{2} - 9$ |
$10$ |
[2,4] |
$2^{10}\cdot 3^{6}\cdot 17^{6}$ |
$3$ |
$21.1627499885$ |
$70.00174624484565$ |
|
|
? |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$777.147824363$ |
| 10.2.23059204000000.1 |
$x^{10} - 6 x^{8} - 8 x^{6} - 24 x^{4} - 22 x^{2} - 9$ |
$10$ |
[2,4] |
$2^{8}\cdot 5^{6}\cdot 7^{8}$ |
$3$ |
$21.6912425757$ |
$44.85913848622377$ |
|
|
? |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$1070.61639193$ |
| 10.2.24010000000000.1 |
$x^{10} - 5 x^{8} - 20 x^{7} - 60 x^{6} - 42 x^{5} - 190 x^{4} + 60 x^{3} - 225 x^{2} + 120 x - 53$ |
$10$ |
[2,4] |
$2^{10}\cdot 5^{10}\cdot 7^{4}$ |
$3$ |
$21.7790642448$ |
$38.02548569032195$ |
|
|
? |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$1230.827278$ |
| 10.6.24010000000000.1 |
$x^{10} - 5 x^{8} - 10 x^{5} - 5 x^{2} + 1$ |
$10$ |
[6,2] |
$2^{10}\cdot 5^{10}\cdot 7^{4}$ |
$3$ |
$21.7790642448$ |
$38.02548569032195$ |
|
|
? |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$7$ |
$2915.30517215$ |
| 10.2.25000000000000.2 |
$x^{10} - 5 x^{8} + 20 x^{6} - 40 x^{4} - 40 x^{2} - 16$ |
$10$ |
[2,4] |
$2^{12}\cdot 5^{14}$ |
$2$ |
$21.8672414789$ |
$48.468937332853066$ |
|
|
? |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$2446.70506475$ |
| 10.2.25000000000000.3 |
$x^{10} + 5 x^{8} + 10 x^{6} - 20 x^{4} - 40 x^{2} - 16$ |
$10$ |
[2,4] |
$2^{12}\cdot 5^{14}$ |
$2$ |
$21.8672414789$ |
$57.63960513284988$ |
|
|
? |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$1435.14536103$ |
| 10.2.26214400000000.1 |
$x^{10} - x^{9} + 10 x^{8} - 4 x^{7} + 28 x^{6} - 20 x^{5} + 24 x^{4} - 40 x^{3} + 6 x^{2} - 22 x + 4$ |
$10$ |
[2,4] |
$2^{26}\cdot 5^{8}$ |
$2$ |
$21.9712108661$ |
$42.42042244732031$ |
|
|
|
$(C_2^4 : C_5):C_4$ (as 10T24) |
$[2]$ |
$2$ |
$5$ |
$2291.63383695$ |
| 10.2.26808753332089.1 |
$x^{10} - 8 x^{8} + 26 x^{6} - 37 x^{4} + 17 x^{2} - 4$ |
$10$ |
[2,4] |
$173^{6}$ |
$1$ |
$22.0205246416$ |
$47.70177914677923$ |
|
|
? |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$1066.36427548$ |
| 10.2.26873856000000.1 |
$x^{10} + x^{8} - 8 x^{6} - 16 x^{4} - 7 x^{2} - 1$ |
$10$ |
[2,4] |
$2^{18}\cdot 3^{8}\cdot 5^{6}$ |
$3$ |
$22.0258662951$ |
$51.425644756236096$ |
|
|
✓ |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$2579.00043799$ |
| 10.2.26873856000000.3 |
$x^{10} - 3 x^{8} + 12 x^{6} - 18 x^{4} + 27 x^{2} - 9$ |
$10$ |
[2,4] |
$2^{18}\cdot 3^{8}\cdot 5^{6}$ |
$3$ |
$22.0258662951$ |
$51.425644756236096$ |
|
|
? |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$3156.52472947$ |
| 10.2.28179280429056.2 |
$x^{10} - 11 x^{8} + 34 x^{6} - 22 x^{4} + 11 x^{2} - 1$ |
$10$ |
[2,4] |
$2^{32}\cdot 3^{8}$ |
$2$ |
$22.1305898756$ |
$46.825419056434505$ |
|
|
? |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$4393.80030834$ |
| 10.2.28179280429056.4 |
$x^{10} + x^{8} + 4 x^{6} - 4 x^{4} - 4 x^{2} - 4$ |
$10$ |
[2,4] |
$2^{32}\cdot 3^{8}$ |
$2$ |
$22.1305898756$ |
$46.825419056434505$ |
|
|
? |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$3147.20300127$ |
| 10.2.29160000000000.2 |
$x^{10} - 5 x^{9} + 5 x^{8} - 20 x^{7} + 15 x^{6} + x^{5} - 15 x^{4} + 10 x^{3} - 5 x^{2} - 5 x + 5$ |
$10$ |
[2,4] |
$2^{12}\cdot 3^{6}\cdot 5^{10}$ |
$3$ |
$22.2064303492$ |
$48.80439556129846$ |
|
|
|
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$1486.08626775$ |
| 10.2.29246464000000.1 |
$x^{10} - 6 x^{8} + 12 x^{6} - 4 x^{4} - 12 x^{2} - 4$ |
$10$ |
[2,4] |
$2^{16}\cdot 5^{6}\cdot 13^{4}$ |
$3$ |
$22.2130061367$ |
$59.3701531784568$ |
|
|
? |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$1770.27870815$ |
| 10.2.29986576000000.1 |
$x^{10} - x^{8} - 5 x^{6} - 15 x^{4} - 25 x^{2} - 25$ |
$10$ |
[2,4] |
$2^{10}\cdot 5^{6}\cdot 37^{4}$ |
$3$ |
$22.2685883897$ |
$74.60356947068861$ |
|
|
? |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$2347.6102087$ |
| 10.2.29986576000000.2 |
$x^{10} - 6 x^{8} + 12 x^{6} - 9 x^{4} + 3 x^{2} - 4$ |
$10$ |
[2,4] |
$2^{10}\cdot 5^{6}\cdot 37^{4}$ |
$3$ |
$22.2685883897$ |
$74.60356947068861$ |
|
|
? |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$2326.43916436$ |
| 10.2.30576476160000.1 |
$x^{10} - 3 x^{9} + 4 x^{7} + 4 x^{6} + 12 x^{5} + 8 x^{4} - 32 x^{3} - 18 x^{2} + 6 x + 8$ |
$10$ |
[2,4] |
$2^{26}\cdot 3^{6}\cdot 5^{4}$ |
$3$ |
$22.3120124346$ |
$52.881306763677685$ |
|
|
|
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$4886.64856401$ |
| 10.2.38982341165056.5 |
$x^{10} - 2 x^{8} - 16 x^{4} + 36 x^{2} - 4$ |
$10$ |
[2,4] |
$2^{16}\cdot 29^{6}$ |
$2$ |
$22.8605561568$ |
$61.54141653687392$ |
|
|
? |
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$3050.49261683$ |
| 10.2.40960000000000.1 |
$x^{10} - 10 x^{6} + 20 x^{2} - 16$ |
$10$ |
[2,4] |
$2^{22}\cdot 5^{10}$ |
$2$ |
$22.9739670999$ |
$42.82013114405259$ |
|
|
|
$(C_2^4 : C_5):C_4$ (as 10T24) |
trivial |
$2$ |
$5$ |
$1334.84481524$ |
