| 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 |
| 10.2.40228093952.1 |
$x^{10} + 2 x^{6} + 2 x^{4} - 2 x^{2} - 2$ |
$10$ |
(2, 4) |
$2^{19}\cdot 277^{2}$ |
$2$ |
$11.4935170807$ |
$118.96316149687134$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$5$ |
$27.229843698$ |
| 10.2.111422210048.2 |
$x^{10} + 2 x^{8} + 2 x^{6} - 2 x^{2} - 2$ |
$10$ |
(2, 4) |
$2^{19}\cdot 461^{2}$ |
$2$ |
$12.7261540727$ |
$153.4698523849769$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$5$ |
$53.6022950857$ |
| 10.2.644811849728.9 |
$x^{10} + 10 x^{6} - 6 x^{4} + 6 x^{2} - 2$ |
$10$ |
(2, 4) |
$2^{19}\cdot 1109^{2}$ |
$2$ |
$15.1685232295$ |
$238.0336662534306$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$5$ |
$283.12543925$ |
| 10.2.844292947968.3 |
$x^{10} - 2 x^{8} + 2 x^{6} - 4 x^{4} + 2 x^{2} - 2$ |
$10$ |
(2, 4) |
$2^{19}\cdot 3^{6}\cdot 47^{2}$ |
$3$ |
$15.582937047$ |
$176.54808269487876$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$5$ |
$278.924046627$ |
| 10.2.5120000000000.3 |
$x^{10} - 10 x^{6} - 30 x^{4} - 10 x^{2} - 2$ |
$10$ |
(2, 4) |
$2^{19}\cdot 5^{10}$ |
$2$ |
$18.6606598307$ |
$45.497561182605686$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
trivial |
trivial |
$2$ |
$5$ |
$749.549383197$ |
| 10.2.427677828251648.5 |
$x^{10} - 26 x^{6} + 26 x^{4} + 182 x^{2} - 338$ |
$10$ |
(2, 4) |
$2^{19}\cdot 13^{8}$ |
$2$ |
$29.0476948501$ |
$67.43308768170668$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$[2]$ |
$[2]$ |
$2$ |
$5$ |
$2271.88064423$ |
| 10.2.483729408000000.18 |
$x^{10} - 180 x^{4} - 648$ |
$10$ |
(2, 4) |
$2^{19}\cdot 3^{10}\cdot 5^{6}$ |
$3$ |
$29.4076451364$ |
$142.01345664298256$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$5$ |
$3244.56430004$ |
| 10.0.806215680000000.5 |
$x^{10} + 6 x^{8} + 30 x^{6} + 90 x^{4} + 90 x^{2} + 30$ |
$10$ |
(0, 5) |
$-\,2^{19}\cdot 3^{9}\cdot 5^{7}$ |
$3$ |
$30.9488933233$ |
$78.55620517023675$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$[2]$ |
$[2]$ |
$2$ |
$4$ |
$5519.40927448$ |
| 10.0.806215680000000.6 |
$x^{10} + 6 x^{8} + 34 x^{6} + 90 x^{4} + 90 x^{2} + 30$ |
$10$ |
(0, 5) |
$-\,2^{19}\cdot 3^{9}\cdot 5^{7}$ |
$3$ |
$30.9488933233$ |
$142.01345664298256$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$[2]$ |
$2$ |
$4$ |
$3041.66040826$ |
| 10.2.1343692800000000.9 |
$x^{10} + 30 x^{6} - 270 x^{4} + 630 x^{2} - 450$ |
$10$ |
(2, 4) |
$2^{19}\cdot 3^{8}\cdot 5^{8}$ |
$3$ |
$32.5709179872$ |
$70.38309659526024$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$[2]$ |
$[2]$ |
$2$ |
$5$ |
$4421.94076532$ |
| 10.0.6220800000000000.11 |
$x^{10} + 90 x^{6} + 810 x^{4} + 2430 x^{2} + 2430$ |
$10$ |
(0, 5) |
$-\,2^{19}\cdot 3^{5}\cdot 5^{11}$ |
$3$ |
$37.9651066214$ |
$78.80408758874658$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$4$ |
$3539.26472043$ |
| 10.2.33592320000000000.32 |
$x^{10} - 10 x^{8} + 70 x^{6} - 210 x^{4} + 270 x^{2} - 18$ |
$10$ |
(2, 4) |
$2^{19}\cdot 3^{8}\cdot 5^{10}$ |
$3$ |
$44.939061648$ |
$163.9191077837171$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$5$ |
$30436.6132046$ |
| 10.2.335...000.137 |
$x^{10} - 10 x^{8} + 10 x^{6} + 130 x^{4} - 70 x^{2} - 1058$ |
$10$ |
(2, 4) |
$2^{19}\cdot 3^{8}\cdot 5^{10}$ |
$3$ |
$44.939061648$ |
$109.5683499600196$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
trivial |
trivial |
$2$ |
$5$ |
$54660.1898716$ |
| 10.0.65303470080000000.11 |
$x^{10} + 26 x^{8} + 202 x^{6} + 408 x^{4} + 150 x^{2} + 30$ |
$10$ |
(0, 5) |
$-\,2^{19}\cdot 3^{13}\cdot 5^{7}$ |
$3$ |
$48.0279031213$ |
$234.21646233215262$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$[2]$ |
$2$ |
$4$ |
$25878.7196704$ |
| 10.2.93312000000000000.12 |
$x^{10} - 10 x^{8} + 30 x^{6} - 10 x^{4} - 50 x^{2} - 18$ |
$10$ |
(2, 4) |
$2^{19}\cdot 3^{6}\cdot 5^{12}$ |
$3$ |
$49.7729921785$ |
$132.0305885927879$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$5$ |
$95015.8620128$ |
| 10.2.93312000000000000.25 |
$x^{10} + 10 x^{8} - 90 x^{6} + 200 x^{4} + 230 x^{2} - 162$ |
$10$ |
(2, 4) |
$2^{19}\cdot 3^{6}\cdot 5^{12}$ |
$3$ |
$49.7729921785$ |
$208.6772391043277$ |
|
|
|
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$5$ |
$320174.452821$ |
| 10.2.108...000.23 |
$x^{10} - 10 x^{8} + 70 x^{6} - 270 x^{4} + 450 x^{2} - 450$ |
$10$ |
(2, 4) |
$2^{19}\cdot 3^{12}\cdot 5^{8}$ |
$3$ |
$50.5450349168$ |
$234.21646233215262$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$[2]$ |
$2$ |
$5$ |
$57781.4997293$ |
| 10.2.262...768.22 |
$x^{10} + 58 x^{6} - 174 x^{2} - 1682$ |
$10$ |
(2, 4) |
$2^{19}\cdot 29^{8}$ |
$2$ |
$55.1919057216$ |
$136.07265568699344$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$[2]$ |
$[2]$ |
$2$ |
$5$ |
$89986.1454813$ |
| 10.2.302...000.125 |
$x^{10} + 20 x^{8} - 960 x^{4} + 3840 x^{2} - 4608$ |
$10$ |
(2, 4) |
$2^{19}\cdot 3^{10}\cdot 5^{10}$ |
$3$ |
$55.9819794922$ |
$236.41226276623973$ |
|
|
|
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$5$ |
$464340.9774$ |
| 10.0.503884800000000000.6 |
$x^{10} - 30 x^{6} + 90 x^{4} + 30 x^{2} + 30$ |
$10$ |
(0, 5) |
$-\,2^{19}\cdot 3^{9}\cdot 5^{11}$ |
$3$ |
$58.9159826737$ |
$122.2917745310347$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$[2, 6]$ |
$[2, 6]$ |
$2$ |
$4$ |
$14146.590182$ |
| 10.0.503...000.35 |
$x^{10} + 10 x^{8} + 70 x^{6} + 360 x^{4} + 270 x^{2} + 270$ |
$10$ |
(0, 5) |
$-\,2^{19}\cdot 3^{9}\cdot 5^{11}$ |
$3$ |
$58.9159826737$ |
$163.9191077837171$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$4$ |
$74632.5660685$ |
| 10.0.503...000.112 |
$x^{10} + 20 x^{8} + 240 x^{6} + 1600 x^{4} + 5120 x^{2} + 7680$ |
$10$ |
(0, 5) |
$-\,2^{19}\cdot 3^{9}\cdot 5^{11}$ |
$3$ |
$58.9159826737$ |
$236.41226276623973$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$[2]$ |
$2$ |
$4$ |
$145916.533134$ |
| 10.2.839...000.38 |
$x^{10} + 10 x^{8} + 30 x^{6} - 210 x^{2} - 162$ |
$10$ |
(2, 4) |
$2^{19}\cdot 3^{8}\cdot 5^{12}$ |
$3$ |
$62.003756314$ |
$208.6772391043277$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$[2]$ |
$2$ |
$5$ |
$362717.363092$ |
| 10.4.139...000.21 |
$x^{10} - 10 x^{8} + 80 x^{4} + 400 x^{2} + 480$ |
$10$ |
(4, 3) |
$-\,2^{19}\cdot 3^{7}\cdot 5^{13}$ |
$3$ |
$65.2533594888$ |
$132.0305885927879$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$[2, 2]$ |
$2$ |
$6$ |
$687988.96799$ |
| 10.4.139...000.34 |
$x^{10} - 90 x^{6} - 630 x^{4} + 1350 x^{2} + 2430$ |
$10$ |
(4, 3) |
$-\,2^{19}\cdot 3^{7}\cdot 5^{13}$ |
$3$ |
$65.2533594888$ |
$208.6772391043277$ |
|
|
|
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$[2, 2]$ |
$2$ |
$6$ |
$1471132.40671$ |
| 10.2.200...000.48 |
$x^{10} - 10 x^{8} + 140 x^{6} - 580 x^{4} + 6680 x^{2} - 2312$ |
$10$ |
(2, 4) |
$2^{19}\cdot 5^{18}$ |
$2$ |
$67.6243337806$ |
$164.8785354604216$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
trivial |
trivial |
$2$ |
$5$ |
$210793.161963$ |
| 10.6.233...000.12 |
$x^{10} - 10 x^{8} - 150 x^{6} + 300 x^{4} + 2250 x^{2} - 450$ |
$10$ |
(6, 2) |
$2^{19}\cdot 3^{6}\cdot 5^{14}$ |
$3$ |
$68.6732736483$ |
$197.43177973614576$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
trivial |
$[2]$ |
$2$ |
$7$ |
$1319522.14875$ |
| 10.6.233...000.16 |
$x^{10} - 10 x^{8} - 150 x^{6} + 1860 x^{4} - 3150 x^{2} - 5202$ |
$10$ |
(6, 2) |
$2^{19}\cdot 3^{6}\cdot 5^{14}$ |
$3$ |
$68.6732736483$ |
$197.43177973614576$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
trivial |
$[2]$ |
$2$ |
$7$ |
$1584413.70604$ |
| 10.4.125...000.78 |
$x^{10} - 360 x^{6} - 4320 x^{4} + 155520$ |
$10$ |
(4, 3) |
$-\,2^{19}\cdot 3^{9}\cdot 5^{13}$ |
$3$ |
$81.2881288291$ |
$208.6772391043277$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$[2, 2, 2]$ |
$2$ |
$6$ |
$1336151.52922$ |
| 10.2.209...000.36 |
$x^{10} - 10 x^{8} - 50 x^{6} - 290 x^{4} - 250 x^{2} - 242$ |
$10$ |
(2, 4) |
$2^{19}\cdot 3^{8}\cdot 5^{14}$ |
$3$ |
$85.5484217084$ |
$374.7466786128911$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$5$ |
$1204352.31311$ |
| 10.2.244...000.59 |
$x^{10} - 30 x^{8} + 240 x^{6} - 300 x^{4} - 1800 x^{2} - 3528$ |
$10$ |
(2, 4) |
$2^{19}\cdot 3^{14}\cdot 5^{10}$ |
$3$ |
$86.875387094$ |
$373.6547629627139$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$[2]$ |
$2$ |
$5$ |
$1073877.27086$ |
| 10.4.349...000.20 |
$x^{10} - 660 x^{6} - 6300 x^{4} - 14400 x^{2} + 1080$ |
$10$ |
(4, 3) |
$-\,2^{19}\cdot 3^{7}\cdot 5^{15}$ |
$3$ |
$90.0319955967$ |
$197.43177973614576$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$[2]$ |
$[2, 2, 2]$ |
$2$ |
$6$ |
$1835601.12955$ |
| 10.4.349...000.44 |
$x^{10} - 210 x^{6} - 450 x^{4} + 11250 x^{2} + 45630$ |
$10$ |
(4, 3) |
$-\,2^{19}\cdot 3^{7}\cdot 5^{15}$ |
$3$ |
$90.0319955967$ |
$197.43177973614576$ |
|
|
? |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$[2]$ |
$[2, 2, 2]$ |
$2$ |
$6$ |
$1252471.04458$ |
| 10.0.408...000.54 |
$x^{10} - 30 x^{8} + 150 x^{6} + 1800 x^{4} + 6750 x^{2} + 6750$ |
$10$ |
(0, 5) |
$-\,2^{19}\cdot 3^{13}\cdot 5^{11}$ |
$3$ |
$91.4285069451$ |
$373.6547629627139$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[6]$ |
$[6]$ |
$2$ |
$4$ |
$604620.258529$ |
| 10.2.680...000.11 |
$x^{10} + 30 x^{6} + 120 x^{4} + 90 x^{2} - 18$ |
$10$ |
(2, 4) |
$2^{19}\cdot 3^{12}\cdot 5^{12}$ |
$3$ |
$96.220254802$ |
$329.8189501715472$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[3]$ |
$[6]$ |
$2$ |
$5$ |
$1255143.40059$ |
| 10.2.680...000.148 |
$x^{10} - 10 x^{8} + 30 x^{6} + 300 x^{4} - 10110 x^{2} - 15138$ |
$10$ |
(2, 4) |
$2^{19}\cdot 3^{12}\cdot 5^{12}$ |
$3$ |
$96.220254802$ |
$434.0661493000463$ |
|
|
|
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$[2]$ |
$2$ |
$5$ |
$4449955.1114$ |
| 10.2.680...000.164 |
$x^{10} - 150 x^{6} + 250 x^{4} + 3750 x^{2} - 11250$ |
$10$ |
(2, 4) |
$2^{19}\cdot 3^{12}\cdot 5^{12}$ |
$3$ |
$96.220254802$ |
$434.0661493000463$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$[2]$ |
$2$ |
$5$ |
$4821401.45857$ |
| 10.2.680...000.235 |
$x^{10} + 30 x^{8} + 270 x^{6} + 90 x^{4} - 1350 x^{2} - 1458$ |
$10$ |
(2, 4) |
$2^{19}\cdot 3^{12}\cdot 5^{12}$ |
$3$ |
$96.220254802$ |
$434.0661493000463$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[6]$ |
$[6]$ |
$2$ |
$5$ |
$818332.655347$ |
| 10.2.680...000.240 |
$x^{10} + 30 x^{8} + 270 x^{6} + 990 x^{4} + 1350 x^{2} - 1458$ |
$10$ |
(2, 4) |
$2^{19}\cdot 3^{12}\cdot 5^{12}$ |
$3$ |
$96.220254802$ |
$434.0661493000463$ |
|
|
|
$C_2 \wr S_5$ (as 10T39) |
trivial |
$[2]$ |
$2$ |
$5$ |
$10794365.491$ |
| 10.4.113...000.40 |
$x^{10} - 10 x^{8} - 200 x^{6} + 480 x^{4} - 1200 x^{2} + 480$ |
$10$ |
(4, 3) |
$-\,2^{19}\cdot 3^{11}\cdot 5^{13}$ |
$3$ |
$101.263137106$ |
$434.0661493000463$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$[2]$ |
$2$ |
$6$ |
$2893129.81204$ |
| 10.4.113...000.63 |
$x^{10} + 50 x^{6} - 480 x^{4} - 1350 x^{2} + 1470$ |
$10$ |
(4, 3) |
$-\,2^{19}\cdot 3^{11}\cdot 5^{13}$ |
$3$ |
$101.263137106$ |
$434.0661493000463$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$[2, 2]$ |
$2$ |
$6$ |
$3926521.89066$ |
| 10.4.113...000.102 |
$x^{10} - 30 x^{8} + 540 x^{6} - 5580 x^{4} + 5400 x^{2} + 9720$ |
$10$ |
(4, 3) |
$-\,2^{19}\cdot 3^{11}\cdot 5^{13}$ |
$3$ |
$101.263137106$ |
$434.0661493000463$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$[2]$ |
$2$ |
$6$ |
$6396383.44559$ |
| 10.4.113...000.147 |
$x^{10} + 20 x^{8} - 80 x^{6} - 2880 x^{4} + 69120$ |
$10$ |
(4, 3) |
$-\,2^{19}\cdot 3^{11}\cdot 5^{13}$ |
$3$ |
$101.263137106$ |
$434.0661493000463$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$[2, 2]$ |
$2$ |
$6$ |
$2856480.02508$ |
| 10.4.113...000.164 |
$x^{10} - 390 x^{6} - 1520 x^{4} + 40050 x^{2} + 259470$ |
$10$ |
(4, 3) |
$-\,2^{19}\cdot 3^{11}\cdot 5^{13}$ |
$3$ |
$101.263137106$ |
$329.8189501715472$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$[2]$ |
$2$ |
$6$ |
$2234134.92532$ |
| 10.2.188...000.7 |
$x^{10} - 4500 x^{4} - 405000$ |
$10$ |
(2, 4) |
$2^{19}\cdot 3^{10}\cdot 5^{14}$ |
$3$ |
$106.570315757$ |
$450.0471351756855$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
trivial |
$2$ |
$5$ |
$2001932.37049$ |
| 10.2.188...000.169 |
$x^{10} - 60 x^{8} + 1440 x^{6} - 12780 x^{4} - 4320 x^{2} - 5832$ |
$10$ |
(2, 4) |
$2^{19}\cdot 3^{10}\cdot 5^{14}$ |
$3$ |
$106.570315757$ |
$450.0471351756855$ |
|
|
|
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$[2]$ |
$2$ |
$5$ |
$6469066.16534$ |
| 10.2.188...000.203 |
$x^{10} + 270 x^{6} - 1350 x^{4} + 2430 x^{2} - 1458$ |
$10$ |
(2, 4) |
$2^{19}\cdot 3^{10}\cdot 5^{14}$ |
$3$ |
$106.570315757$ |
$341.96187353175196$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$[2]$ |
$2$ |
$5$ |
$5082365.04906$ |
| 10.0.314...000.34 |
$x^{10} + 150 x^{6} + 1000 x^{4} - 750 x^{2} + 750$ |
$10$ |
(0, 5) |
$-\,2^{19}\cdot 3^{9}\cdot 5^{15}$ |
$3$ |
$112.15564247$ |
$341.96187353175196$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$[2]$ |
$2$ |
$4$ |
$1966583.45947$ |
| 10.0.314...000.47 |
$x^{10} + 40 x^{6} + 1920$ |
$10$ |
(0, 5) |
$-\,2^{19}\cdot 3^{9}\cdot 5^{15}$ |
$3$ |
$112.15564247$ |
$450.0471351756855$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2]$ |
$[2]$ |
$2$ |
$4$ |
$1839576.5996$ |
| 10.0.314...000.55 |
$x^{10} + 40 x^{8} + 510 x^{6} + 2400 x^{4} + 8250 x^{2} + 2430$ |
$10$ |
(0, 5) |
$-\,2^{19}\cdot 3^{9}\cdot 5^{15}$ |
$3$ |
$112.15564247$ |
$450.0471351756855$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
$[2, 6]$ |
$[2, 6]$ |
$2$ |
$4$ |
$1133372.12958$ |
