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 |
10.2.799905449.1 |
$x^{10} - x^{9} + x^{7} + x^{6} - x^{5} - x^{4} + x^{3} - x - 1$ |
$10$ |
[2,4] |
$7^{2}\cdot 41\cdot 631^{2}$ |
$3$ |
$7.7679042833$ |
$425.5549318243181$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$5$ |
$1.64493276266$ |
10.2.801214577.1 |
$x^{10} - 3 x^{9} + 3 x^{8} - x^{7} + x^{5} - 3 x^{4} + 4 x^{3} - x^{2} - x + 1$ |
$10$ |
[2,4] |
$801214577$ |
$1$ |
$7.76917464587$ |
$28305.73399507598$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.6458655819$ |
10.2.801589013.1 |
$x^{10} - 2 x^{8} - x^{7} - x^{6} + x^{5} + 3 x^{4} - 2 x^{3} - 2 x^{2} + x + 1$ |
$10$ |
[2,4] |
$53\cdot 3889^{2}$ |
$2$ |
$7.76953765064$ |
$454.0011013202501$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$5$ |
$1.64744846782$ |
10.2.802448461.1 |
$x^{10} - 2 x^{7} - x^{6} + 2 x^{5} + x^{4} - 2 x^{2} - x + 1$ |
$10$ |
[2,4] |
$53\cdot 71\cdot 213247$ |
$3$ |
$7.77037028356$ |
$28327.521264664156$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.64755738233$ |
10.2.803282693.1 |
$x^{10} - 3 x^{9} + 7 x^{8} - 11 x^{7} + 12 x^{6} - 8 x^{5} + 2 x^{4} + 4 x^{3} - 6 x^{2} + 4 x - 1$ |
$10$ |
[2,4] |
$803282693$ |
$1$ |
$7.77117771996$ |
$28342.242201350266$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.64887968245$ |
10.2.809040437.1 |
$x^{10} - 2 x^{9} + 4 x^{7} - 4 x^{6} + 3 x^{4} - x^{3} - x^{2} + 1$ |
$10$ |
[2,4] |
$809040437$ |
$1$ |
$7.77673003436$ |
$28443.63614237814$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.65687849827$ |
10.2.814270253.1 |
$x^{10} - x^{9} - 2 x^{8} + 4 x^{7} - x^{6} - 5 x^{5} + 5 x^{4} + x^{3} - 3 x^{2} + x + 1$ |
$10$ |
[2,4] |
$47\cdot 1753\cdot 9883$ |
$3$ |
$7.78174252075$ |
$28535.421023703155$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.66312411125$ |
10.2.817298432.1 |
$x^{10} + x^{8} - 2 x^{7} + x^{4} + 2 x^{3} - x^{2} - 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 798143$ |
$2$ |
$7.78463163117$ |
$3422.0470085736833$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.66778396748$ |
10.2.819649013.1 |
$x^{10} - 2 x^{9} + 2 x^{7} - x^{6} + x^{2} - x - 1$ |
$10$ |
[2,4] |
$819649013$ |
$1$ |
$7.78686762813$ |
$28629.512971756958$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.6697499319160445$ |
10.2.820675277.1 |
$x^{10} - 2 x^{9} + 2 x^{8} - 5 x^{7} + 7 x^{6} - 4 x^{5} + 4 x^{4} - 8 x^{3} + 5 x^{2} - 1$ |
$10$ |
[2,4] |
$317\cdot 1609^{2}$ |
$2$ |
$7.78784205533$ |
$714.1799493124964$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$5$ |
$1.67116072579$ |
10.2.821009933.1 |
$x^{10} - x^{9} - 3 x^{8} + x^{7} + 6 x^{6} - 6 x^{4} - x^{3} + 3 x^{2} - 1$ |
$10$ |
[2,4] |
$5059\cdot 162287$ |
$2$ |
$7.78815957067$ |
$28653.270895309666$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.6712704511020062$ |
10.2.823435181.1 |
$x^{10} - x^{9} + 3 x^{8} - x^{7} + 3 x^{5} - 4 x^{4} + x^{3} - 2 x + 1$ |
$10$ |
[2,4] |
$113\cdot 7287037$ |
$2$ |
$7.79045712599$ |
$28695.56030120339$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.6742160265087045$ |
10.2.826110449.1 |
$x^{10} - x^{8} - x^{7} - x^{5} + 2 x^{4} + 3 x^{3} - 3 x^{2} + 1$ |
$10$ |
[2,4] |
$1229\cdot 672181$ |
$2$ |
$7.79298448371$ |
$28742.137168276127$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.6785661649701986$ |
10.2.827119069.1 |
$x^{10} - x^{9} + 4 x^{8} - 4 x^{7} + 7 x^{6} - 8 x^{5} + 7 x^{4} - 7 x^{3} + 4 x^{2} - 3 x + 1$ |
$10$ |
[2,4] |
$7^{2}\cdot 61\cdot 276721$ |
$3$ |
$7.79393542736$ |
$10870.136475684194$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.679076107691851$ |
10.2.827363461.1 |
$x^{10} - x^{9} - x^{8} + 5 x^{7} - 4 x^{6} - 2 x^{5} + 7 x^{4} - 4 x^{3} - 2 x^{2} + 3 x - 1$ |
$10$ |
[2,4] |
$827363461$ |
$1$ |
$7.7941656871$ |
$28763.926383579834$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.6809607555544814$ |
10.2.828364813.1 |
$x^{10} - x^{9} + x^{8} + 2 x^{7} - 4 x^{6} + 3 x^{4} - 2 x^{3} - 2 x^{2} + 2 x + 1$ |
$10$ |
[2,4] |
$157\cdot 2297^{2}$ |
$2$ |
$7.79510849595$ |
$600.5239379075575$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$5$ |
$1.6806211151$ |
10.2.830003621.1 |
$x^{10} - 3 x^{9} + 7 x^{8} - 11 x^{7} + 13 x^{6} - 13 x^{5} + 9 x^{4} - 5 x^{3} + x^{2} + x - 1$ |
$10$ |
[2,4] |
$2399\cdot 345979$ |
$2$ |
$7.79664928177$ |
$28809.783425079753$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.6845591915489664$ |
10.2.830597309.1 |
$x^{10} - x^{9} - 2 x^{8} + x^{7} + x^{6} + 2 x^{5} + x^{4} - 2 x^{3} + x - 1$ |
$10$ |
[2,4] |
$193\cdot 4303613$ |
$2$ |
$7.7972067839$ |
$28820.085166425168$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.6839050873591648$ |
10.2.830677609.1 |
$x^{10} - 2 x^{9} + 3 x^{8} - 3 x^{7} + 3 x^{6} - 4 x^{5} + 5 x^{4} - 7 x^{3} + 5 x^{2} - 3 x + 1$ |
$10$ |
[2,4] |
$5569\cdot 149161$ |
$2$ |
$7.797282162$ |
$28821.478258409996$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.6833725710593588$ |
10.2.831295013.1 |
$x^{10} - x^{9} - 2 x^{8} + 2 x^{7} + 3 x^{6} - 4 x^{5} - 3 x^{4} + 4 x^{3} + 2 x^{2} - 2 x - 1$ |
$10$ |
[2,4] |
$831295013$ |
$1$ |
$7.79786150395$ |
$28832.187100530547$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.6847271695962687$ |
10.2.831888493.1 |
$x^{10} - x^{9} - 2 x^{8} + 2 x^{7} + 3 x^{6} - 3 x^{5} - 3 x^{4} + 3 x^{3} + 3 x^{2} - x - 1$ |
$10$ |
[2,4] |
$8111\cdot 102563$ |
$2$ |
$7.79841803186$ |
$28842.477234107337$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.6858460337863315$ |
10.2.833906069.1 |
$x^{10} - 3 x^{8} - 3 x^{7} + x^{6} + 5 x^{5} + 5 x^{4} - 3 x^{2} - 3 x - 1$ |
$10$ |
[2,4] |
$7193\cdot 115933$ |
$2$ |
$7.8003073182$ |
$28877.431828332657$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.688830331996101$ |
10.2.834771989.1 |
$x^{10} - 2 x^{9} + 4 x^{8} - 7 x^{7} + 8 x^{6} - 8 x^{5} + 6 x^{4} - 3 x^{3} + x - 1$ |
$10$ |
[2,4] |
$29\cdot 307\cdot 93763$ |
$3$ |
$7.80111691633$ |
$28892.420961214033$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.6893371807326218$ |
10.2.836077225.1 |
$x^{10} - 2 x^{9} + 4 x^{8} - 5 x^{7} + 7 x^{6} - 8 x^{5} + 8 x^{4} - 6 x^{3} + 2 x^{2} - x - 1$ |
$10$ |
[2,4] |
$5^{2}\cdot 5783^{2}$ |
$2$ |
$7.80233582898$ |
$170.0441119239358$ |
|
|
? |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$1.68996118963$ |
10.2.836169077.1 |
$x^{10} - 2 x^{9} - 2 x^{8} + 5 x^{7} + 3 x^{6} - 7 x^{5} - 2 x^{4} + 5 x^{3} + x^{2} - 2 x - 1$ |
$10$ |
[2,4] |
$149\cdot 5611873$ |
$2$ |
$7.80242154172$ |
$28916.588266944633$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.6916270392297335$ |
10.2.838803593.1 |
$x^{10} - x^{9} - 2 x^{8} + 3 x^{7} + x^{6} - x^{5} - x^{4} - x^{3} + 2 x^{2} + x - 1$ |
$10$ |
[2,4] |
$79\cdot 10617767$ |
$2$ |
$7.80487637041$ |
$28962.106156148242$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.69460475791$ |
10.2.840291328.1 |
$x^{10} - 2 x^{9} + 2 x^{8} - 4 x^{7} + 7 x^{6} - 8 x^{5} + 6 x^{4} - 6 x^{3} + 6 x^{2} - 4 x + 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 820597$ |
$2$ |
$7.80625957032$ |
$3322.7388116864136$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.6962617325251366$ |
10.2.844599673.1 |
$x^{10} - x^{9} + x^{7} + 2 x^{5} - 4 x^{4} + 2 x^{3} + 2 x^{2} - 3 x + 1$ |
$10$ |
[2,4] |
$101\cdot 307\cdot 27239$ |
$3$ |
$7.8102527941$ |
$29061.997058013752$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.7019625279950237$ |
10.2.846083941.1 |
$x^{10} - x^{9} + x^{8} + x^{7} - 4 x^{6} + 8 x^{5} - 10 x^{4} + 9 x^{3} - 7 x^{2} + 4 x - 1$ |
$10$ |
[2,4] |
$499\cdot 1695559$ |
$2$ |
$7.81162425461$ |
$29087.522084220236$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.704596759959611$ |
10.2.848429441.1 |
$x^{10} - x^{7} - 3 x^{6} + 3 x^{5} + 3 x^{4} - x^{3} - 1$ |
$10$ |
[2,4] |
$41\cdot 4549^{2}$ |
$2$ |
$7.81378708352$ |
$431.86687763707926$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$5$ |
$1.71143081603$ |
10.2.851109913.1 |
$x^{10} - 2 x^{9} + x^{6} + 2 x^{5} - 4 x^{4} + 2 x^{3} + 2 x^{2} - 2 x - 1$ |
$10$ |
[2,4] |
$17^{2}\cdot 97^{2}\cdot 313$ |
$3$ |
$7.81625221721$ |
$718.4267533993984$ |
|
|
? |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$5$ |
$1.71171754603$ |
10.2.851332877.1 |
$x^{10} - x^{9} - x^{8} + 2 x^{7} + 2 x^{6} - 6 x^{5} + 5 x^{4} + x^{3} - 5 x^{2} + 4 x - 1$ |
$10$ |
[2,4] |
$43\cdot 19798439$ |
$2$ |
$7.81645695427$ |
$29177.609172103188$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.7125083050826007$ |
10.2.851763637.1 |
$x^{10} - x^{9} - 2 x^{8} + x^{7} + 2 x^{5} + 2 x^{4} - 4 x^{3} - x^{2} + 2 x - 1$ |
$10$ |
[2,4] |
$851763637$ |
$1$ |
$7.81685236372$ |
$29184.98992633028$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.7127001932105461$ |
10.2.853697693.1 |
$x^{10} - 4 x^{9} + 8 x^{8} - 11 x^{7} + 11 x^{6} - 7 x^{5} + 3 x^{4} - 2 x^{2} + x - 1$ |
$10$ |
[2,4] |
$23\cdot 37117291$ |
$2$ |
$7.81862548528$ |
$29218.105568294464$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.7143525360225325$ |
10.2.856749056.1 |
$x^{10} - x^{8} - 2 x^{7} + x^{6} + 2 x^{5} - x^{4} - 2 x^{3} + 2 x + 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 103\cdot 8123$ |
$3$ |
$7.82141560388$ |
$3355.1201775290497$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.7181304948991665$ |
10.2.856799533.1 |
$x^{10} - 2 x^{9} + 2 x^{8} + x^{7} - 2 x^{6} + 2 x^{4} - 2 x^{3} - 2 x^{2} + 2 x - 1$ |
$10$ |
[2,4] |
$2837\cdot 302009$ |
$2$ |
$7.82146168401$ |
$29271.138225221104$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.7177170913989903$ |
10.2.857695393.1 |
$x^{10} - 2 x^{9} + 5 x^{7} - 5 x^{6} - 2 x^{5} + 8 x^{4} - 4 x^{3} - 2 x^{2} + 3 x - 1$ |
$10$ |
[2,4] |
$311\cdot 2757863$ |
$2$ |
$7.82227910276$ |
$29286.437014427003$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.718020794185385$ |
10.2.858063061.1 |
$x^{10} - x^{9} - x^{8} + 3 x^{7} - 4 x^{5} + 2 x^{4} + 3 x^{3} - 3 x^{2} + 1$ |
$10$ |
[2,4] |
$17959\cdot 47779$ |
$2$ |
$7.82261435547$ |
$29292.71344549699$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.7222955234497919$ |
10.2.859848569.1 |
$x^{10} - 2 x^{9} + 4 x^{8} - 5 x^{7} + 6 x^{6} - 7 x^{5} + 7 x^{4} - 8 x^{3} + 5 x^{2} - 3 x + 1$ |
$10$ |
[2,4] |
$859848569$ |
$1$ |
$7.82424060877$ |
$29323.17460644396$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.7227979318102846$ |
10.2.860443648.1 |
$x^{10} + x^{8} - 2 x^{7} - x^{6} - 2 x^{5} + 2 x^{3} + x^{2} + 2 x - 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 840277$ |
$2$ |
$7.82478193571$ |
$3362.3466022886946$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.7206957109353098$ |
10.2.860714261.1 |
$x^{10} - x^{9} + x^{7} - 3 x^{6} + 3 x^{5} - x^{4} - x^{3} + 3 x^{2} - 2 x + 1$ |
$10$ |
[2,4] |
$11^{2}\cdot 7113341$ |
$2$ |
$7.82502799343$ |
$8845.719360232948$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.7245150934522735$ |
10.2.860949101.1 |
$x^{10} - 3 x^{9} + 6 x^{8} - 9 x^{7} + 8 x^{6} - 6 x^{5} + 2 x^{4} + x^{2} + 1$ |
$10$ |
[2,4] |
$860949101$ |
$1$ |
$7.82524146776$ |
$29341.93417278418$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.7215430203380402$ |
10.2.862175261.1 |
$x^{10} - 3 x^{9} + 4 x^{8} - x^{7} - 3 x^{6} + 6 x^{5} - 8 x^{4} + 10 x^{3} - 8 x^{2} + 4 x - 1$ |
$10$ |
[2,4] |
$199\cdot 4332539$ |
$2$ |
$7.82635522167$ |
$29362.82106678444$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.7236474653611091$ |
10.2.862897933.1 |
$x^{10} - 3 x^{9} + 6 x^{8} - 9 x^{7} + 11 x^{6} - 9 x^{5} + 5 x^{4} - 3 x^{2} + 3 x - 1$ |
$10$ |
[2,4] |
$6763\cdot 127591$ |
$2$ |
$7.82701097647$ |
$29375.12439122599$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.7267499205527177$ |
10.2.863165333.1 |
$x^{10} - 2 x^{9} + 3 x^{8} - 3 x^{7} + 5 x^{5} - 10 x^{4} + 10 x^{3} - 8 x^{2} + 4 x - 1$ |
$10$ |
[2,4] |
$31\cdot 41\cdot 679123$ |
$3$ |
$7.82725349077$ |
$29379.675508759454$ |
|
|
? |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.7250827280182657$ |
10.2.867798793.1 |
$x^{10} - 2 x^{8} - 3 x^{7} + 5 x^{5} + 5 x^{4} - 3 x^{2} - 3 x - 1$ |
$10$ |
[2,4] |
$103\cdot 257\cdot 32783$ |
$3$ |
$7.83144503488$ |
$29458.424822111585$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.7325378453382856$ |
10.2.869334889.1 |
$x^{10} - 2 x^{9} + 3 x^{8} - x^{7} - 2 x^{6} + 5 x^{5} - 4 x^{4} + x^{3} + x^{2} - 2 x + 1$ |
$10$ |
[2,4] |
$47\cdot 18496487$ |
$2$ |
$7.83283018082$ |
$29484.485564445582$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.7325507626380365$ |
10.2.869414653.1 |
$x^{10} - x^{9} - x^{8} + 4 x^{7} - x^{6} - 6 x^{5} + 8 x^{4} - x^{3} - 5 x^{2} + 4 x - 1$ |
$10$ |
[2,4] |
$869414653$ |
$1$ |
$7.83290204635$ |
$29485.838176996087$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.7367862636094118$ |
10.2.869777173.1 |
$x^{10} - 2 x^{9} + 4 x^{8} - 4 x^{7} + 5 x^{6} - 5 x^{5} + 6 x^{4} - 7 x^{3} + 5 x^{2} - 3 x + 1$ |
$10$ |
[2,4] |
$869777173$ |
$1$ |
$7.83322859375$ |
$29491.984894204732$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.7339301003774494$ |
10.2.872338141.1 |
$x^{10} - x^{9} - x^{8} + x^{6} + 2 x^{5} - 2 x^{4} - 4 x^{3} + x^{2} + 3 x + 1$ |
$10$ |
[2,4] |
$173\cdot 1487\cdot 3391$ |
$3$ |
$7.8355319558$ |
$29535.371015106615$ |
|
|
✓ |
$S_{10}$ (as 10T45) |
trivial |
$2$ |
$5$ |
$1.7374626264699395$ |