Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
10.0.209352647.1 |
x10 - 3x9 + 7x8 - 11x7 + 13x6 - 12x5 + 9x4 - 5x3 + 3x2 - 2x + 1 |
$10$ |
[0,5] |
$-\,7^{2}\cdot 23\cdot 431^{2}$ |
$3$ |
$6.79341030426$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.568036883757$ |
10.0.212309359.1 |
x10 - 3x9 + 5x8 - 7x7 + 9x6 - 10x5 + 9x4 - 7x3 + 5x2 - 2x + 1 |
$10$ |
[0,5] |
$-\,31\cdot 2617^{2}$ |
$2$ |
$6.80294428088$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.572857558707$ |
10.0.214816879.1 |
x10 - 2x9 + 4x8 - 7x7 + 9x6 - 10x5 + 10x4 - 8x3 + 6x2 - 3x + 1 |
$10$ |
[0,5] |
$-\,17^{2}\cdot 79\cdot 97^{2}$ |
$3$ |
$6.81093664096$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.577674891408$ |
10.0.220168975.1 |
x10 - x9 - x8 + 2x7 - x6 - x5 + 4x4 - x3 - 3x2 + x + 1 |
$10$ |
[0,5] |
$-\,5^{2}\cdot 13^{2}\cdot 31\cdot 41^{2}$ |
$4$ |
$6.82771857501$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.586605631071$ |
10.0.224198759.1 |
x10 - x9 - 2x8 + 4x7 - 4x5 + 3x4 + x3 - 2x2 + 1 |
$10$ |
[0,5] |
$-\,71\cdot 1777^{2}$ |
$2$ |
$6.84011369338$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.59340069383$ |
10.0.226876987.1 |
x10 - 2x9 + 3x8 - 3x7 + 2x6 + x5 - x4 - 3x3 + 6x2 - 4x + 1 |
$10$ |
[0,5] |
$-\,43\cdot 2297^{2}$ |
$2$ |
$6.8482411447$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.597809920275$ |
10.0.262091507.1 |
x10 - x9 - 2x6 + 3x5 + 3x4 - 4x3 - 2x2 + 2x + 1 |
$10$ |
[0,5] |
$-\,83\cdot 1777^{2}$ |
$2$ |
$6.94776778804$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.656821013577$ |
10.0.263786699.1 |
x10 - 2x9 + 2x8 - 2x7 + 4x6 - 5x5 + 4x4 - 2x3 + 3x2 - 3x + 1 |
$10$ |
[0,5] |
$-\,11\cdot 59^{2}\cdot 83^{2}$ |
$3$ |
$6.95224853606$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.663236848943$ |
10.0.277010267.1 |
x10 - 2x9 + x8 + 2x7 - 3x6 + 3x5 - 2x4 + 3x2 - 3x + 1 |
$10$ |
[0,5] |
$-\,107\cdot 1609^{2}$ |
$2$ |
$6.98633789626$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.679993136866$ |
10.0.290954507.1 |
x10 - x9 + 2x8 + 2x7 - x6 + 4x5 + 4x4 + 2x2 + 3x + 1 |
$10$ |
[0,5] |
$-\,17^{2}\cdot 97^{2}\cdot 107$ |
$3$ |
$7.02073383839$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.702250275284$ |
10.0.325246087.1 |
x10 - 3x9 + 6x8 - 10x7 + 13x6 - 13x5 + 11x4 - 8x3 + 5x2 - 2x + 1 |
$10$ |
[0,5] |
$-\,103\cdot 1777^{2}$ |
$2$ |
$7.09939283685$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.752440468285$ |
10.0.328787887.1 |
x10 - 2x9 + 3x8 - 3x7 + 5x6 - 6x5 + 3x4 - 3x3 + 3x2 - x + 1 |
$10$ |
[0,5] |
$-\,127\cdot 1609^{2}$ |
$2$ |
$7.10708616721$ |
|
|
not computed |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.761759694633$ |
10.0.328787887.2 |
x10 - 2x9 + 3x6 - x5 - x4 - 2x3 + 2x2 + 1 |
$10$ |
[0,5] |
$-\,127\cdot 1609^{2}$ |
$2$ |
$7.10708616721$ |
|
|
not computed |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.76915406635$ |
10.0.330230659.1 |
x10 - x9 + x8 + 2x7 - 3x6 + 2x5 - 2x3 + x2 - x + 1 |
$10$ |
[0,5] |
$-\,11^{2}\cdot 19\cdot 379^{2}$ |
$3$ |
$7.11019872499$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.770950046286$ |
10.0.339143411.1 |
x10 - 3x9 + 5x8 - 6x7 + 6x6 - 4x5 + x4 + 2x3 - 2x2 + 1 |
$10$ |
[0,5] |
$-\,131\cdot 1609^{2}$ |
$2$ |
$7.12915961712$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.777396737365$ |
10.0.359854459.1 |
x10 - 3x9 + 6x8 - 9x7 + 11x6 - 10x5 + 8x4 - 5x3 + 3x2 - 2x + 1 |
$10$ |
[0,5] |
$-\,139\cdot 1609^{2}$ |
$2$ |
$7.17154435557$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.81336454205$ |
10.0.364067099.1 |
x10 - x9 - 2x6 + x5 + 2x4 - 2x3 + 3x2 - 2x + 1 |
$10$ |
[0,5] |
$-\,11^{3}\cdot 523^{2}$ |
$2$ |
$7.17989583039$ |
|
|
not computed |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.826936802139$ |
10.0.370209983.1 |
x10 + 2x8 + 3x6 - x5 + 3x4 + 2x2 + 1 |
$10$ |
[0,5] |
$-\,11\cdot 13\cdot 1609^{2}$ |
$3$ |
$7.19191941593$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.824223583763$ |
10.0.377968939.1 |
x10 - 2x9 + 4x8 - 5x7 + 5x6 - 6x5 + 7x4 - 4x3 + 3x2 - 3x + 1 |
$10$ |
[0,5] |
$-\,17^{2}\cdot 97^{2}\cdot 139$ |
$3$ |
$7.20685212745$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.830618920882$ |
10.0.379908823.1 |
x10 + x8 - x7 - x5 - x3 + x2 + 1 |
$10$ |
[0,5] |
$-\,7\cdot 53^{2}\cdot 139^{2}$ |
$3$ |
$7.21054244994$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.856501846271$ |
10.0.386633299.1 |
x10 - x9 + 2x8 - 2x7 + 2x6 - 3x5 + 2x4 - 2x3 + 2x2 - x + 1 |
$10$ |
[0,5] |
$-\,13^{2}\cdot 19\cdot 347^{2}$ |
$3$ |
$7.22320474844$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.843223617742$ |
10.0.386864567.1 |
x10 - x9 + 3x8 - x7 + 4x6 + 5x4 + x3 + 3x2 + x + 1 |
$10$ |
[0,5] |
$-\,19^{2}\cdot 47\cdot 151^{2}$ |
$3$ |
$7.22363669433$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.840987825694$ |
10.0.432343127.1 |
x10 - 3x9 + 5x8 - 5x7 + 5x6 - 6x5 + 7x4 - 5x3 + 3x2 - 2x + 1 |
$10$ |
[0,5] |
$-\,167\cdot 1609^{2}$ |
$2$ |
$7.30437154456$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.905139783856$ |
10.0.437865967.1 |
x10 - x9 - x8 + 2x7 + 2x6 - 5x5 + 2x4 + 2x3 - x2 - x + 1 |
$10$ |
[0,5] |
$-\,7\cdot 11^{2}\cdot 719^{2}$ |
$3$ |
$7.31364909208$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.935373385345$ |
10.0.437925347.1 |
x10 - 3x9 + 6x8 - 10x7 + 14x6 - 15x5 + 14x4 - 10x3 + 6x2 - 3x + 1 |
$10$ |
[0,5] |
$-\,83\cdot 2297^{2}$ |
$2$ |
$7.31374826808$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.904836799867$ |
10.0.440866291.1 |
x10 - x9 + x8 - 3x7 + 3x6 - x5 + 3x4 - 3x3 + x2 - x + 1 |
$10$ |
[0,5] |
$-\,19\cdot 4817^{2}$ |
$2$ |
$7.3186451295$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.924915033309$ |
10.0.443229763.1 |
x10 - 3x9 + 4x8 - 4x7 + 4x6 - 5x4 + 4x3 - x + 1 |
$10$ |
[0,5] |
$-\,17^{2}\cdot 97^{2}\cdot 163$ |
$3$ |
$7.32255920172$ |
|
|
not computed |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.943232786232$ |
10.0.449448427.1 |
x10 - 2x9 + 2x8 - 3x7 + 8x6 - 11x5 + 8x4 - 3x3 + 2x2 - 2x + 1 |
$10$ |
[0,5] |
$-\,43\cdot 53^{2}\cdot 61^{2}$ |
$3$ |
$7.33276870618$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.932430924092$ |
10.0.454106567.1 |
x10 - 2x9 + 2x8 - x7 + 2x6 - 3x5 + x4 + 2x3 - x2 - x + 1 |
$10$ |
[0,5] |
$-\,17^{2}\cdot 97^{2}\cdot 167$ |
$3$ |
$7.34033326652$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.940846654649$ |
10.0.476322007.1 |
x10 - x9 - 2x8 + 4x7 + x6 - 5x5 + x4 + 4x3 - x2 - 2x + 1 |
$10$ |
[0,5] |
$-\,7\cdot 73^{2}\cdot 113^{2}$ |
$3$ |
$7.37547617968$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$1.00383062843$ |
10.0.484120747.1 |
x10 - x9 + x8 - x7 + x6 - 4x5 + 3x4 - x3 + x + 1 |
$10$ |
[0,5] |
$-\,11\cdot 17\cdot 1609^{2}$ |
$3$ |
$7.38746386304$ |
|
|
not computed |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.980166278371$ |
10.0.484176016.1 |
x10 - x8 + x6 + 2x2 + 1 |
$10$ |
[0,5] |
$-\,2^{4}\cdot 5501^{2}$ |
$2$ |
$7.3875481967$ |
|
|
not computed |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$1.08216442445$ |
10.0.485605687.1 |
x10 - 3x9 + 5x8 - 6x7 + 7x6 - 7x5 + 6x4 - 5x3 + 4x2 - 2x + 1 |
$10$ |
[0,5] |
$-\,7\cdot 8329^{2}$ |
$2$ |
$7.3897266928$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$1.01495612987$ |
10.0.486045407.1 |
x10 - x9 + 2x8 - 4x7 + 5x6 - 6x5 + 7x4 - 6x3 + 5x2 - 3x + 1 |
$10$ |
[0,5] |
$-\,23\cdot 4597^{2}$ |
$2$ |
$7.3903955662$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$1.08406425262$ |
10.0.486736979.1 |
x10 - 2x9 + 3x8 - 4x7 + 7x6 - 10x5 + 9x4 - 4x3 + x2 - x + 1 |
$10$ |
[0,5] |
$-\,17^{2}\cdot 97^{2}\cdot 179$ |
$3$ |
$7.39144643944$ |
|
|
not computed |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.9800046881$ |
10.0.486736979.2 |
x10 - 2x9 - 2x8 + 4x7 + 4x6 - 4x5 - 4x4 + x3 + x2 + x + 1 |
$10$ |
[0,5] |
$-\,17^{2}\cdot 97^{2}\cdot 179$ |
$3$ |
$7.39144643944$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.974241656128$ |
10.0.501239855.1 |
x10 - x9 - x8 + x7 + x5 + x4 - 2x3 - x2 + x + 1 |
$10$ |
[0,5] |
$-\,5\cdot 19\cdot 2297^{2}$ |
$3$ |
$7.41318024205$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$1.05729447918$ |
10.0.508490587.1 |
x10 + 2x8 - x7 + 4x6 - x5 + 4x4 - x3 + 2x2 + 1 |
$10$ |
[0,5] |
$-\,11\cdot 17^{3}\cdot 97^{2}$ |
$3$ |
$7.42383467466$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$0.998345765058$ |
10.0.514709827.1 |
x10 - 4x9 + 9x8 - 14x7 + 16x6 - 13x5 + 8x4 - 4x3 + 2x2 - x + 1 |
$10$ |
[0,5] |
$-\,163\cdot 1777^{2}$ |
$2$ |
$7.43286501771$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$1.01758301301$ |
10.0.526794304.1 |
x10 - 4x9 + 8x8 - 9x7 + 8x6 - 8x5 + 8x4 - 4x3 + x2 - x + 1 |
$10$ |
[0,5] |
$-\,2^{6}\cdot 19^{2}\cdot 151^{2}$ |
$3$ |
$7.45013439281$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$1.13996042827$ |
10.0.526794304.2 |
x10 + 3x6 - x4 + 4x2 + 1 |
$10$ |
[0,5] |
$-\,2^{6}\cdot 19^{2}\cdot 151^{2}$ |
$3$ |
$7.45013439281$ |
|
|
not computed |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$1.0369077211$ |
10.0.530439175.1 |
x10 - x9 + x7 + x6 - 3x5 + x4 + x3 - x + 1 |
$10$ |
[0,5] |
$-\,5^{2}\cdot 7\cdot 1741^{2}$ |
$3$ |
$7.4552731348$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$1.053486414$ |
10.0.546253891.1 |
x10 - 2x9 + 2x8 - x7 - 2x6 + 2x5 - 2x3 + 4x2 - 2x + 1 |
$10$ |
[0,5] |
$-\,211\cdot 1609^{2}$ |
$2$ |
$7.47720786893$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$1.05442559996$ |
10.0.552906407.1 |
x10 - x9 + 2x8 - 3x7 + 3x6 - 3x5 + 3x4 - 3x3 + 2x2 - x + 1 |
$10$ |
[0,5] |
$-\,23\cdot 4903^{2}$ |
$2$ |
$7.48626441349$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$1.04972698416$ |
10.0.562874607.1 |
x10 - 4x9 + 8x8 - 11x7 + 14x6 - 15x5 + 11x4 - 4x3 + x2 - x + 1 |
$10$ |
[0,5] |
$-\,3^{2}\cdot 17^{2}\cdot 23\cdot 97^{2}$ |
$4$ |
$7.49965293275$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$1.07103275549$ |
10.0.562973339.1 |
x10 - x9 + 3x8 - 2x7 + 6x6 - 3x5 + 6x4 - 2x3 + 4x2 + 1 |
$10$ |
[0,5] |
$-\,59\cdot 3089^{2}$ |
$2$ |
$7.49978447134$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$1.0804509124$ |
10.0.587675987.1 |
x10 - 2x8 + 2x6 - x5 - 2x4 - x3 + x2 + 2x + 1 |
$10$ |
[0,5] |
$-\,227\cdot 1609^{2}$ |
$2$ |
$7.53206040953$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$1.11466952529$ |
10.0.590495323.1 |
x10 - x9 + 2x8 - 2x7 + 2x6 - 3x5 + 3x4 - 4x3 + 4x2 - 2x + 1 |
$10$ |
[0,5] |
$-\,11\cdot 17\cdot 1777^{2}$ |
$3$ |
$7.53566608756$ |
|
|
not computed |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$1.09025803881$ |
10.0.592440064.1 |
x10 - x9 + 3x8 - 4x7 + 5x6 - 7x5 + 7x4 - 6x3 + 5x2 - 3x + 1 |
$10$ |
[0,5] |
$-\,2^{8}\cdot 19\cdot 349^{2}$ |
$3$ |
$7.5381442181$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$1.22778512725$ |
10.0.621349399.1 |
x10 - x9 - x8 + 3x6 - 2x5 - 3x4 + 4x3 - x + 1 |
$10$ |
[0,5] |
$-\,11^{4}\cdot 31\cdot 37^{2}$ |
$3$ |
$7.57414453312$ |
|
|
✓ |
$C_2 \wr S_5$ (as 10T39) |
trivial |
$2$ |
$4$ |
$1.26310066768$ |