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 |
10.2.836077225.1 |
$x^{10} - 2 x^{9} + 4 x^{8} - 5 x^{7} + 7 x^{6} - 8 x^{5} + 8 x^{4} - 6 x^{3} + 2 x^{2} - x - 1$ |
$10$ |
[2,4] |
$5^{2}\cdot 5783^{2}$ |
$2$ |
$7.80233582898$ |
$170.0441119239358$ |
|
|
? |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$1.68996118963$ |
10.2.1050472921.1 |
$x^{10} - x^{9} - x^{8} + 2 x^{7} - x^{5} + 2 x^{3} - x^{2} - x + 1$ |
$10$ |
[2,4] |
$32411^{2}$ |
$1$ |
$7.98249189346$ |
$180.03055296254578$ |
|
|
✓ |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$1.95436523296$ |
10.2.1112689449.1 |
$x^{10} - x^{8} - 3 x^{7} + 2 x^{6} + x^{5} + 2 x^{4} - 3 x^{3} - x^{2} + 1$ |
$10$ |
[2,4] |
$3^{2}\cdot 11119^{2}$ |
$2$ |
$8.02855518703$ |
$182.6389881706532$ |
|
|
? |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$2.06062327305$ |
10.2.1235874025.1 |
$x^{10} - 3 x^{9} + 5 x^{8} - 6 x^{7} + 7 x^{6} - 9 x^{5} + 12 x^{4} - 11 x^{3} + 7 x^{2} - x - 1$ |
$10$ |
[2,4] |
$5^{2}\cdot 79^{2}\cdot 89^{2}$ |
$3$ |
$8.1132978622$ |
$187.4966666370365$ |
|
|
? |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$2.16277435346$ |
10.2.1294776289.1 |
$x^{10} - 4 x^{6} + 3 x^{4} + 2 x^{2} - 1$ |
$10$ |
[2,4] |
$35983^{2}$ |
$1$ |
$8.15116104599$ |
$189.69185538657163$ |
|
|
? |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$2.26116535916$ |
10.2.1332031009.1 |
$x^{10} - x^{9} + x^{7} - x^{6} + x^{5} - x^{4} + x^{3} - x + 1$ |
$10$ |
[2,4] |
$36497^{2}$ |
$1$ |
$8.17431620701$ |
$191.04188022525324$ |
|
|
✓ |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$2.30590519217$ |
10.2.1338315889.1 |
$x^{10} - 2 x^{8} - x^{6} + 5 x^{4} - x^{2} - 1$ |
$10$ |
[2,4] |
$36583^{2}$ |
$1$ |
$8.17816490432$ |
$191.26682932489888$ |
|
|
? |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$2.30837201867$ |
10.2.1404975289.1 |
$x^{10} - 2 x^{9} + x^{8} - x^{7} - 2 x^{6} + 4 x^{5} + x^{3} + 2 x^{2} - 2 x - 1$ |
$10$ |
[2,4] |
$37483^{2}$ |
$1$ |
$8.21801384493$ |
$193.60526852335397$ |
|
|
✓ |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$2.38748599352$ |
10.2.1487567761.1 |
$x^{10} - x^{6} - x^{5} - x^{4} + 1$ |
$10$ |
[2,4] |
$38569^{2}$ |
$1$ |
$8.26509168848$ |
$196.38991827484423$ |
|
|
✓ |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$2.47246005818$ |
10.2.1492508689.1 |
$x^{10} - 2 x^{9} + 6 x^{8} - 5 x^{7} + 7 x^{6} + 2 x^{5} - 2 x^{4} + 8 x^{3} - 4 x^{2} + 3 x - 1$ |
$10$ |
[2,4] |
$7^{2}\cdot 5519^{2}$ |
$2$ |
$8.26783282835$ |
$196.55279189062668$ |
|
|
✓ |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$2.44654946164$ |
10.2.1524824401.1 |
$x^{10} - x^{9} - 4 x^{7} + 3 x^{6} - x^{5} + 7 x^{4} - 2 x^{3} + x^{2} - 4 x - 1$ |
$10$ |
[2,4] |
$17^{2}\cdot 2297^{2}$ |
$2$ |
$8.2855622265$ |
$197.60819821049935$ |
|
|
✓ |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$2.45140405744$ |
10.2.1539071361.1 |
$x^{10} - 2 x^{9} + 4 x^{8} - 4 x^{7} + 5 x^{6} - 6 x^{5} + 4 x^{4} - 2 x^{3} - 2 x^{2} + 2 x - 1$ |
$10$ |
[2,4] |
$3^{6}\cdot 1453^{2}$ |
$2$ |
$8.2932713551$ |
$137.33279881699775$ |
|
|
? |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$2.51403389086$ |
10.2.1712387161.1 |
$x^{10} - x^{8} - 2 x^{4} + 4 x^{2} - 1$ |
$10$ |
[2,4] |
$41381^{2}$ |
$1$ |
$8.38224202495$ |
$203.42320418280704$ |
|
|
? |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$2.69257432408$ |
10.2.1729811281.1 |
$x^{10} - 2 x^{9} + x^{8} - 3 x^{7} + 4 x^{6} - 3 x^{5} + 4 x^{4} - 3 x^{3} + x^{2} - 2 x + 1$ |
$10$ |
[2,4] |
$11^{2}\cdot 19^{2}\cdot 199^{2}$ |
$3$ |
$8.39073243583$ |
$203.93871628506443$ |
|
|
? |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$2.65067444635$ |
10.2.1757202561.1 |
$x^{10} - 2 x^{7} + x^{6} - x^{5} + x^{4} - 2 x^{3} + 1$ |
$10$ |
[2,4] |
$3^{2}\cdot 89^{2}\cdot 157^{2}$ |
$3$ |
$8.40392528681$ |
$204.74130018147292$ |
|
|
? |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$2.79273658679$ |
10.2.1801408249.1 |
$x^{10} - x^{9} + x^{8} - 2 x^{6} + x^{5} - 2 x^{4} + x^{2} - x + 1$ |
$10$ |
[2,4] |
$42443^{2}$ |
$1$ |
$8.42483132825$ |
$206.0169895906646$ |
|
|
✓ |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$2.72753654739$ |
10.2.1895296225.1 |
$x^{10} - 2 x^{9} + 3 x^{8} - 3 x^{7} + 2 x^{6} - 3 x^{5} + 2 x^{4} - 3 x^{3} + 3 x^{2} - 2 x + 1$ |
$10$ |
[2,4] |
$5^{2}\cdot 8707^{2}$ |
$2$ |
$8.46774380437$ |
$208.65042535302916$ |
|
|
? |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$2.82485936577$ |
10.2.1936704064.1 |
$x^{10} - 2 x^{4} + 3 x^{2} - 1$ |
$10$ |
[2,4] |
$2^{6}\cdot 5501^{2}$ |
$2$ |
$8.48606446101$ |
$209.78083801910984$ |
|
|
? |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$2.94882249214$ |
10.2.2022480784.1 |
$x^{10} + x^{8} - 2 x^{2} - 1$ |
$10$ |
[2,4] |
$2^{4}\cdot 11243^{2}$ |
$2$ |
$8.52292055778$ |
$212.06602745371546$ |
|
|
? |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$3.31057854564$ |
10.2.2045210176.1 |
$x^{10} - 2 x^{9} + 3 x^{8} - 5 x^{6} + 7 x^{5} - 3 x^{4} - 3 x^{3} + 3 x^{2} - 3 x + 1$ |
$10$ |
[2,4] |
$2^{6}\cdot 5653^{2}$ |
$2$ |
$8.53245083479$ |
$212.6593520163174$ |
|
|
? |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$3.33677932503$ |
10.2.2087667481.1 |
$x^{10} - 2 x^{9} - x^{8} + 4 x^{7} + x^{6} - 3 x^{5} - 3 x^{4} + 3 x^{3} + 4 x^{2} - 2 x - 1$ |
$10$ |
[2,4] |
$45691^{2}$ |
$1$ |
$8.5500003526$ |
$213.75453211569572$ |
|
|
? |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$2.97080371762$ |
10.2.2089129849.1 |
$x^{10} - x^{9} - 3 x^{8} + 5 x^{7} + 2 x^{6} - 7 x^{5} + 2 x^{4} + 5 x^{3} - 3 x^{2} - x + 1$ |
$10$ |
[2,4] |
$45707^{2}$ |
$1$ |
$8.55059907379$ |
$213.7919549468595$ |
|
|
✓ |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$3.37699255166$ |
10.2.2094618289.1 |
$x^{10} - 2 x^{9} + 2 x^{8} - 2 x^{7} - 3 x^{6} + 7 x^{5} - 3 x^{4} - 2 x^{3} + 2 x^{2} - 2 x + 1$ |
$10$ |
[2,4] |
$45767^{2}$ |
$1$ |
$8.552842786$ |
$213.9322322605923$ |
|
|
? |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$3.03320243124$ |
10.2.2122168489.1 |
$x^{10} - x^{9} - 2 x^{8} + 2 x^{7} - 2 x^{6} - 4 x^{5} + 7 x^{4} - 7 x^{3} + 3 x^{2} - 1$ |
$10$ |
[2,4] |
$7^{2}\cdot 6581^{2}$ |
$2$ |
$8.56402617826$ |
$214.63224361684337$ |
|
|
? |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$3.40753367503$ |
10.2.2153980921.1 |
$x^{10} + 2 x^{6} - 3 x^{2} - 1$ |
$10$ |
[2,4] |
$46411^{2}$ |
$1$ |
$8.57677832008$ |
$215.4321238812819$ |
|
|
? |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$3.03738204661$ |
10.2.2349922576.1 |
$x^{10} - x^{9} - x^{6} - 2 x^{5} - x^{4} - x + 1$ |
$10$ |
[2,4] |
$2^{4}\cdot 12119^{2}$ |
$2$ |
$8.65177776522$ |
$174.75115566814412$ |
|
|
? |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$3.64532405145$ |
10.2.2369645041.1 |
$x^{10} - 2 x^{9} + 4 x^{7} - 3 x^{6} + x^{5} - 3 x^{4} + 4 x^{3} - 2 x + 1$ |
$10$ |
[2,4] |
$48679^{2}$ |
$1$ |
$8.65901176282$ |
$220.63317973505255$ |
|
|
? |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$3.26262563724$ |
10.2.2373540961.1 |
$x^{10} - 2 x^{8} - 3 x^{7} + 2 x^{6} + 6 x^{5} - x^{4} - 4 x^{3} - x^{2} + 2 x + 1$ |
$10$ |
[2,4] |
$11^{2}\cdot 43^{2}\cdot 103^{2}$ |
$3$ |
$8.66043433388$ |
$220.72380931834246$ |
|
|
? |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$3.64879162436$ |
10.2.2392872889.1 |
$x^{10} - 5 x^{9} + 12 x^{8} - 18 x^{7} + 19 x^{6} - 15 x^{5} + 12 x^{4} - 10 x^{3} + 9 x^{2} - 5 x + 1$ |
$10$ |
[2,4] |
$11^{2}\cdot 4447^{2}$ |
$2$ |
$8.66746233186$ |
$221.17187886347577$ |
|
|
? |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$3.31565372186$ |
10.2.2462243641.1 |
$x^{10} - x^{9} - 2 x^{8} + x^{6} - 3 x^{5} - 3 x^{4} - 4 x^{3} - 5 x^{2} - 2 x - 1$ |
$10$ |
[2,4] |
$11^{2}\cdot 13^{2}\cdot 347^{2}$ |
$3$ |
$8.6922678885$ |
$222.75771591574556$ |
|
|
? |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$3.31538728997$ |
10.2.2582570761.1 |
$x^{10} - 2 x^{9} + 3 x^{8} - 6 x^{7} + 8 x^{6} - 9 x^{5} + 8 x^{4} - 6 x^{3} + 3 x^{2} - 2 x + 1$ |
$10$ |
[2,4] |
$89^{2}\cdot 571^{2}$ |
$2$ |
$8.73383982702$ |
$225.43069888548897$ |
|
|
? |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$3.84716554195$ |
10.2.2651014144.1 |
$x^{10} + 2 x^{8} + x^{6} - 2 x^{4} - 2 x^{2} - 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 1609^{2}$ |
$2$ |
$8.75671478406$ |
$147.13272006692335$ |
|
|
✓ |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$3.52327837545$ |
10.2.2651014144.2 |
$x^{10} - 2 x^{8} + 3 x^{6} - 3 x^{4} + x^{2} - 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 1609^{2}$ |
$2$ |
$8.75671478406$ |
$147.13272006692335$ |
|
|
✓ |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$3.44895780375$ |
10.2.2651014144.3 |
$x^{10} - x^{6} + x^{4} + x^{2} - 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 1609^{2}$ |
$2$ |
$8.75671478406$ |
$147.13272006692335$ |
|
|
✓ |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$3.57771437355$ |
10.2.2655650089.1 |
$x^{10} - x^{8} + x^{6} - x^{5} - 3 x^{4} - 6 x^{3} - 6 x^{2} - x - 1$ |
$10$ |
[2,4] |
$29^{2}\cdot 1777^{2}$ |
$2$ |
$8.75824490556$ |
$227.00881040171106$ |
|
|
? |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$3.41805860452$ |
10.2.2707641225.1 |
$x^{10} - 2 x^{9} + 4 x^{8} - 4 x^{7} + x^{6} - x^{5} + x^{4} - 4 x^{3} + 4 x^{2} - 2 x + 1$ |
$10$ |
[2,4] |
$3^{2}\cdot 5^{2}\cdot 3469^{2}$ |
$3$ |
$8.77524219565$ |
$228.11181468744664$ |
|
|
? |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$3.52188815594$ |
10.2.2757615169.1 |
$x^{10} - 2 x^{9} + 4 x^{7} - x^{6} - 5 x^{5} + x^{4} + 4 x^{3} - 2 x - 1$ |
$10$ |
[2,4] |
$17^{2}\cdot 3089^{2}$ |
$2$ |
$8.7913053741$ |
$229.1571513176056$ |
|
|
✓ |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$3.58102263843$ |
10.2.2768022544.1 |
$x^{10} - x^{7} + x^{6} + x^{5} - x^{4} - x^{3} - 1$ |
$10$ |
[2,4] |
$2^{4}\cdot 7^{2}\cdot 1879^{2}$ |
$3$ |
$8.7946176345$ |
$182.05351723747205$ |
|
|
? |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$4.02663437004$ |
10.2.2784461824.1 |
$x^{10} + x^{8} - x^{4} - x^{2} - 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 17^{2}\cdot 97^{2}$ |
$3$ |
$8.79982684928$ |
$148.95036428305238$ |
|
|
✓ |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$3.57444454481$ |
10.2.2784461824.2 |
$x^{10} + 3 x^{8} + 5 x^{6} + 3 x^{4} - 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 17^{2}\cdot 97^{2}$ |
$3$ |
$8.79982684928$ |
$148.95036428305238$ |
|
|
✓ |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$3.62337940413$ |
10.2.2784461824.3 |
$x^{10} - 2 x^{8} + x^{6} - x^{4} + 3 x^{2} - 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 17^{2}\cdot 97^{2}$ |
$3$ |
$8.79982684928$ |
$148.95036428305238$ |
|
|
? |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$3.6925307128$ |
10.2.2930165161.1 |
$x^{10} - 3 x^{9} + 3 x^{8} - 4 x^{6} + 5 x^{5} - 4 x^{4} + 3 x^{2} - 3 x + 1$ |
$10$ |
[2,4] |
$7^{2}\cdot 11^{2}\cdot 19^{2}\cdot 37^{2}$ |
$4$ |
$8.84482429689$ |
$232.66069715360177$ |
|
|
✓ |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$3.71468117339$ |
10.2.3116765584.1 |
$x^{10} - 2 x^{8} + 3 x^{2} - 1$ |
$10$ |
[2,4] |
$2^{4}\cdot 17^{2}\cdot 821^{2}$ |
$3$ |
$8.89959849613$ |
$236.2794955132586$ |
|
|
? |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$4.33718874961$ |
10.2.3128276761.1 |
$x^{10} - x^{8} - 4 x^{6} + 6 x^{4} - 1$ |
$10$ |
[2,4] |
$55931^{2}$ |
$1$ |
$8.90287994241$ |
$236.49735727910365$ |
|
|
? |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$4.12890724749$ |
10.2.3154731889.1 |
$x^{10} - 3 x^{9} + 4 x^{8} - 3 x^{7} + x^{6} - x^{5} + x^{4} - 3 x^{3} + 4 x^{2} - 3 x + 1$ |
$10$ |
[2,4] |
$56167^{2}$ |
$1$ |
$8.91038040702$ |
$236.9957805531567$ |
|
|
? |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$3.76735066497$ |
10.2.3218406361.1 |
$x^{10} - x^{9} - x^{8} + x^{7} - 2 x^{6} + 5 x^{5} - 2 x^{4} + x^{3} - x^{2} - x + 1$ |
$10$ |
[2,4] |
$56731^{2}$ |
$1$ |
$8.9282036488$ |
$238.18270298239543$ |
|
|
? |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$4.50777033426$ |
10.2.3222605824.1 |
$x^{10} - 4 x^{9} + 7 x^{8} - 6 x^{7} + 10 x^{5} - 18 x^{4} + 18 x^{3} - 12 x^{2} + 6 x - 1$ |
$10$ |
[2,4] |
$2^{12}\cdot 887^{2}$ |
$2$ |
$8.9293679413$ |
$141.67045873151878$ |
|
|
✓ |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$4.53775749754$ |
10.2.3233514496.1 |
$x^{10} - x^{8} + x^{6} - 2 x^{4} + x^{2} - 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 1777^{2}$ |
$2$ |
$8.93238597983$ |
$154.6233063884407$ |
|
|
✓ |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$3.9601894649$ |
10.2.3233514496.2 |
$x^{10} - 2 x^{8} + 3 x^{6} - 2 x^{4} + 2 x^{2} - 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 1777^{2}$ |
$2$ |
$8.93238597983$ |
$154.6233063884407$ |
|
|
✓ |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$4.19708849684$ |
10.2.3233514496.3 |
$x^{10} - 2 x^{6} + x^{4} + 2 x^{2} - 1$ |
$10$ |
[2,4] |
$2^{10}\cdot 1777^{2}$ |
$2$ |
$8.93238597983$ |
$154.6233063884407$ |
|
|
✓ |
$(C_2^4:A_5) : C_2$ (as 10T37) |
trivial |
$2$ |
$5$ |
$3.84584551708$ |