| 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 |
| 5.1.1609.1 |
$x^{5} - x^{3} - x^{2} + x + 1$ |
$5$ |
[1,2] |
$1609$ |
$1$ |
$4.37835739203$ |
$40.11234224026316$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.268355550838$ |
| 5.1.1649.1 |
$x^{5} - x^{4} + x^{2} - x + 1$ |
$5$ |
[1,2] |
$17\cdot 97$ |
$2$ |
$4.39991342464$ |
$40.607881008493905$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.273599709102$ |
| 5.1.1777.1 |
$x^{5} - x^{4} + x^{3} - 2 x^{2} + x - 1$ |
$5$ |
[1,2] |
$1777$ |
$1$ |
$4.46619298991$ |
$42.15447781671598$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.290415099662$ |
| 5.1.2209.1 |
$x^{5} - 2 x^{4} + 2 x^{3} - x^{2} + 1$ |
$5$ |
[1,2] |
$47^{2}$ |
$1$ |
$4.66486567972$ |
$6.855654600401044$ |
|
|
✓ |
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$0.346947612066$ |
| 5.1.2297.1 |
$x^{5} - x^{4} + x^{3} - x^{2} - 1$ |
$5$ |
[1,2] |
$2297$ |
$1$ |
$4.70145408445$ |
$47.92702786528704$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.357352114929$ |
| 5.1.2617.1 |
$x^{5} + x^{3} - 2 x^{2} - 1$ |
$5$ |
[1,2] |
$2617$ |
$1$ |
$4.82570472203$ |
$51.15662224971465$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.394462762943$ |
| 5.1.2665.1 |
$x^{5} - x^{4} + x^{3} - x^{2} + 2 x - 1$ |
$5$ |
[1,2] |
$5\cdot 13\cdot 41$ |
$3$ |
$4.84327849939$ |
$51.62363799656123$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.399660818464$ |
| 5.1.2869.1 |
$x^{5} - x - 1$ |
$5$ |
[1,2] |
$19\cdot 151$ |
$2$ |
$4.91525563382$ |
$53.563046963368315$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.432343878825$ |
| 5.1.3017.1 |
$x^{5} - x^{2} + 1$ |
$5$ |
[1,2] |
$7\cdot 431$ |
$2$ |
$4.96495208964$ |
$54.92722457943783$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.437122673287$ |
| 5.1.3089.1 |
$x^{5} - x^{3} + 2 x - 1$ |
$5$ |
[1,2] |
$3089$ |
$1$ |
$4.98842654594$ |
$55.57877292636101$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.486630116907$ |
| 5.1.3233.1 |
$x^{5} - x^{2} - 1$ |
$5$ |
[1,2] |
$53\cdot 61$ |
$2$ |
$5.0340919158$ |
$56.859475903318$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.503137602609$ |
| 5.1.3369.1 |
$x^{5} + x^{3} - x^{2} - x - 1$ |
$5$ |
[1,2] |
$3\cdot 1123$ |
$2$ |
$5.07574975343$ |
$58.0430874437258$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.518409869312$ |
| 5.1.3857.1 |
$x^{5} - x^{4} + x^{3} - x^{2} + 1$ |
$5$ |
[1,2] |
$7\cdot 19\cdot 29$ |
$3$ |
$5.2149473454$ |
$62.10475022089695$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.574676824693$ |
| 5.1.3889.1 |
$x^{5} - x^{4} + x^{3} + x - 1$ |
$5$ |
[1,2] |
$3889$ |
$1$ |
$5.22357204058$ |
$62.36184731067546$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.532749828479$ |
| 5.1.4169.1 |
$x^{5} + 2 x^{3} - x^{2} + 2 x - 1$ |
$5$ |
[1,2] |
$11\cdot 379$ |
$2$ |
$5.29671223777$ |
$64.56779382943171$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.607298353079$ |
| 5.1.4261.1 |
$x^{5} - 2 x^{2} - 2 x - 1$ |
$5$ |
[1,2] |
$4261$ |
$1$ |
$5.31988576671$ |
$65.27633568147036$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.758429941403$ |
| 5.1.4409.1 |
$x^{5} - x^{4} + x^{2} + x - 1$ |
$5$ |
[1,2] |
$4409$ |
$1$ |
$5.3563385594$ |
$66.40030120413611$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.631438453903$ |
| 5.1.4417.1 |
$x^{5} - 2 x^{4} + 2 x^{3} - x^{2} - 1$ |
$5$ |
[1,2] |
$7\cdot 631$ |
$2$ |
$5.35828093372$ |
$66.46051459325304$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.571446122147$ |
| 5.1.4429.1 |
$x^{5} - x^{4} + 2 x^{3} - x^{2} + 1$ |
$5$ |
[1,2] |
$43\cdot 103$ |
$2$ |
$5.36118922487$ |
$66.55073252789934$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.780070782411$ |
| 5.1.4432.1 |
$x^{5} - x^{4} + 2 x^{2} - x + 1$ |
$5$ |
[1,2] |
$2^{4}\cdot 277$ |
$2$ |
$5.36191531255$ |
$28.97769793904893$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.780720256768$ |
| 5.1.4477.1 |
$x^{5} + x^{3} + x - 1$ |
$5$ |
[1,2] |
$11^{2}\cdot 37$ |
$2$ |
$5.37275972428$ |
$30.08587537137172$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.786371046393$ |
| 5.3.4511.1 |
$x^{5} - x^{3} - 2 x^{2} + 1$ |
$5$ |
[3,1] |
$-\,13\cdot 347$ |
$2$ |
$5.38089559333$ |
$67.16397844082793$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$0.628579167485$ |
| 5.1.4549.1 |
$x^{5} - x^{4} + 2 x^{3} - 2 x^{2} - 1$ |
$5$ |
[1,2] |
$4549$ |
$1$ |
$5.38993077448$ |
$67.446274915669$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.601042087852$ |
| 5.1.4597.1 |
$x^{5} + x^{3} - 2 x^{2} - x - 1$ |
$5$ |
[1,2] |
$4597$ |
$1$ |
$5.40125772864$ |
$67.80117993073571$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.801495712181$ |
| 5.1.4757.1 |
$x^{5} - x^{4} + 2 x^{3} - x^{2} + 2 x - 1$ |
$5$ |
[1,2] |
$67\cdot 71$ |
$2$ |
$5.43834343727$ |
$68.97100840208152$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.822644320451$ |
| 5.1.4817.1 |
$x^{5} - 2 x^{4} + 2 x^{3} - x^{2} + 2 x - 1$ |
$5$ |
[1,2] |
$4817$ |
$1$ |
$5.45199349845$ |
$69.40461079784254$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.687711449121$ |
| 5.1.4897.1 |
$x^{5} - x^{4} - x^{3} + x^{2} + 1$ |
$5$ |
[1,2] |
$59\cdot 83$ |
$2$ |
$5.46998355669$ |
$69.97856814768362$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.612023201458$ |
| 5.3.4903.1 |
$x^{5} - x^{4} - x^{3} + 2 x^{2} - x - 1$ |
$5$ |
[3,1] |
$-\,4903$ |
$1$ |
$5.47132330872$ |
$70.02142529254886$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$0.668925630977$ |
| 5.1.5025.1 |
$x^{5} - x^{4} - x^{2} + x + 1$ |
$5$ |
[1,2] |
$3\cdot 5^{2}\cdot 67$ |
$3$ |
$5.49828456648$ |
$41.45510615605851$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.708326486922$ |
| 5.1.5164.1 |
$x^{5} - x^{4} - x^{3} + 2 x + 1$ |
$5$ |
[1,2] |
$2^{2}\cdot 1291$ |
$2$ |
$5.5283718475$ |
$71.86097689288673$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.873888115674$ |
| 5.1.5437.1 |
$x^{5} - 2 x^{4} + 2 x^{3} - 2 x^{2} - 1$ |
$5$ |
[1,2] |
$5437$ |
$1$ |
$5.58562617452$ |
$73.7360156233031$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.909810356182$ |
| 5.1.5501.1 |
$x^{5} - 2 x^{4} + 2 x^{2} - x + 1$ |
$5$ |
[1,2] |
$5501$ |
$1$ |
$5.59871459382$ |
$74.16872656315464$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.68402903196$ |
| 5.3.5519.1 |
$x^{5} - x^{4} - x^{3} + 3 x^{2} - 1$ |
$5$ |
[3,1] |
$-\,5519$ |
$1$ |
$5.60237375466$ |
$74.28997240543302$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$0.732128382974$ |
| 5.1.5584.1 |
$x^{5} - x^{4} + x + 1$ |
$5$ |
[1,2] |
$2^{4}\cdot 349$ |
$2$ |
$5.61550840903$ |
$32.526453286890316$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.927152539126$ |
| 5.1.5653.1 |
$x^{5} - x^{4} + 2 x - 1$ |
$5$ |
[1,2] |
$5653$ |
$1$ |
$5.62931818739$ |
$75.18643494673756$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.714858266315$ |
| 5.1.5753.1 |
$x^{5} - x^{4} - x^{3} + 2 x^{2} - x + 1$ |
$5$ |
[1,2] |
$11\cdot 523$ |
$2$ |
$5.64909495501$ |
$75.8485332752058$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.777786743614$ |
| 5.3.5783.1 |
$x^{5} - 2 x^{4} + x^{3} + 2 x^{2} - 2 x - 1$ |
$5$ |
[3,1] |
$-\,5783$ |
$1$ |
$5.65497433803$ |
$76.04603868710059$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$0.757141624325$ |
| 5.1.5864.1 |
$x^{5} - x^{4} + x^{3} + 2 x^{2} - 2 x + 1$ |
$5$ |
[1,2] |
$2^{3}\cdot 733$ |
$2$ |
$5.67072768331$ |
$76.57675887630658$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.957732052495$ |
| 5.1.5913.1 |
$x^{5} - x^{4} + 2 x^{3} - x^{2} + x + 1$ |
$5$ |
[1,2] |
$3^{4}\cdot 73$ |
$2$ |
$5.68017316557$ |
$36.967757191167294$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.794503605626$ |
| 5.1.6241.1 |
$x^{5} - x^{4} + x^{3} - 2 x^{2} + 3 x - 1$ |
$5$ |
[1,2] |
$79^{2}$ |
$1$ |
$5.74183669575$ |
$8.888194417315589$ |
|
|
✓ |
$D_{5}$ (as 5T2) |
trivial |
$2$ |
$2$ |
$0.803647538428$ |
| 5.1.6449.1 |
$x^{5} - x^{4} + x^{3} - 3 x^{2} - 1$ |
$5$ |
[1,2] |
$6449$ |
$1$ |
$5.77960922231$ |
$80.30566605165541$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.826566357784$ |
| 5.1.6581.1 |
$x^{5} - 2 x^{2} - 1$ |
$5$ |
[1,2] |
$6581$ |
$1$ |
$5.80307760104$ |
$81.12336284942828$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$1.04188879242$ |
| 5.1.6757.1 |
$x^{5} - x^{4} + 3 x^{2} - 2 x + 1$ |
$5$ |
[1,2] |
$29\cdot 233$ |
$2$ |
$5.83378989382$ |
$82.20097323024831$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$1.08518392663$ |
| 5.1.6793.1 |
$x^{5} - x^{4} + x^{3} + x + 1$ |
$5$ |
[1,2] |
$6793$ |
$1$ |
$5.83999295111$ |
$82.41965784932621$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.97237060045$ |
| 5.3.7031.1 |
$x^{5} - x^{3} - x^{2} - x + 1$ |
$5$ |
[3,1] |
$-\,79\cdot 89$ |
$2$ |
$5.88035329589$ |
$83.85105843100611$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$0.888380795899$ |
| 5.1.7096.1 |
$x^{5} - x^{2} + x + 1$ |
$5$ |
[1,2] |
$2^{3}\cdot 887$ |
$2$ |
$5.89118581837$ |
$84.23775875461075$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$1.10002131304$ |
| 5.1.7177.1 |
$x^{5} - x^{4} + 3 x^{3} - x^{2} + 2 x - 1$ |
$5$ |
[1,2] |
$7177$ |
$1$ |
$5.90457426388$ |
$84.71717653463199$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$1.01016967835$ |
| 5.1.7265.1 |
$x^{5} - x^{4} + x^{3} + 2 x^{2} - x + 1$ |
$5$ |
[1,2] |
$5\cdot 1453$ |
$2$ |
$5.91898342382$ |
$85.23496934944014$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.920865082729$ |
| 5.1.7333.1 |
$x^{5} - 2 x^{4} + 2 x^{3} - 2 x^{2} + 3 x - 1$ |
$5$ |
[1,2] |
$7333$ |
$1$ |
$5.93002244277$ |
$85.63293758829018$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$2$ |
$0.84949301581$ |
| 5.3.7367.1 |
$x^{5} - 2 x^{4} + 3 x^{2} - 2 x - 1$ |
$5$ |
[3,1] |
$-\,53\cdot 139$ |
$2$ |
$5.93551127049$ |
$85.83122974768565$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$0.904106825927$ |
