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 |
5.3.4511.1 |
$x^{5} - x^{3} - 2 x^{2} + 1$ |
$5$ |
[3,1] |
$-\,13\cdot 347$ |
$2$ |
$5.38089559333$ |
$67.16397844082793$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$0.628579167485$ |
5.3.4903.1 |
$x^{5} - x^{4} - x^{3} + 2 x^{2} - x - 1$ |
$5$ |
[3,1] |
$-\,4903$ |
$1$ |
$5.47132330872$ |
$70.02142529254886$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$0.668925630977$ |
5.3.5519.1 |
$x^{5} - x^{4} - x^{3} + 3 x^{2} - 1$ |
$5$ |
[3,1] |
$-\,5519$ |
$1$ |
$5.60237375466$ |
$74.28997240543302$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$0.732128382974$ |
5.3.5783.1 |
$x^{5} - 2 x^{4} + x^{3} + 2 x^{2} - 2 x - 1$ |
$5$ |
[3,1] |
$-\,5783$ |
$1$ |
$5.65497433803$ |
$76.04603868710059$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$0.757141624325$ |
5.3.7031.1 |
$x^{5} - x^{3} - x^{2} - x + 1$ |
$5$ |
[3,1] |
$-\,79\cdot 89$ |
$2$ |
$5.88035329589$ |
$83.85105843100611$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$0.888380795899$ |
5.3.7367.1 |
$x^{5} - 2 x^{4} + 3 x^{2} - 2 x - 1$ |
$5$ |
[3,1] |
$-\,53\cdot 139$ |
$2$ |
$5.93551127049$ |
$85.83122974768565$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$0.904106825927$ |
5.3.7463.1 |
$x^{5} - 2 x^{4} + x^{3} - 2 x + 1$ |
$5$ |
[3,1] |
$-\,17\cdot 439$ |
$2$ |
$5.95090049275$ |
$86.38865666278183$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$0.926583855017$ |
5.3.8519.1 |
$x^{5} - x^{4} - x^{2} - x + 1$ |
$5$ |
[3,1] |
$-\,7\cdot 1217$ |
$2$ |
$6.11051372122$ |
$92.29842902238369$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$0.999142814665$ |
5.3.8647.1 |
$x^{5} - 3 x^{3} - 2 x^{2} + 2 x + 1$ |
$5$ |
[3,1] |
$-\,8647$ |
$1$ |
$6.12876673034$ |
$92.98924669014154$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$1.02787912946$ |
5.3.9439.1 |
$x^{5} - x^{4} - x^{3} + x^{2} - 2 x + 1$ |
$5$ |
[3,1] |
$-\,9439$ |
$1$ |
$6.23713576052$ |
$97.15451610707554$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$1.21312946247$ |
5.3.9759.1 |
$x^{5} - 2 x^{4} + x^{2} - 2 x - 1$ |
$5$ |
[3,1] |
$-\,3\cdot 3253$ |
$2$ |
$6.27886381559$ |
$98.78765105011861$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$1.24138586861$ |
5.3.10407.1 |
$x^{5} - x^{4} - 3 x^{3} + 3 x - 1$ |
$5$ |
[3,1] |
$-\,3\cdot 3469$ |
$2$ |
$6.36011708725$ |
$102.01470482239313$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$1.29968455596$ |
5.3.11119.1 |
$x^{5} - 2 x^{4} + x^{3} + x^{2} - 3 x + 1$ |
$5$ |
[3,1] |
$-\,11119$ |
$1$ |
$6.44485492951$ |
$105.4466689848475$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$1.19655267604$ |
5.3.11243.1 |
$x^{5} - x^{4} - 2 x + 1$ |
$5$ |
[3,1] |
$-\,11243$ |
$1$ |
$6.45916594224$ |
$106.03301372685773$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$1.27597060679$ |
5.3.11551.1 |
$x^{5} - x^{4} - 2 x^{3} + 3 x^{2} - x - 1$ |
$5$ |
[3,1] |
$-\,11551$ |
$1$ |
$6.49417394267$ |
$107.47557862137798$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$1.39602772946$ |
5.3.12447.1 |
$x^{5} + x^{3} - x^{2} - 3 x - 1$ |
$5$ |
[3,1] |
$-\,3^{3}\cdot 461$ |
$2$ |
$6.59193532748$ |
$77.35562983523201$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$1.47353341675$ |
5.3.13219.1 |
$x^{5} - 2 x^{2} - x + 1$ |
$5$ |
[3,1] |
$-\,13219$ |
$1$ |
$6.67174932739$ |
$114.97391008398384$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$1.4282230441$ |
5.3.13523.1 |
$x^{5} - x^{4} - x^{3} - x^{2} - 3 x + 1$ |
$5$ |
[3,1] |
$-\,13523$ |
$1$ |
$6.7021571931$ |
$116.28843450661807$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$1.94231467204$ |
5.3.13799.1 |
$x^{5} - x^{4} - x^{3} + 2 x^{2} - 3 x + 1$ |
$5$ |
[3,1] |
$-\,13799$ |
$1$ |
$6.72929431099$ |
$117.46914488494414$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$1.4643954612$ |
5.3.13883.1 |
$x^{5} - x^{4} - 2 x^{3} + x + 2$ |
$5$ |
[3,1] |
$-\,13883$ |
$1$ |
$6.73746721252$ |
$117.8261431092438$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$1.97769282832$ |
5.3.14103.1 |
$x^{5} - 2 x^{4} + 2 x^{3} - x^{2} - 2 x + 1$ |
$5$ |
[3,1] |
$-\,3^{2}\cdot 1567$ |
$2$ |
$6.75868648308$ |
$68.5638388656878$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$1.60398325545$ |
5.3.14631.1 |
$x^{5} - x^{4} - 3 x^{3} + 3 x^{2} - 1$ |
$5$ |
[3,1] |
$-\,3\cdot 4877$ |
$2$ |
$6.80855267956$ |
$120.95867062761562$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$1.65878969233$ |
5.3.14891.1 |
$x^{5} - x^{4} - 3 x^{3} + 3 x^{2} + x - 2$ |
$5$ |
[3,1] |
$-\,14891$ |
$1$ |
$6.8325807449$ |
$122.02868515230344$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$2.0760375874$ |
5.3.14911.1 |
$x^{5} - x^{4} - 2 x^{3} - x^{2} + 3 x + 1$ |
$5$ |
[3,1] |
$-\,13\cdot 31\cdot 37$ |
$3$ |
$6.83441511814$ |
$122.11060560000512$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$1.67981747987$ |
5.3.15536.1 |
$x^{5} - 2 x^{4} + 2$ |
$5$ |
[3,1] |
$-\,2^{4}\cdot 971$ |
$2$ |
$6.89077139991$ |
$54.254230914862234$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$2.13808345853$ |
5.3.15919.1 |
$x^{5} - 2 x^{3} - 3 x^{2} + 1$ |
$5$ |
[3,1] |
$-\,15919$ |
$1$ |
$6.92441608506$ |
$126.17051953606278$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$1.809226746$ |
5.3.16816.1 |
$x^{5} - 2 x^{3} - 2 x^{2} - 4 x - 2$ |
$5$ |
[3,1] |
$-\,2^{4}\cdot 1051$ |
$2$ |
$7.0007495271$ |
$56.444984035827815$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$2.2650046595$ |
5.3.17151.1 |
$x^{5} - x^{3} - 2 x - 1$ |
$5$ |
[3,1] |
$-\,3\cdot 5717$ |
$2$ |
$7.02842296944$ |
$130.96182649917495$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$1.84474320275$ |
5.3.17348.1 |
$x^{5} - x^{4} - 2 x^{3} - x^{2} + 2 x + 2$ |
$5$ |
[3,1] |
$-\,2^{2}\cdot 4337$ |
$2$ |
$7.04449528357$ |
$131.71180660821565$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$2.32166707121$ |
5.3.18063.1 |
$x^{5} - x^{4} + x^{3} - 2 x^{2} - x + 1$ |
$5$ |
[3,1] |
$-\,3^{4}\cdot 223$ |
$2$ |
$7.10162893521$ |
$35.962463598304126$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$1.96979771022$ |
5.3.18463.1 |
$x^{5} - x^{4} - 3 x^{3} + 4 x^{2} + x - 1$ |
$5$ |
[3,1] |
$-\,37\cdot 499$ |
$2$ |
$7.13280668679$ |
$135.87862230682205$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$1.93552863121$ |
5.3.18583.1 |
$x^{5} - x^{4} - x^{3} - 2 x^{2} + x + 1$ |
$5$ |
[3,1] |
$-\,18583$ |
$1$ |
$7.14205458996$ |
$136.31947769852994$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$1.94636349026$ |
5.3.18839.1 |
$x^{5} - x^{4} + 3 x^{2} - x - 1$ |
$5$ |
[3,1] |
$-\,18839$ |
$1$ |
$7.161624879$ |
$137.2552366942697$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$1.8261292549$ |
5.3.19015.1 |
$x^{5} - 2 x^{3} - x^{2} - 2 x - 1$ |
$5$ |
[3,1] |
$-\,5\cdot 3803$ |
$2$ |
$7.17495639354$ |
$137.8948875049398$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$1.74644196144$ |
5.3.19951.1 |
$x^{5} - 2 x^{4} + x^{3} - 3 x^{2} + 3 x + 1$ |
$5$ |
[3,1] |
$-\,71\cdot 281$ |
$2$ |
$7.24424173091$ |
$141.24800883552305$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$2.03268966315$ |
5.3.21191.1 |
$x^{5} - x^{4} - x^{2} - 3 x - 1$ |
$5$ |
[3,1] |
$-\,21191$ |
$1$ |
$7.33213225923$ |
$145.5712883778941$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$1.93450979256$ |
5.3.21227.1 |
$x^{5} - x^{4} - 4 x^{2} + 3 x + 2$ |
$5$ |
[3,1] |
$-\,21227$ |
$1$ |
$7.33462178381$ |
$145.69488666387713$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$2.67366796844$ |
5.3.22331.1 |
$x^{5} - 2 x^{4} + 4 x^{2} - x - 1$ |
$5$ |
[3,1] |
$-\,137\cdot 163$ |
$2$ |
$7.40937600068$ |
$149.4356048604214$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$1.9891406347$ |
5.3.22424.1 |
$x^{5} - 2 x^{3} - x^{2} - x + 1$ |
$5$ |
[3,1] |
$-\,2^{3}\cdot 2803$ |
$2$ |
$7.41553718415$ |
$149.74645237867907$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$2.76003508518$ |
5.3.22448.1 |
$x^{5} - x^{4} - 2 x^{3} + 2 x^{2} - x - 1$ |
$5$ |
[3,1] |
$-\,2^{4}\cdot 23\cdot 61$ |
$3$ |
$7.41712384798$ |
$65.21580088926439$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$2.86477407146$ |
5.3.22583.1 |
$x^{5} - x^{2} - 2 x + 1$ |
$5$ |
[3,1] |
$-\,11\cdot 2053$ |
$2$ |
$7.42602363112$ |
$150.2764119880429$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$1.93941948265$ |
5.3.22687.1 |
$x^{5} - x^{4} + x^{3} - x^{2} - 2 x + 1$ |
$5$ |
[3,1] |
$-\,7^{2}\cdot 463$ |
$2$ |
$7.43285078176$ |
$56.929781309961136$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$1.95362445218$ |
5.3.22935.1 |
$x^{5} + x^{3} - 2 x^{2} - 4 x + 1$ |
$5$ |
[3,1] |
$-\,3\cdot 5\cdot 11\cdot 139$ |
$4$ |
$7.44903043826$ |
$151.44305860619693$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$2.31044863242$ |
5.3.23103.1 |
$x^{5} - x^{4} + x^{2} - 3 x + 1$ |
$5$ |
[3,1] |
$-\,3^{2}\cdot 17\cdot 151$ |
$3$ |
$7.45991150572$ |
$87.75534171775527$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$2.33091635633$ |
5.3.23119.1 |
$x^{5} - 3 x^{2} + 1$ |
$5$ |
[3,1] |
$-\,61\cdot 379$ |
$2$ |
$7.46094449307$ |
$152.04933409916663$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$2.27920752421$ |
5.3.23339.1 |
$x^{5} - x^{4} + 2 x^{2} - 2 x - 1$ |
$5$ |
[3,1] |
$-\,23339$ |
$1$ |
$7.47509039368$ |
$152.77107055984126$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$2.08590583429$ |
5.3.23679.1 |
$x^{5} - 2 x^{4} + x^{2} - 2 x + 3$ |
$5$ |
[3,1] |
$-\,3^{3}\cdot 877$ |
$2$ |
$7.49674384054$ |
$67.5057454940964$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$2.65227818165$ |
5.3.23831.1 |
$x^{5} - 3 x^{3} - 2 x^{2} + 4 x - 1$ |
$5$ |
[3,1] |
$-\,23831$ |
$1$ |
$7.50634382705$ |
$154.3729250872704$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$2.12564475096$ |
5.3.23891.1 |
$x^{5} - x^{4} - 3 x^{3} - x^{2} + 3 x + 2$ |
$5$ |
[3,1] |
$-\,7\cdot 3413$ |
$2$ |
$7.51011981412$ |
$154.56713751635564$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$2.89262586592$ |
5.3.24299.1 |
$x^{5} - x^{4} - x^{3} + 3 x^{2} - x - 2$ |
$5$ |
[3,1] |
$-\,11\cdot 47^{2}$ |
$2$ |
$7.53559727162$ |
$43.19447977961657$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$2$ |
$3$ |
$2.93068377955$ |