| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Narrow class group |
Unit group torsion |
Unit group rank |
Regulator |
Unit signature rank |
Max $p$ |
| 5.3.4950967.1 |
$x^{5} - 29 x^{2} + 58 x - 29$ |
$5$ |
(3, 1) |
$-\,7\cdot 29^{4}$ |
$2$ |
$21.8241835873$ |
$39.12617727552311$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$38.8191483054$ |
$3$ |
$29$ |
| 5.1.6365529.1 |
$x^{5} - 2 x^{4} - 10 x^{3} - 25 x^{2} - 24 x - 12$ |
$5$ |
(1, 2) |
$3^{2}\cdot 29^{4}$ |
$2$ |
$22.9491656209$ |
$25.614095574192245$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$177.952173561$ |
$1$ |
$29$ |
| 5.3.45265984.1 |
$x^{5} - 2 x^{4} - 10 x^{3} + 4 x^{2} + 5 x + 46$ |
$5$ |
(3, 1) |
$-\,2^{6}\cdot 29^{4}$ |
$2$ |
$33.9746031955$ |
$59.15321989923478$ |
|
|
|
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$642.403874998$ |
$3$ |
$29$ |
| 5.1.45265984.1 |
$x^{5} - x^{4} + 12 x^{3} - 14 x^{2} + 42 x - 62$ |
$5$ |
(1, 2) |
$2^{6}\cdot 29^{4}$ |
$2$ |
$33.9746031955$ |
$41.82764291976793$ |
|
|
? |
$A_5$ (as 5T4) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$111.014359063$ |
$1$ |
$29$ |
| 5.1.45265984.2 |
$x^{5} - x^{4} - 17 x^{3} - 43 x^{2} - 16 x - 4$ |
$5$ |
(1, 2) |
$2^{6}\cdot 29^{4}$ |
$2$ |
$33.9746031955$ |
$41.82764291976793$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$453.528746442$ |
$1$ |
$29$ |
| 5.1.56582480.1 |
$x^{5} - x^{4} + 12 x^{3} - 14 x^{2} + 13 x - 149$ |
$5$ |
(1, 2) |
$2^{4}\cdot 5\cdot 29^{4}$ |
$3$ |
$35.5251888848$ |
$57.57413171494601$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$217.738451572$ |
$1$ |
$29$ |
| 5.1.56582480.2 |
$x^{5} - x^{4} + 12 x^{3} - 14 x^{2} - 16 x - 4$ |
$5$ |
(1, 2) |
$2^{4}\cdot 5\cdot 29^{4}$ |
$3$ |
$35.5251888848$ |
$66.13531039134111$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$193.664260369$ |
$1$ |
$29$ |
| 5.3.65069852.1 |
$x^{5} - x^{4} - 17 x^{3} - 14 x^{2} + 42 x + 54$ |
$5$ |
(3, 1) |
$-\,2^{2}\cdot 23\cdot 29^{4}$ |
$3$ |
$36.5322115417$ |
$112.58200532559964$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
$[2]$ |
$2$ |
$3$ |
$603.692489938$ |
$2$ |
$29$ |
| 5.1.70728100.1 |
$x^{5} - x^{4} - 17 x^{3} + 73 x^{2} - 132 x + 112$ |
$5$ |
(1, 2) |
$2^{2}\cdot 5^{2}\cdot 29^{4}$ |
$3$ |
$37.1465426112$ |
$52.49163064372914$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
trivial |
$2$ |
$2$ |
$459.438065546$ |
$1$ |
$29$ |
| 5.1.77093629.1 |
$x^{5} - 58 x^{2} - 87 x - 261$ |
$5$ |
(1, 2) |
$29^{4}\cdot 109$ |
$2$ |
$37.7923325869$ |
$154.39443668424948$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$222.167888353$ |
$1$ |
$109$ |
| 5.1.79215472.1 |
$x^{5} - x^{4} + 12 x^{3} - 14 x^{2} - 45 x + 83$ |
$5$ |
(1, 2) |
$2^{4}\cdot 7\cdot 29^{4}$ |
$3$ |
$37.9981106308$ |
$98.5917887027$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$747.57908049$ |
$1$ |
$29$ |
| 5.1.85581001.1 |
$x^{5} - x^{4} + 12 x^{3} + 44 x^{2} - 16 x + 112$ |
$5$ |
(1, 2) |
$11^{2}\cdot 29^{4}$ |
$2$ |
$38.5900616499$ |
$49.0472588867866$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$294.743058369$ |
$1$ |
$29$ |
| 5.1.88410125.1 |
$x^{5} - x^{4} + 12 x^{3} - 14 x^{2} + 13 x - 4$ |
$5$ |
(1, 2) |
$5^{3}\cdot 29^{4}$ |
$2$ |
$38.8418941963$ |
$49.44767789468953$ |
|
|
✓ |
$F_5$ (as 5T3) |
trivial |
trivial |
$2$ |
$2$ |
$279.307826585$ |
$1$ |
$29$ |
| 5.3.107506712.1 |
$x^{5} - x^{4} + 12 x^{3} - 72 x^{2} - 45 x + 25$ |
$5$ |
(3, 1) |
$-\,2^{3}\cdot 19\cdot 29^{4}$ |
$3$ |
$40.3912334722$ |
$182.322468533773$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$377.682517214$ |
$3$ |
$29$ |
| 5.1.119530489.1 |
$x^{5} - 29 x^{3} + 116 x - 377$ |
$5$ |
(1, 2) |
$13^{2}\cdot 29^{4}$ |
$2$ |
$41.256818949$ |
$53.31999186387194$ |
|
|
? |
$A_5$ (as 5T4) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$73.9715366571$ |
$1$ |
$29$ |
| 5.1.149943572.1 |
$x^{5} - x^{4} + 12 x^{3} - 14 x^{2} + 42 x - 4$ |
$5$ |
(1, 2) |
$2^{2}\cdot 29^{4}\cdot 53$ |
$3$ |
$43.1703500823$ |
$170.90036760919926$ |
|
|
|
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$768.204392635$ |
$1$ |
$53$ |
| 5.1.152772696.1 |
$x^{5} - 2 x^{4} - 10 x^{3} + 33 x^{2} + 63 x + 75$ |
$5$ |
(1, 2) |
$2^{3}\cdot 3^{3}\cdot 29^{4}$ |
$3$ |
$43.3320413146$ |
$150.69708639076558$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$483.318120884$ |
$1$ |
$29$ |
| 5.1.159138225.1 |
$x^{5} - x^{4} - 17 x^{3} - 43 x^{2} - 74 x - 91$ |
$5$ |
(1, 2) |
$3^{2}\cdot 5^{2}\cdot 29^{4}$ |
$3$ |
$43.6872695244$ |
$57.27485888607036$ |
|
|
? |
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$554.838501478$ |
$1$ |
$29$ |
| 5.1.175405688.1 |
$x^{5} - 2 x^{4} + 19 x^{3} - 83 x^{2} + 208 x - 244$ |
$5$ |
(1, 2) |
$2^{3}\cdot 29^{4}\cdot 31$ |
$3$ |
$44.5460022314$ |
$232.8864596298634$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$236.92177580727127$ |
$1$ |
$31$ |
| 5.1.210062457.1 |
$x^{5} - 29 x^{3} + 348 x - 696$ |
$5$ |
(1, 2) |
$3^{3}\cdot 11\cdot 29^{4}$ |
$3$ |
$46.1816758021$ |
$176.70799724167992$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$680.5413852866869$ |
$1$ |
$29$ |
| 5.1.226329920.1 |
$x^{5} - 58 x^{2} - 87 x - 290$ |
$5$ |
(1, 2) |
$2^{6}\cdot 5\cdot 29^{4}$ |
$3$ |
$46.8757677652$ |
$93.52945290718888$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$659.308757482$ |
$1$ |
$29$ |
| 5.3.228451763.1 |
$x^{5} - x^{4} - 17 x^{3} - 14 x^{2} + 42 x + 25$ |
$5$ |
(3, 1) |
$-\,17\cdot 19\cdot 29^{4}$ |
$3$ |
$46.9633320764$ |
$265.77838584246905$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$646.1168882436717$ |
$3$ |
$29$ |
| 5.3.229159044.1 |
$x^{5} - 2 x^{4} - 10 x^{3} + 33 x^{2} - 24 x - 12$ |
$5$ |
(3, 1) |
$-\,2^{2}\cdot 3^{4}\cdot 29^{4}$ |
$3$ |
$46.9923755941$ |
$127.9705589729565$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$1377.46916524$ |
$3$ |
$29$ |
| 5.1.231988168.1 |
$x^{5} - 2 x^{4} - 10 x^{3} + 4 x^{2} - 24 x - 128$ |
$5$ |
(1, 2) |
$2^{3}\cdot 29^{4}\cdot 41$ |
$3$ |
$47.1078373687$ |
$267.8275941742525$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$1188.19699348722$ |
$1$ |
$41$ |
| 5.1.243304664.1 |
$x^{5} - x^{4} - 17 x^{3} + 15 x^{2} + 158 x - 4$ |
$5$ |
(1, 2) |
$2^{3}\cdot 29^{4}\cdot 43$ |
$3$ |
$47.5587122658$ |
$274.2821970628341$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$1094.51256608$ |
$1$ |
$43$ |
| 5.1.243304664.2 |
$x^{5} - 29 x^{3} - 145 x^{2} - 232 x - 232$ |
$5$ |
(1, 2) |
$2^{3}\cdot 29^{4}\cdot 43$ |
$3$ |
$47.5587122658$ |
$274.2821970628341$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$410.3868956858853$ |
$1$ |
$43$ |
| 5.1.248962912.1 |
$x^{5} - x^{4} - 17 x^{3} - 43 x^{2} + 158 x - 178$ |
$5$ |
(1, 2) |
$2^{5}\cdot 11\cdot 29^{4}$ |
$3$ |
$47.7778861263$ |
$196.1890355471464$ |
|
|
|
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$1196.57946797$ |
$1$ |
$29$ |
| 5.1.255328441.1 |
$x^{5} - x^{4} + 12 x^{3} + 15 x^{2} + 13 x - 4$ |
$5$ |
(1, 2) |
$19^{2}\cdot 29^{4}$ |
$2$ |
$48.0197438074$ |
$64.4607269314509$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$565.970395877$ |
$1$ |
$29$ |
| 5.1.286448805.1 |
$x^{5} - x^{4} - 17 x^{3} - 72 x^{2} - 132 x - 120$ |
$5$ |
(1, 2) |
$3^{4}\cdot 5\cdot 29^{4}$ |
$3$ |
$49.1370865914$ |
$143.0754344910882$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$462.958210041$ |
$1$ |
$29$ |
| 5.3.316861888.1 |
$x^{5} - x^{4} + 12 x^{3} - 72 x^{2} - 103 x - 33$ |
$5$ |
(3, 1) |
$-\,2^{6}\cdot 7\cdot 29^{4}$ |
$3$ |
$50.1388075718$ |
$110.66554109371755$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$1609.25193119$ |
$3$ |
$29$ |
| 5.3.324641979.1 |
$x^{5} - 2 x^{4} - 10 x^{3} + 4 x^{2} + 34 x + 17$ |
$5$ |
(3, 1) |
$-\,3^{3}\cdot 17\cdot 29^{4}$ |
$3$ |
$50.3826417484$ |
$219.6768653594751$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$756.047002593$ |
$3$ |
$29$ |
| 5.3.324641979.2 |
$x^{5} - 58 x^{2} - 87 x + 261$ |
$5$ |
(3, 1) |
$-\,3^{3}\cdot 17\cdot 29^{4}$ |
$3$ |
$50.3826417484$ |
$219.6768653594751$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
$[2]$ |
$2$ |
$3$ |
$906.995417493$ |
$2$ |
$29$ |
| 5.1.374151649.1 |
$x^{5} - x^{4} + 12 x^{3} + 15 x^{2} + 71 x + 431$ |
$5$ |
(1, 2) |
$23^{2}\cdot 29^{4}$ |
$2$ |
$51.8333803674$ |
$70.92221917454985$ |
|
|
? |
$A_5$ (as 5T4) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$71.6566816605$ |
$1$ |
$29$ |
| 5.3.401028327.1 |
$x^{5} - x^{4} - 17 x^{3} - 14 x^{2} + 71 x + 112$ |
$5$ |
(3, 1) |
$-\,3^{4}\cdot 7\cdot 29^{4}$ |
$3$ |
$52.557537651$ |
$94.2246259555832$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
$[2]$ |
$2$ |
$3$ |
$2074.09546514$ |
$2$ |
$29$ |
| 5.3.406686575.1 |
$x^{5} - x^{4} - 17 x^{3} + 15 x^{2} + 100 x + 25$ |
$5$ |
(3, 1) |
$-\,5^{2}\cdot 23\cdot 29^{4}$ |
$3$ |
$52.7050181538$ |
$207.3778268998044$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
$[2]$ |
$2$ |
$3$ |
$863.4173914714032$ |
$2$ |
$29$ |
| 5.3.497218543.1 |
$x^{5} - 29 x^{2} - 116 x + 145$ |
$5$ |
(3, 1) |
$-\,19\cdot 29^{4}\cdot 37$ |
$3$ |
$54.8667787471$ |
$392.09929445441486$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$569.2458725182507$ |
$3$ |
$37$ |
| 5.1.515607849.1 |
$x^{5} - 2 x^{4} + 19 x^{3} + 62 x^{2} + 92 x + 17$ |
$5$ |
(1, 2) |
$3^{6}\cdot 29^{4}$ |
$2$ |
$55.2667471548$ |
$110.82575500707496$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
trivial |
$2$ |
$2$ |
$708.688322549$ |
$1$ |
$29$ |
| 5.1.515607849.2 |
$x^{5} - x^{4} - 17 x^{3} + 15 x^{2} - 132 x + 663$ |
$5$ |
(1, 2) |
$3^{6}\cdot 29^{4}$ |
$2$ |
$55.2667471548$ |
$110.82575500707496$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
trivial |
$2$ |
$2$ |
$607.017035345$ |
$1$ |
$29$ |
| 5.1.554508304.1 |
$x^{5} - 29 x^{3} + 406 x - 812$ |
$5$ |
(1, 2) |
$2^{4}\cdot 7^{2}\cdot 29^{4}$ |
$3$ |
$56.0765918602$ |
$108.22985767175714$ |
|
|
|
$A_5$ (as 5T4) |
trivial |
trivial |
$2$ |
$2$ |
$2196.66470028$ |
$1$ |
$29$ |
| 5.1.588457792.1 |
$x^{5} - 58 x - 116$ |
$5$ |
(1, 2) |
$2^{6}\cdot 13\cdot 29^{4}$ |
$3$ |
$56.7470204644$ |
$150.81171127902158$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$595.32544728$ |
$1$ |
$29$ |
| 5.1.591994197.1 |
$x^{5} - 2 x^{4} - 10 x^{3} + 4 x^{2} - 53 x - 157$ |
$5$ |
(1, 2) |
$3^{3}\cdot 29^{4}\cdot 31$ |
$3$ |
$56.8150626509$ |
$296.64751120788156$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$495.712959446$ |
$1$ |
$31$ |
| 5.3.667673264.1 |
$x^{5} - 2 x^{4} - 10 x^{3} + 4 x^{2} + 5 x - 12$ |
$5$ |
(3, 1) |
$-\,2^{4}\cdot 29^{4}\cdot 59$ |
$3$ |
$58.1986347884$ |
$255.00345563981938$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$3165.87199451$ |
$3$ |
$59$ |
| 5.3.667673264.2 |
$x^{5} - 2 x^{4} - 10 x^{3} + 4 x^{2} + 34 x + 46$ |
$5$ |
(3, 1) |
$-\,2^{4}\cdot 29^{4}\cdot 59$ |
$3$ |
$58.1986347884$ |
$197.77363723260348$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$494.374657689$ |
$3$ |
$59$ |
| 5.1.679697041.1 |
$x^{5} - x^{4} + 12 x^{3} - 43 x^{2} + 71 x - 33$ |
$5$ |
(1, 2) |
$29^{4}\cdot 31^{2}$ |
$2$ |
$58.406754698$ |
$82.33779742540177$ |
|
|
? |
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$631.77276962$ |
$1$ |
$31$ |
| 5.3.693135380.1 |
$x^{5} - x^{4} + 12 x^{3} + 44 x^{2} - 45 x - 91$ |
$5$ |
(3, 1) |
$-\,2^{2}\cdot 5\cdot 7^{2}\cdot 29^{4}$ |
$4$ |
$58.6359024236$ |
$174.97758417555437$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
$[2]$ |
$2$ |
$3$ |
$938.705205012$ |
$2$ |
$29$ |
| 5.1.701622752.1 |
$x^{5} - 2 x^{4} - 39 x^{3} + 62 x^{2} + 440 x - 592$ |
$5$ |
(1, 2) |
$2^{5}\cdot 29^{4}\cdot 31$ |
$3$ |
$58.7788023377$ |
$329.3511897016071$ |
|
|
|
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$2156.27976841$ |
$1$ |
$31$ |
| 5.3.724255744.1 |
$x^{5} - 2 x^{4} - 10 x^{3} - 112 x^{2} + 353 x - 70$ |
$5$ |
(3, 1) |
$-\,2^{10}\cdot 29^{4}$ |
$2$ |
$59.1532198992$ |
$99.48346112796243$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$2883.3048487$ |
$3$ |
$29$ |
| 5.1.744766893.1 |
$x^{5} - x^{4} + 12 x^{3} - 14 x^{2} + 71 x - 120$ |
$5$ |
(1, 2) |
$3^{4}\cdot 13\cdot 29^{4}$ |
$3$ |
$59.484535215$ |
$230.70220606339146$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$1721.7179535519454$ |
$1$ |
$29$ |
| 5.5.763863480.1 |
$x^{5} - x^{4} - 46 x^{3} + 131 x^{2} + 100 x - 410$ |
$5$ |
(5, 0) |
$2^{3}\cdot 3^{3}\cdot 5\cdot 29^{4}$ |
$4$ |
$59.7865026934$ |
$336.96892918091027$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$4$ |
$2307.35573297$ |
$5$ |
$29$ |
| 5.3.817616836.1 |
$x^{5} - x^{4} - 46 x^{3} + 15 x^{2} + 651 x + 808$ |
$5$ |
(3, 1) |
$-\,2^{2}\cdot 17^{2}\cdot 29^{4}$ |
$3$ |
$60.6052106581$ |
$195.54543188510937$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$5229.378366050942$ |
$3$ |
$29$ |
