| 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 $p$ |
| 5.1.564680169.1 |
$x^{5} - x^{4} + 36 x^{3} - 25 x^{2} - 131 x - 276$ |
$5$ |
(1, 2) |
$3^{2}\cdot 89^{4}$ |
$2$ |
$56.2808317686$ |
$62.81634059089073$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$2429.8370853$ |
$1$ |
$89$ |
| 5.3.1003875856.1 |
$x^{5} - 2 x^{4} - 34 x^{3} + 156 x^{2} + 40 x - 1000$ |
$5$ |
(3, 1) |
$-\,2^{4}\cdot 89^{4}$ |
$2$ |
$63.1445687928$ |
$91.3871919252943$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$1958.80691175$ |
$3$ |
$89$ |
| 5.1.2007751712.1 |
$x^{5} - x^{4} + 36 x^{3} + 64 x^{2} + 403 x + 169$ |
$5$ |
(1, 2) |
$2^{5}\cdot 89^{4}$ |
$2$ |
$72.5340622993$ |
$129.2410062479442$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$2083.5247206$ |
$1$ |
$89$ |
| 5.1.2007751712.2 |
$x^{5} - x^{4} - 53 x^{3} + 331 x^{2} - 754 x + 614$ |
$5$ |
(1, 2) |
$2^{5}\cdot 89^{4}$ |
$2$ |
$72.5340622993$ |
$129.2410062479442$ |
|
|
? |
$S_5$ (as 5T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$1384.23383964$ |
$1$ |
$89$ |
| 5.5.2258720676.1 |
$x^{5} - x^{4} - 53 x^{3} + 64 x^{2} + 314 x - 98$ |
$5$ |
(5, 0) |
$2^{2}\cdot 3^{2}\cdot 89^{4}$ |
$3$ |
$74.2630027436$ |
$99.71472513477265$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
$[2]$ |
$2$ |
$4$ |
$4597.38535716$ |
$4$ |
$89$ |
| 5.1.3074369809.1 |
$x^{5} - 2 x^{4} - 34 x^{3} + 67 x^{2} + 574 x - 21$ |
$5$ |
(1, 2) |
$7^{2}\cdot 89^{4}$ |
$2$ |
$78.9862001378$ |
$95.95354521262794$ |
|
|
? |
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$1739.6529423$ |
$1$ |
$89$ |
| 5.3.4015503424.1 |
$x^{5} - 2 x^{4} - 34 x^{3} + 156 x^{2} - 316 x + 424$ |
$5$ |
(3, 1) |
$-\,2^{6}\cdot 89^{4}$ |
$2$ |
$83.3197580445$ |
$145.06812459863193$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
$[2]$ |
$2$ |
$3$ |
$1904.56145911$ |
$2$ |
$89$ |
| 5.3.4015503424.2 |
$x^{5} - 2 x^{4} - 34 x^{3} + 156 x^{2} + 1197 x + 1670$ |
$5$ |
(3, 1) |
$-\,2^{6}\cdot 89^{4}$ |
$2$ |
$83.3197580445$ |
$145.06812459863193$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$8148.93027057$ |
$3$ |
$89$ |
| 5.1.4015503424.1 |
$x^{5} - x^{4} + 36 x^{3} - 114 x^{2} + 314 x - 454$ |
$5$ |
(1, 2) |
$2^{6}\cdot 89^{4}$ |
$2$ |
$83.3197580445$ |
$102.57865463770763$ |
|
|
? |
$A_5$ (as 5T4) |
$[6]$ |
$[6]$ |
$2$ |
$2$ |
$412.794158605$ |
$1$ |
$89$ |
| 5.3.4454699111.1 |
$x^{5} - 89 x^{2} - 89 x + 89$ |
$5$ |
(3, 1) |
$-\,71\cdot 89^{4}$ |
$2$ |
$85.0675010379$ |
$305.59143629547054$ |
|
|
? |
$S_5$ (as 5T5) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$1969.03764144$ |
$3$ |
$89$ |
| 5.3.5019379280.1 |
$x^{5} - 2 x^{4} - 34 x^{3} - 22 x^{2} + 129 x + 68$ |
$5$ |
(3, 1) |
$-\,2^{4}\cdot 5\cdot 89^{4}$ |
$3$ |
$87.1224345236$ |
$229.37284481038833$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$3222.00485602$ |
$3$ |
$89$ |
| 5.1.5019379280.1 |
$x^{5} - 2 x^{4} - 34 x^{3} - 22 x^{2} + 574 x + 68$ |
$5$ |
(1, 2) |
$2^{4}\cdot 5\cdot 89^{4}$ |
$3$ |
$87.1224345236$ |
$182.0533475724745$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$5188.40807513$ |
$1$ |
$89$ |
| 5.1.5082121521.1 |
$x^{5} - 89 x^{2} - 534 x - 801$ |
$5$ |
(1, 2) |
$3^{4}\cdot 89^{4}$ |
$2$ |
$87.3391596765$ |
$130.6632538864305$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
trivial |
$2$ |
$2$ |
$1252.2950518$ |
$1$ |
$89$ |
| 5.1.7842780125.1 |
$x^{5} - x^{4} + 36 x^{3} + 64 x^{2} + 136 x + 80$ |
$5$ |
(1, 2) |
$5^{3}\cdot 89^{4}$ |
$2$ |
$95.2563656978$ |
$121.26612735805837$ |
|
|
? |
$F_5$ (as 5T3) |
trivial |
trivial |
$2$ |
$2$ |
$2760.07769919$ |
$1$ |
$89$ |
| 5.3.10038758560.1 |
$x^{5} - x^{4} - 53 x^{3} + 153 x^{2} + 136 x - 276$ |
$5$ |
(3, 1) |
$-\,2^{5}\cdot 5\cdot 89^{4}$ |
$3$ |
$100.077397221$ |
$288.9916754508783$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$9890.76114081$ |
$3$ |
$89$ |
| 5.1.11858283549.1 |
$x^{5} - x^{4} + 36 x^{3} - 292 x^{2} + 937 x - 1344$ |
$5$ |
(1, 2) |
$3^{3}\cdot 7\cdot 89^{4}$ |
$3$ |
$103.467597784$ |
$218.72678345201473$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$3867.04180343$ |
$1$ |
$89$ |
| 5.1.14117004225.1 |
$x^{5} - 2 x^{4} + 55 x^{3} + 423 x^{2} + 663 x + 513$ |
$5$ |
(1, 2) |
$3^{2}\cdot 5^{2}\cdot 89^{4}$ |
$3$ |
$107.139227071$ |
$140.46160765901098$ |
|
|
? |
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$6060.29172996$ |
$1$ |
$89$ |
| 5.1.18069765408.1 |
$x^{5} - x^{4} + 36 x^{3} + 242 x^{2} + 136 x + 792$ |
$5$ |
(1, 2) |
$2^{5}\cdot 3^{2}\cdot 89^{4}$ |
$3$ |
$112.561663537$ |
$251.26536236356293$ |
|
|
|
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$13629.1556992$ |
$1$ |
$89$ |
| 5.3.20328486084.1 |
$x^{5} - x^{4} - 53 x^{3} + 64 x^{2} + 314 x + 703$ |
$5$ |
(3, 1) |
$-\,2^{2}\cdot 3^{4}\cdot 89^{4}$ |
$3$ |
$115.244712113$ |
$174.67831935290027$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$8169.955554728391$ |
$3$ |
$89$ |
| 5.3.20328486084.2 |
$x^{5} - x^{4} - 53 x^{3} - 25 x^{2} + 670 x + 1148$ |
$5$ |
(3, 1) |
$-\,2^{2}\cdot 3^{4}\cdot 89^{4}$ |
$3$ |
$115.244712113$ |
$313.8366605515177$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$25085.13617223962$ |
$3$ |
$89$ |
| 5.1.22649949001.1 |
$x^{5} - 2 x^{4} + 55 x^{3} + 512 x^{2} + 663 x + 958$ |
$5$ |
(1, 2) |
$19^{2}\cdot 89^{4}$ |
$2$ |
$117.76424326$ |
$158.08432376360088$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$13659.7126269$ |
$1$ |
$89$ |
| 5.1.32124027392.1 |
$x^{5} - x^{4} + 36 x^{3} + 64 x^{2} - 932 x + 5420$ |
$5$ |
(1, 2) |
$2^{9}\cdot 89^{4}$ |
$2$ |
$126.289137586$ |
$243.97453188513757$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$10128.0433414$ |
$1$ |
$89$ |
| 5.1.33190645489.1 |
$x^{5} - 534 x^{2} + 623 x - 890$ |
$5$ |
(1, 2) |
$23^{2}\cdot 89^{4}$ |
$2$ |
$127.116855081$ |
$173.93057124449408$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$51907.3067897$ |
$1$ |
$89$ |
| 5.1.36139530816.1 |
$x^{5} - 2 x^{4} - 34 x^{3} + 512 x^{2} - 2007 x + 3450$ |
$5$ |
(1, 2) |
$2^{6}\cdot 3^{2}\cdot 89^{4}$ |
$3$ |
$129.299397741$ |
$177.67144160457048$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$74680.5019635$ |
$1$ |
$89$ |
| 5.1.45739093689.1 |
$x^{5} - 2 x^{4} + 55 x^{3} - 289 x^{2} + 1820 x - 1801$ |
$5$ |
(1, 2) |
$3^{6}\cdot 89^{4}$ |
$2$ |
$135.536888373$ |
$271.7905206764879$ |
|
|
|
$A_5$ (as 5T4) |
trivial |
trivial |
$2$ |
$2$ |
$8574.90173713$ |
$1$ |
$89$ |
| 5.1.45739093689.2 |
$x^{5} - 2 x^{4} + 55 x^{3} - 111 x^{2} + 663 x - 822$ |
$5$ |
(1, 2) |
$3^{6}\cdot 89^{4}$ |
$2$ |
$135.536888373$ |
$271.7905206764879$ |
|
|
? |
$A_5$ (as 5T4) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$5363.8532594$ |
$1$ |
$89$ |
| 5.3.49189916944.1 |
$x^{5} - x^{4} + 36 x^{3} + 64 x^{2} - 309 x + 169$ |
$5$ |
(3, 1) |
$-\,2^{4}\cdot 7^{2}\cdot 89^{4}$ |
$3$ |
$137.522962045$ |
$241.78778285085878$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$28012.2112666$ |
$3$ |
$89$ |
| 5.1.60295293601.1 |
$x^{5} - 89 x^{3} - 890 x^{2} - 4272 x - 9167$ |
$5$ |
(1, 2) |
$31^{2}\cdot 89^{4}$ |
$2$ |
$143.237483646$ |
$201.926283580712$ |
|
|
? |
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$3657.26537035$ |
$1$ |
$89$ |
| 5.1.62742241000.1 |
$x^{5} - 445 x - 2492$ |
$5$ |
(1, 2) |
$2^{3}\cdot 5^{3}\cdot 89^{4}$ |
$3$ |
$144.381651554$ |
$342.99240393245833$ |
|
|
|
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$49217.7800758$ |
$1$ |
$89$ |
| 5.5.76859245225.1 |
$x^{5} - x^{4} - 142 x^{3} - 25 x^{2} + 4497 x + 9247$ |
$5$ |
(5, 0) |
$5^{2}\cdot 7^{2}\cdot 89^{4}$ |
$3$ |
$150.362390996$ |
$388.052692873978$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
$[2]$ |
$2$ |
$4$ |
$7260.17033692$ |
$4$ |
$89$ |
| 5.1.76859245225.1 |
$x^{5} - 2 x^{4} - 34 x^{3} + 67 x^{2} + 574 x - 644$ |
$5$ |
(1, 2) |
$5^{2}\cdot 7^{2}\cdot 89^{4}$ |
$3$ |
$150.362390996$ |
$214.5586497775356$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$15143.365249$ |
$1$ |
$89$ |
| 5.1.81313944336.1 |
$x^{5} - x^{4} + 36 x^{3} - 648 x^{2} - 1377 x - 8019$ |
$5$ |
(1, 2) |
$2^{4}\cdot 3^{4}\cdot 89^{4}$ |
$3$ |
$152.066309308$ |
$313.8366605515177$ |
|
|
? |
$A_5$ (as 5T4) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$9690.617247716658$ |
$1$ |
$89$ |
| 5.1.81313944336.2 |
$x^{5} - x^{4} + 36 x^{3} + 64 x^{2} + 47 x + 2661$ |
$5$ |
(1, 2) |
$2^{4}\cdot 3^{4}\cdot 89^{4}$ |
$3$ |
$152.066309308$ |
$313.8366605515177$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
trivial |
$2$ |
$2$ |
$26822.045176103988$ |
$1$ |
$89$ |
| 5.3.83509922771.1 |
$x^{5} - 2 x^{4} - 34 x^{3} - 912 x^{2} + 4668 x + 12083$ |
$5$ |
(3, 1) |
$-\,11^{3}\cdot 89^{4}$ |
$2$ |
$152.878923657$ |
$219.05668904021792$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$12496.9101719$ |
$3$ |
$89$ |
| 5.1.105469707121.1 |
$x^{5} - x^{4} + 36 x^{3} + 153 x^{2} - 2178 x - 15584$ |
$5$ |
(1, 2) |
$41^{2}\cdot 89^{4}$ |
$2$ |
$160.186365611$ |
$232.22230617410713$ |
|
|
? |
$A_5$ (as 5T4) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$3491.79726141$ |
$1$ |
$89$ |
| 5.1.105469707121.2 |
$x^{5} - 2 x^{4} - 34 x^{3} + 601 x^{2} + 1642 x - 9188$ |
$5$ |
(1, 2) |
$41^{2}\cdot 89^{4}$ |
$2$ |
$160.186365611$ |
$232.22230617410713$ |
|
|
|
$A_5$ (as 5T4) |
$[6]$ |
$[6]$ |
$2$ |
$2$ |
$1906.29978872$ |
$1$ |
$89$ |
| 5.1.116010403609.1 |
$x^{5} - x^{4} - 142 x^{3} + 420 x^{2} + 12240 x + 32832$ |
$5$ |
(1, 2) |
$43^{2}\cdot 89^{4}$ |
$2$ |
$163.267366464$ |
$237.8188272228279$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$14880.3950339$ |
$1$ |
$89$ |
| 5.1.125484482000.1 |
$x^{5} - 1424$ |
$5$ |
(1, 2) |
$2^{4}\cdot 5^{3}\cdot 89^{4}$ |
$3$ |
$165.850965631$ |
$211.1365909605945$ |
|
|
? |
$F_5$ (as 5T3) |
$[5]$ |
$[5]$ |
$2$ |
$2$ |
$2059.02215612$ |
$1$ |
$89$ |
| 5.1.127053038025.1 |
$x^{5} - x^{4} - 53 x^{3} - 203 x^{2} - 220 x - 365$ |
$5$ |
(1, 2) |
$3^{4}\cdot 5^{2}\cdot 89^{4}$ |
$3$ |
$166.263535322$ |
$292.1719178513722$ |
|
|
? |
$A_5$ (as 5T4) |
$[5]$ |
$[5]$ |
$2$ |
$2$ |
$2091.37122472$ |
$1$ |
$89$ |
| 5.1.128496109568.1 |
$x^{5} - x^{4} + 36 x^{3} + 420 x^{2} + 1916 x + 1860$ |
$5$ |
(1, 2) |
$2^{11}\cdot 89^{4}$ |
$2$ |
$166.639516089$ |
$243.97453188513757$ |
|
|
? |
$F_5$ (as 5T3) |
$[55]$ |
$[55]$ |
$2$ |
$2$ |
$320.754277527$ |
$1$ |
$89$ |
| 5.1.128496109568.2 |
$x^{5} - x^{4} - 142 x^{3} - 114 x^{2} + 6811 x + 23309$ |
$5$ |
(1, 2) |
$2^{11}\cdot 89^{4}$ |
$2$ |
$166.639516089$ |
$243.97453188513757$ |
|
|
? |
$F_5$ (as 5T3) |
$[5]$ |
$[5]$ |
$2$ |
$2$ |
$3794.65792915$ |
$1$ |
$89$ |
| 5.1.160620136960.1 |
$x^{5} - 2 x^{4} - 34 x^{3} + 156 x^{2} - 227 x + 246$ |
$5$ |
(1, 2) |
$2^{9}\cdot 5\cdot 89^{4}$ |
$3$ |
$174.244869047$ |
$545.5436380738576$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$45038.0978343$ |
$1$ |
$89$ |
| 5.1.169655019664.1 |
$x^{5} - x^{4} + 36 x^{3} - 114 x^{2} + 136 x + 80$ |
$5$ |
(1, 2) |
$2^{4}\cdot 13^{2}\cdot 89^{4}$ |
$3$ |
$176.162450446$ |
$261.5252808378831$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$45202.7249691$ |
$1$ |
$89$ |
| 5.1.169655019664.2 |
$x^{5} - 2 x^{4} + 55 x^{3} - 22 x^{2} - 1295 x + 2738$ |
$5$ |
(1, 2) |
$2^{4}\cdot 13^{2}\cdot 89^{4}$ |
$3$ |
$176.162450446$ |
$261.5252808378831$ |
|
|
? |
$A_5$ (as 5T4) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$3533.23522494$ |
$1$ |
$89$ |
| 5.5.176242954969.1 |
$x^{5} - 2 x^{4} - 123 x^{3} + 245 x^{2} + 3333 x - 9722$ |
$5$ |
(5, 0) |
$53^{2}\cdot 89^{4}$ |
$2$ |
$177.509807553$ |
$511.71630080908557$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
trivial |
$2$ |
$4$ |
$96777.0647339$ |
$5$ |
$89$ |
| 5.3.181199592008.1 |
$x^{5} - 2 x^{4} - 34 x^{3} + 156 x^{2} + 40 x - 288$ |
$5$ |
(3, 1) |
$-\,2^{3}\cdot 19^{2}\cdot 89^{4}$ |
$3$ |
$178.497214452$ |
$447.1299893301274$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
$[2]$ |
$2$ |
$3$ |
$57240.5914463$ |
$2$ |
$89$ |
| 5.3.182956374756.1 |
$x^{5} - x^{4} - 53 x^{3} - 203 x^{2} - 220 x + 436$ |
$5$ |
(3, 1) |
$-\,2^{2}\cdot 3^{6}\cdot 89^{4}$ |
$3$ |
$178.84199641$ |
$543.5810413529758$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$34146.7208436$ |
$3$ |
$89$ |
| 5.3.182956374756.2 |
$x^{5} - 890 x^{2} + 3471 x - 534$ |
$5$ |
(3, 1) |
$-\,2^{2}\cdot 3^{6}\cdot 89^{4}$ |
$3$ |
$178.84199641$ |
$543.5810413529758$ |
|
|
|
$S_5$ (as 5T5) |
trivial |
$[2]$ |
$2$ |
$3$ |
$206887.8367865503$ |
$2$ |
$89$ |
| 5.1.182956374756.1 |
$x^{5} - x^{4} - 53 x^{3} - 381 x^{2} + 1560 x - 1344$ |
$5$ |
(1, 2) |
$2^{2}\cdot 3^{6}\cdot 89^{4}$ |
$3$ |
$178.84199641$ |
$431.44055843684157$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
trivial |
$2$ |
$2$ |
$22432.379268321984$ |
$1$ |
$89$ |
| 5.1.182956374756.2 |
$x^{5} - 2 x^{4} + 55 x^{3} + 423 x^{2} + 396 x - 1089$ |
$5$ |
(1, 2) |
$2^{2}\cdot 3^{6}\cdot 89^{4}$ |
$3$ |
$178.84199641$ |
$431.44055843684157$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
trivial |
$2$ |
$2$ |
$35613.12804227656$ |
$1$ |
$89$ |
