| 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 $p$ |
| 5.3.2823163220.1 |
$x^{5} - 2 x^{4} - 42 x^{3} + 213 x^{2} - 326 x + 122$ |
$5$ |
(3, 1) |
$-\,2^{2}\cdot 5\cdot 109^{4}$ |
$3$ |
$77.6510258331$ |
$190.74633236974816$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$4632.52298011$ |
$3$ |
$109$ |
| 5.3.3811270347.1 |
$x^{5} - 2 x^{4} - 42 x^{3} - 5 x^{2} + x - 96$ |
$5$ |
(3, 1) |
$-\,3^{3}\cdot 109^{4}$ |
$2$ |
$82.4544219103$ |
$153.66772516230674$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$7372.5916395$ |
$3$ |
$109$ |
| 5.1.4093586669.1 |
$x^{5} - 2 x^{4} - 42 x^{3} + 104 x^{2} + 437 x - 1513$ |
$5$ |
(1, 2) |
$29\cdot 109^{4}$ |
$2$ |
$83.6413045617$ |
$229.68900017880728$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$1198.0078750669131$ |
$1$ |
$109$ |
| 5.1.9034122304.1 |
$x^{5} - 2 x^{4} - 42 x^{3} - 332 x^{2} - 871 x - 1186$ |
$5$ |
(1, 2) |
$2^{6}\cdot 109^{4}$ |
$2$ |
$97.9889701117$ |
$120.63857312238144$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$7653.37856458$ |
$1$ |
$109$ |
| 5.1.11292652880.1 |
$x^{5} - 2 x^{4} - 42 x^{3} + 104 x^{2} + 546 x - 1622$ |
$5$ |
(1, 2) |
$2^{4}\cdot 5\cdot 109^{4}$ |
$3$ |
$102.461142866$ |
$166.054327091154$ |
|
|
? |
$S_5$ (as 5T5) |
$[10]$ |
$[10]$ |
$2$ |
$2$ |
$249.478412518$ |
$1$ |
$109$ |
| 5.1.11433811041.1 |
$x^{5} - x^{4} - 65 x^{3} + 122 x^{2} + 1819 x - 1747$ |
$5$ |
(1, 2) |
$3^{4}\cdot 109^{4}$ |
$2$ |
$102.716024482$ |
$153.66772516230674$ |
|
|
? |
$A_5$ (as 5T4) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$1469.68938961$ |
$1$ |
$109$ |
| 5.1.12563076329.1 |
$x^{5} - 2 x^{4} - 42 x^{3} + 104 x^{2} + x - 4238$ |
$5$ |
(1, 2) |
$89\cdot 109^{4}$ |
$2$ |
$104.669271066$ |
$402.3798289435884$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$5293.015401876733$ |
$1$ |
$109$ |
| 5.1.17080137481.1 |
$x^{5} - 2 x^{4} + 67 x^{3} - 550 x^{2} + 1309 x - 968$ |
$5$ |
(1, 2) |
$11^{2}\cdot 109^{4}$ |
$2$ |
$111.300796535$ |
$141.4612661539573$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$4357.49182489$ |
$1$ |
$109$ |
| 5.1.17080137481.2 |
$x^{5} - 2 x^{4} + 67 x^{3} - 223 x^{2} + 1309 x - 5764$ |
$5$ |
(1, 2) |
$11^{2}\cdot 109^{4}$ |
$2$ |
$111.300796535$ |
$141.4612661539573$ |
|
|
? |
$A_5$ (as 5T4) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$1346.1647562990174$ |
$1$ |
$109$ |
| 5.1.17644770125.1 |
$x^{5} - x^{4} + 44 x^{3} - 96 x^{2} + 184 x - 112$ |
$5$ |
(1, 2) |
$5^{3}\cdot 109^{4}$ |
$2$ |
$112.027127663$ |
$142.61614781576037$ |
|
|
? |
$F_5$ (as 5T3) |
trivial |
trivial |
$2$ |
$2$ |
$3580.95062786$ |
$1$ |
$109$ |
| 5.1.25973101624.1 |
$x^{5} - 2 x^{4} - 42 x^{3} - 332 x^{2} - 871 x - 4674$ |
$5$ |
(1, 2) |
$2^{3}\cdot 23\cdot 109^{4}$ |
$3$ |
$121.03326889$ |
$578.5622719077835$ |
|
|
|
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$45448.1225429$ |
$1$ |
$109$ |
| 5.1.26678892429.1 |
$x^{5} - 327 x^{2} + 327 x - 981$ |
$5$ |
(1, 2) |
$3^{3}\cdot 7\cdot 109^{4}$ |
$3$ |
$121.68402291$ |
$257.23565153485083$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$6078.86978024$ |
$1$ |
$109$ |
| 5.3.27102366912.1 |
$x^{5} - 218 x - 436$ |
$5$ |
(3, 1) |
$-\,2^{6}\cdot 3\cdot 109^{4}$ |
$3$ |
$122.067891809$ |
$208.95213800057783$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$16364.0488925$ |
$3$ |
$109$ |
| 5.3.27102366912.2 |
$x^{5} - 2 x^{4} - 42 x^{3} - 332 x^{2} - 108 x + 12984$ |
$5$ |
(3, 1) |
$-\,2^{6}\cdot 3\cdot 109^{4}$ |
$3$ |
$122.067891809$ |
$208.95213800057783$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
$[2]$ |
$2$ |
$3$ |
$13319.1054968$ |
$2$ |
$109$ |
| 5.1.45170611520.1 |
$x^{5} - 2 x^{4} - 42 x^{3} + 104 x^{2} + x + 2738$ |
$5$ |
(1, 2) |
$2^{6}\cdot 5\cdot 109^{4}$ |
$3$ |
$135.198288559$ |
$269.756050210224$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$14920.6531586$ |
$1$ |
$109$ |
| 5.3.45735244164.1 |
$x^{5} - x^{4} - 65 x^{3} + 13 x^{2} + 620 x - 1856$ |
$5$ |
(3, 1) |
$-\,2^{2}\cdot 3^{4}\cdot 109^{4}$ |
$3$ |
$135.534606867$ |
$205.43204896355897$ |
|
|
|
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$72794.9476836$ |
$3$ |
$109$ |
| 5.1.50958096121.1 |
$x^{5} + 109 x^{3} - 218 x^{2} + 1635 x - 6758$ |
$5$ |
(1, 2) |
$19^{2}\cdot 109^{4}$ |
$2$ |
$138.497724716$ |
$185.91652736345125$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$10948.8854903$ |
$1$ |
$109$ |
| 5.5.62250749001.1 |
$x^{5} - 2 x^{4} - 42 x^{3} - 5 x^{2} + 328 x + 231$ |
$5$ |
(5, 0) |
$3^{2}\cdot 7^{2}\cdot 109^{4}$ |
$3$ |
$144.154736384$ |
$270.3339057306049$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
$[2]$ |
$2$ |
$4$ |
$10388.7937125$ |
$4$ |
$109$ |
| 5.1.74672667169.1 |
$x^{5} - 2 x^{4} - 42 x^{3} - 5 x^{2} + 546 x + 1321$ |
$5$ |
(1, 2) |
$23^{2}\cdot 109^{4}$ |
$2$ |
$149.49695013$ |
$204.55265290234445$ |
|
|
? |
$A_5$ (as 5T4) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$700.20276943$ |
$1$ |
$109$ |
| 5.1.74672667169.2 |
$x^{5} - 2 x^{4} + 67 x^{3} - 877 x^{2} + 1309 x - 1949$ |
$5$ |
(1, 2) |
$23^{2}\cdot 109^{4}$ |
$2$ |
$149.49695013$ |
$204.55265290234445$ |
|
|
? |
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$3408.7646165255633$ |
$1$ |
$109$ |
| 5.1.81307100736.1 |
$x^{5} - 2 x^{4} - 42 x^{3} - 332 x^{2} - 326 x - 96$ |
$5$ |
(1, 2) |
$2^{6}\cdot 3^{2}\cdot 109^{4}$ |
$3$ |
$152.06374956$ |
$208.95213800057783$ |
|
|
? |
$A_5$ (as 5T4) |
$[15]$ |
$[15]$ |
$2$ |
$2$ |
$1352.05256483$ |
$1$ |
$109$ |
| 5.1.81307100736.2 |
$x^{5} - 2 x^{4} - 42 x^{3} + 104 x^{2} + 546 x + 776$ |
$5$ |
(1, 2) |
$2^{6}\cdot 3^{2}\cdot 109^{4}$ |
$3$ |
$152.06374956$ |
$208.95213800057783$ |
|
|
? |
$A_5$ (as 5T4) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$3417.08879557$ |
$1$ |
$109$ |
| 5.1.102904299369.1 |
$x^{5} - x^{4} - 65 x^{3} + 13 x^{2} + 1274 x - 3491$ |
$5$ |
(1, 2) |
$3^{6}\cdot 109^{4}$ |
$2$ |
$159.399407962$ |
$319.64174923530027$ |
|
|
? |
$A_5$ (as 5T4) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$2796.23234995$ |
$1$ |
$109$ |
| 5.1.102904299369.2 |
$x^{5} - x^{4} - 65 x^{3} - 96 x^{2} + 1383 x + 3594$ |
$5$ |
(1, 2) |
$3^{6}\cdot 109^{4}$ |
$2$ |
$159.399407962$ |
$319.64174923530027$ |
|
|
? |
$A_5$ (as 5T4) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$10764.0246229$ |
$1$ |
$109$ |
| 5.1.102904299369.3 |
$x^{5} - 2 x^{4} + 67 x^{3} + 1303 x^{2} + 5560 x + 7207$ |
$5$ |
(1, 2) |
$3^{6}\cdot 109^{4}$ |
$2$ |
$159.399407962$ |
$319.64174923530027$ |
|
|
|
$A_5$ (as 5T4) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$10459.368598659355$ |
$1$ |
$109$ |
| 5.3.182940976656.1 |
$x^{5} - x^{4} - 65 x^{3} + 13 x^{2} + 620 x + 2068$ |
$5$ |
(3, 1) |
$-\,2^{4}\cdot 3^{4}\cdot 109^{4}$ |
$3$ |
$178.838985944$ |
$258.8281628122222$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$33693.964964$ |
$3$ |
$109$ |
| 5.5.237286868641.1 |
$x^{5} - 2 x^{4} - 260 x^{3} + 2066 x^{2} - 2397 x - 8816$ |
$5$ |
(5, 0) |
$41^{2}\cdot 109^{4}$ |
$2$ |
$188.388653071$ |
$273.10718553462925$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$4$ |
$442227.23958711216$ |
$5$ |
$109$ |
| 5.5.261001439689.1 |
$x^{5} - 109 x^{3} - 436 x^{2} + 981$ |
$5$ |
(5, 0) |
$43^{2}\cdot 109^{4}$ |
$2$ |
$192.012092547$ |
$279.68902574448185$ |
|
|
? |
$A_5$ (as 5T4) |
$[3]$ |
$[3]$ |
$2$ |
$4$ |
$10876.0369433$ |
$5$ |
$109$ |
| 5.3.282316322000.1 |
$x^{5} - 2 x^{4} + 67 x^{3} - 332 x^{2} + 437 x - 96$ |
$5$ |
(3, 1) |
$-\,2^{4}\cdot 5^{3}\cdot 109^{4}$ |
$3$ |
$195.050558183$ |
$403.3793809089088$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$77597.4662434$ |
$3$ |
$109$ |
| 5.1.282316322000.1 |
$x^{5} - x^{4} + 44 x^{3} - 96 x^{2} + 184 x - 1202$ |
$5$ |
(1, 2) |
$2^{4}\cdot 5^{3}\cdot 109^{4}$ |
$3$ |
$195.050558183$ |
$320.16242679854145$ |
|
|
? |
$S_5$ (as 5T5) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$9301.02982251$ |
$1$ |
$109$ |
| 5.1.282316322000.2 |
$x^{5} - 218$ |
$5$ |
(1, 2) |
$2^{4}\cdot 5^{3}\cdot 109^{4}$ |
$3$ |
$195.050558183$ |
$248.30913563226702$ |
|
|
? |
$F_5$ (as 5T3) |
$[10]$ |
$[10]$ |
$2$ |
$2$ |
$1632.63718653$ |
$1$ |
$109$ |
| 5.1.411617197476.1 |
$x^{5} - x^{4} - 65 x^{3} + 13 x^{2} + 1274 x - 548$ |
$5$ |
(1, 2) |
$2^{2}\cdot 3^{6}\cdot 109^{4}$ |
$3$ |
$210.328779779$ |
$507.39964898907107$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
trivial |
$2$ |
$2$ |
$25746.54406$ |
$1$ |
$109$ |
| 5.1.441119253125.1 |
$x^{5} - 109$ |
$5$ |
(1, 2) |
$5^{5}\cdot 109^{4}$ |
$2$ |
$213.260882819$ |
$271.49179151395816$ |
|
|
✓ |
$F_5$ (as 5T3) |
$[5]$ |
$[5]$ |
$2$ |
$2$ |
$5925.08528579$ |
$1$ |
$109$ |
| 5.1.441119253125.2 |
$x^{5} - 545 x^{2} + 8175 x - 38259$ |
$5$ |
(1, 2) |
$5^{5}\cdot 109^{4}$ |
$2$ |
$213.260882819$ |
$271.49179151395816$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$37780.10561972883$ |
$1$ |
$109$ |
| 5.3.442671992896.1 |
$x^{5} - 2 x^{4} - 42 x^{3} + 104 x^{2} - 435 x + 122$ |
$5$ |
(3, 1) |
$-\,2^{6}\cdot 7^{2}\cdot 109^{4}$ |
$3$ |
$213.410807535$ |
$451.3882082532268$ |
|
|
|
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$164863.765524$ |
$3$ |
$109$ |
| 5.1.491371558441.1 |
$x^{5} - 2 x^{4} + 67 x^{3} + 2284 x^{2} + 15479 x + 24538$ |
$5$ |
(1, 2) |
$59^{2}\cdot 109^{4}$ |
$2$ |
$217.912429674$ |
$327.61758465000895$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$14856.117516707358$ |
$1$ |
$109$ |
| 5.1.633658984729.1 |
$x^{5} - 327 x^{2} + 6976 x + 17004$ |
$5$ |
(1, 2) |
$67^{2}\cdot 109^{4}$ |
$2$ |
$229.28261139$ |
$349.12311166250504$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$51449.41939837399$ |
$1$ |
$109$ |
| 5.1.652715336464.1 |
$x^{5} - x^{4} + 44 x^{3} + 122 x^{2} + 184 x - 112$ |
$5$ |
(1, 2) |
$2^{4}\cdot 17^{2}\cdot 109^{4}$ |
$3$ |
$230.645381937$ |
$351.71885826969174$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$143805.836682$ |
$1$ |
$109$ |
| 5.1.711578289601.1 |
$x^{5} - x^{4} + 44 x^{3} + 449 x^{2} - 4503 x + 29318$ |
$5$ |
(1, 2) |
$71^{2}\cdot 109^{4}$ |
$2$ |
$234.662956407$ |
$359.3936278781415$ |
|
|
|
$A_5$ (as 5T4) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$22819.191771593752$ |
$1$ |
$109$ |
| 5.1.815329537936.1 |
$x^{5} - x^{4} + 44 x^{3} - 96 x^{2} + 620 x - 2292$ |
$5$ |
(1, 2) |
$2^{4}\cdot 19^{2}\cdot 109^{4}$ |
$3$ |
$241.138544534$ |
$371.8330547269025$ |
|
|
? |
$A_5$ (as 5T4) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$10184.8594081$ |
$1$ |
$109$ |
| 5.1.880968082801.1 |
$x^{5} - 2 x^{4} - 151 x^{3} - 441 x^{2} + 546 x - 6200$ |
$5$ |
(1, 2) |
$79^{2}\cdot 109^{4}$ |
$2$ |
$244.901832548$ |
$379.10083762030416$ |
|
|
? |
$A_5$ (as 5T4) |
$[15]$ |
$[15]$ |
$2$ |
$2$ |
$1691.1363652751513$ |
$1$ |
$109$ |
| 5.1.903412230400.1 |
$x^{5} + 545 x - 872$ |
$5$ |
(1, 2) |
$2^{8}\cdot 5^{2}\cdot 109^{4}$ |
$3$ |
$246.137164461$ |
$498.8628833831981$ |
|
|
? |
$A_5$ (as 5T4) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$15678.5685484$ |
$1$ |
$109$ |
| 5.3.1044005758756.1 |
$x^{5} - 218 x^{2} + 327 x + 1090$ |
$5$ |
(3, 1) |
$-\,2^{2}\cdot 43^{2}\cdot 109^{4}$ |
$3$ |
$253.36147508$ |
$559.3780514889637$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
$[2]$ |
$2$ |
$3$ |
$150724.089368$ |
$2$ |
$109$ |
| 5.1.1168930731241.1 |
$x^{5} - 2 x^{4} - 42 x^{3} - 5 x^{2} + 1418 x + 1212$ |
$5$ |
(1, 2) |
$7^{2}\cdot 13^{2}\cdot 109^{4}$ |
$3$ |
$259.153903801$ |
$406.8758324992067$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$67510.2291838$ |
$1$ |
$109$ |
| 5.1.1383491135961.1 |
$x^{5} - 2 x^{4} + 67 x^{3} - 877 x^{2} - 11989 x - 28654$ |
$5$ |
(1, 2) |
$3^{4}\cdot 11^{2}\cdot 109^{4}$ |
$3$ |
$268.037325706$ |
$509.65818675082676$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
trivial |
$2$ |
$2$ |
$96678.84366178898$ |
$1$ |
$109$ |
| 5.1.1383491135961.2 |
$x^{5} - 109 x^{2} + 3924 x + 12099$ |
$5$ |
(1, 2) |
$3^{4}\cdot 11^{2}\cdot 109^{4}$ |
$3$ |
$268.037325706$ |
$509.65818675082676$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
trivial |
$2$ |
$2$ |
$22214.274730838475$ |
$1$ |
$109$ |
| 5.1.1383491135961.3 |
$x^{5} - x^{4} - 65 x^{3} + 994 x^{2} - 3631 x + 18091$ |
$5$ |
(1, 2) |
$3^{4}\cdot 11^{2}\cdot 109^{4}$ |
$3$ |
$268.037325706$ |
$760.0540058578778$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
trivial |
$2$ |
$2$ |
$18871.430059361533$ |
$1$ |
$109$ |
| 5.1.1383491135961.4 |
$x^{5} - 109 x^{3} - 327 x^{2} + 20601 x + 72267$ |
$5$ |
(1, 2) |
$3^{4}\cdot 11^{2}\cdot 109^{4}$ |
$3$ |
$268.037325706$ |
$612.0673509770605$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
trivial |
$2$ |
$2$ |
$44572.600462301765$ |
$1$ |
$109$ |
| 5.1.1429226380125.1 |
$x^{5} - 2943$ |
$5$ |
(1, 2) |
$3^{4}\cdot 5^{3}\cdot 109^{4}$ |
$3$ |
$269.786494259$ |
$343.4517276895542$ |
|
|
? |
$F_5$ (as 5T3) |
$[5]$ |
$[5]$ |
$2$ |
$2$ |
$8488.68138575$ |
$1$ |
$109$ |
| 5.1.1429226380125.2 |
$x^{5} - 545 x^{2} - 1635 x - 1308$ |
$5$ |
(1, 2) |
$3^{4}\cdot 5^{3}\cdot 109^{4}$ |
$3$ |
$269.786494259$ |
$587.5673647942456$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$55162.1290118$ |
$1$ |
$109$ |
