| 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 |
| 5.5.14641.1 |
$x^{5} - x^{4} - 4 x^{3} + 3 x^{2} + 3 x - 1$ |
$5$ |
[5,0] |
$11^{4}$ |
$1$ |
$6.80948312752$ |
$6.809483127522301$ |
|
✓ |
✓ |
$C_5$ (as 5T1) |
trivial |
$2$ |
$4$ |
$1.63569412559$ |
| 5.5.390625.1 |
$x^{5} - 10 x^{3} - 5 x^{2} + 10 x - 1$ |
$5$ |
[5,0] |
$5^{8}$ |
$1$ |
$13.132639022$ |
$13.132639022018836$ |
|
✓ |
|
$C_5$ (as 5T1) |
trivial |
$2$ |
$4$ |
$16.0696118231$ |
| 5.5.923521.1 |
$x^{5} - x^{4} - 12 x^{3} + 21 x^{2} + x - 5$ |
$5$ |
[5,0] |
$31^{4}$ |
$1$ |
$15.598734101$ |
$15.59873410095393$ |
|
✓ |
|
$C_5$ (as 5T1) |
trivial |
$2$ |
$4$ |
$30.3695765133$ |
| 5.5.2825761.1 |
$x^{5} - x^{4} - 16 x^{3} - 5 x^{2} + 21 x + 9$ |
$5$ |
[5,0] |
$41^{4}$ |
$1$ |
$19.5086440773$ |
$19.50864407731132$ |
|
✓ |
|
$C_5$ (as 5T1) |
trivial |
$2$ |
$4$ |
$123.329982692$ |
| 5.5.13845841.1 |
$x^{5} - x^{4} - 24 x^{3} + 17 x^{2} + 41 x + 13$ |
$5$ |
[5,0] |
$61^{4}$ |
$1$ |
$26.8079662462$ |
$26.807966246166025$ |
|
✓ |
|
$C_5$ (as 5T1) |
trivial |
$2$ |
$4$ |
$93.7680714453$ |
| 5.5.25411681.1 |
$x^{5} - x^{4} - 28 x^{3} - 37 x^{2} + 25 x - 1$ |
$5$ |
[5,0] |
$71^{4}$ |
$1$ |
$30.2695997909$ |
$30.269599790850265$ |
|
✓ |
|
$C_5$ (as 5T1) |
trivial |
$2$ |
$4$ |
$70.6106756434$ |
| 5.5.104060401.1 |
$x^{5} - x^{4} - 40 x^{3} - 93 x^{2} - 21 x + 17$ |
$5$ |
[5,0] |
$101^{4}$ |
$1$ |
$40.128885573$ |
$40.12888557303687$ |
|
✓ |
|
$C_5$ (as 5T1) |
trivial |
$2$ |
$4$ |
$119.525694644$ |
| 5.5.294499921.1 |
$x^{5} - x^{4} - 52 x^{3} + 89 x^{2} + 109 x - 193$ |
$5$ |
[5,0] |
$131^{4}$ |
$1$ |
$49.4102483206$ |
$49.410248320622195$ |
|
✓ |
|
$C_5$ (as 5T1) |
trivial |
$2$ |
$4$ |
$247.953961572$ |
| 5.5.519885601.1 |
$x^{5} - x^{4} - 60 x^{3} + 12 x^{2} + 784 x - 128$ |
$5$ |
[5,0] |
$151^{4}$ |
$1$ |
$55.3581486897$ |
$55.358148689726$ |
|
✓ |
|
$C_5$ (as 5T1) |
trivial |
$2$ |
$4$ |
$9575.16761977$ |
| 5.5.1073283121.1 |
$x^{5} - x^{4} - 72 x^{3} + 123 x^{2} + 223 x + 49$ |
$5$ |
[5,0] |
$181^{4}$ |
$1$ |
$63.9945308995$ |
$63.99453089948475$ |
|
✓ |
|
$C_5$ (as 5T1) |
trivial |
$2$ |
$4$ |
$1245.95724225$ |
| 5.5.1330863361.1 |
$x^{5} - x^{4} - 76 x^{3} + 359 x^{2} - 437 x + 155$ |
$5$ |
[5,0] |
$191^{4}$ |
$1$ |
$66.8077266614$ |
$66.80772666139775$ |
|
✓ |
|
$C_5$ (as 5T1) |
$[11]$ |
$2$ |
$4$ |
$185.439033921$ |
| 5.5.1982119441.1 |
$x^{5} - x^{4} - 84 x^{3} + 59 x^{2} + 1661 x - 269$ |
$5$ |
[5,0] |
$211^{4}$ |
$1$ |
$72.3479057657$ |
$72.34790576574842$ |
|
✓ |
|
$C_5$ (as 5T1) |
trivial |
$2$ |
$4$ |
$577.507733173$ |
| 5.5.3373402561.1 |
$x^{5} - x^{4} - 96 x^{3} + 212 x^{2} + 1232 x - 512$ |
$5$ |
[5,0] |
$241^{4}$ |
$1$ |
$80.4662262575$ |
$80.4662262574868$ |
|
✓ |
|
$C_5$ (as 5T1) |
trivial |
$2$ |
$4$ |
$30917.0186222$ |
| 5.5.3969126001.1 |
$x^{5} - x^{4} - 100 x^{3} + 20 x^{2} + 1504 x - 1024$ |
$5$ |
[5,0] |
$251^{4}$ |
$1$ |
$83.1264008617$ |
$83.12640086168598$ |
|
✓ |
|
$C_5$ (as 5T1) |
trivial |
$2$ |
$4$ |
$52885.8852389$ |
| 5.5.5393580481.1 |
$x^{5} - x^{4} - 108 x^{3} + 401 x^{2} - 13 x - 845$ |
$5$ |
[5,0] |
$271^{4}$ |
$1$ |
$88.3843622794$ |
$88.38436227941675$ |
|
✓ |
|
$C_5$ (as 5T1) |
trivial |
$2$ |
$4$ |
$4098.90045327$ |
| 5.5.5719140625.1 |
$x^{5} - 110 x^{3} - 605 x^{2} - 990 x - 451$ |
$5$ |
[5,0] |
$5^{8}\cdot 11^{4}$ |
$2$ |
$89.4264838403$ |
$89.42648384027824$ |
|
✓ |
|
$C_5$ (as 5T1) |
$[5]$ |
$2$ |
$4$ |
$272.480237494$ |
| 5.5.5719140625.2 |
$x^{5} - 110 x^{3} - 495 x^{2} - 440 x - 99$ |
$5$ |
[5,0] |
$5^{8}\cdot 11^{4}$ |
$2$ |
$89.4264838403$ |
$89.42648384027824$ |
|
✓ |
|
$C_5$ (as 5T1) |
$[5]$ |
$2$ |
$4$ |
$2302.76208389$ |
| 5.5.5719140625.3 |
$x^{5} - 110 x^{3} - 55 x^{2} + 660 x + 649$ |
$5$ |
[5,0] |
$5^{8}\cdot 11^{4}$ |
$2$ |
$89.4264838403$ |
$89.42648384027824$ |
|
✓ |
|
$C_5$ (as 5T1) |
$[5]$ |
$2$ |
$4$ |
$382.646168029$ |
| 5.5.5719140625.4 |
$x^{5} - 110 x^{3} - 220 x^{2} + 1485 x + 1276$ |
$5$ |
[5,0] |
$5^{8}\cdot 11^{4}$ |
$2$ |
$89.4264838403$ |
$89.42648384027824$ |
|
✓ |
|
$C_5$ (as 5T1) |
$[5]$ |
$2$ |
$4$ |
$8475.85345405$ |
| 5.5.6234839521.1 |
$x^{5} - x^{4} - 112 x^{3} + 191 x^{2} + 2257 x - 967$ |
$5$ |
[5,0] |
$281^{4}$ |
$1$ |
$90.9840062401$ |
$90.9840062401245$ |
|
✓ |
|
$C_5$ (as 5T1) |
trivial |
$2$ |
$4$ |
$1165.65240048$ |
| 5.5.9354951841.1 |
$x^{5} - x^{4} - 124 x^{3} - 535 x^{2} - 413 x + 539$ |
$5$ |
[5,0] |
$311^{4}$ |
$1$ |
$98.6752672315$ |
$98.67526723145183$ |
|
✓ |
|
$C_5$ (as 5T1) |
trivial |
$2$ |
$4$ |
$5087.72088405$ |
| 5.5.12003612721.1 |
$x^{5} - x^{4} - 132 x^{3} + 887 x^{2} - 1843 x + 1027$ |
$5$ |
[5,0] |
$331^{4}$ |
$1$ |
$103.719972995$ |
$103.7199729945502$ |
|
✓ |
|
$C_5$ (as 5T1) |
trivial |
$2$ |
$4$ |
$2582.67345578$ |
| 5.5.13521270961.1 |
$x^{5} - x^{4} - 136 x^{3} + 300 x^{2} + 2016 x - 3136$ |
$5$ |
[5,0] |
$11^{4}\cdot 31^{4}$ |
$2$ |
$106.219316671$ |
$106.21931667115254$ |
|
✓ |
|
$C_5$ (as 5T1) |
$[5]$ |
$2$ |
$4$ |
$15927.8863443$ |
| 5.5.13521270961.2 |
$x^{5} - x^{4} - 136 x^{3} - 41 x^{2} + 3039 x - 1431$ |
$5$ |
[5,0] |
$11^{4}\cdot 31^{4}$ |
$2$ |
$106.219316671$ |
$106.21931667115254$ |
|
✓ |
|
$C_5$ (as 5T1) |
$[5]$ |
$2$ |
$4$ |
$2564.52443732$ |
| 5.5.13521270961.3 |
$x^{5} - x^{4} - 136 x^{3} - 723 x^{2} - 1053 x - 67$ |
$5$ |
[5,0] |
$11^{4}\cdot 31^{4}$ |
$2$ |
$106.219316671$ |
$106.21931667115254$ |
|
✓ |
|
$C_5$ (as 5T1) |
$[5]$ |
$2$ |
$4$ |
$489.762552216$ |
| 5.5.13521270961.4 |
$x^{5} - x^{4} - 136 x^{3} + 641 x^{2} - 371 x - 67$ |
$5$ |
[5,0] |
$11^{4}\cdot 31^{4}$ |
$2$ |
$106.219316671$ |
$106.21931667115254$ |
|
✓ |
|
$C_5$ (as 5T1) |
$[5]$ |
$2$ |
$4$ |
$383.707630684$ |
| 5.5.25856961601.1 |
$x^{5} - x^{4} - 160 x^{3} - 369 x^{2} + 879 x + 29$ |
$5$ |
[5,0] |
$401^{4}$ |
$1$ |
$120.924833503$ |
$120.92483350286062$ |
|
✓ |
|
$C_5$ (as 5T1) |
trivial |
$2$ |
$4$ |
$1555.36216125$ |
| 5.5.31414372081.1 |
$x^{5} - x^{4} - 168 x^{3} - 219 x^{2} + 3853 x + 3517$ |
$5$ |
[5,0] |
$421^{4}$ |
$1$ |
$125.726167348$ |
$125.72616734794764$ |
|
✓ |
|
$C_5$ (as 5T1) |
trivial |
$2$ |
$4$ |
$1697.49706573$ |
| 5.5.34507149121.1 |
$x^{5} - x^{4} - 172 x^{3} + 724 x^{2} + 1824 x - 1728$ |
$5$ |
[5,0] |
$431^{4}$ |
$1$ |
$128.109641576$ |
$128.10964157622095$ |
|
✓ |
|
$C_5$ (as 5T1) |
trivial |
$2$ |
$4$ |
$391579.04227$ |
| 5.5.41371966801.1 |
$x^{5} - x^{4} - 180 x^{3} + 1389 x^{2} - 3341 x + 2551$ |
$5$ |
[5,0] |
$11^{4}\cdot 41^{4}$ |
$2$ |
$132.843782685$ |
$132.8437826852893$ |
|
✓ |
|
$C_5$ (as 5T1) |
$[5]$ |
$2$ |
$4$ |
$358.821278588$ |
| 5.5.41371966801.2 |
$x^{5} - x^{4} - 180 x^{3} - 415 x^{2} + 1169 x + 2551$ |
$5$ |
[5,0] |
$11^{4}\cdot 41^{4}$ |
$2$ |
$132.843782685$ |
$132.8437826852893$ |
|
✓ |
|
$C_5$ (as 5T1) |
$[5]$ |
$2$ |
$4$ |
$2009.77128675$ |
| 5.5.41371966801.3 |
$x^{5} - x^{4} - 180 x^{3} - 415 x^{2} + 3875 x + 2551$ |
$5$ |
[5,0] |
$11^{4}\cdot 41^{4}$ |
$2$ |
$132.843782685$ |
$132.8437826852893$ |
|
✓ |
|
$C_5$ (as 5T1) |
$[5]$ |
$2$ |
$4$ |
$1485.1344106$ |
| 5.5.41371966801.4 |
$x^{5} - x^{4} - 180 x^{3} + 36 x^{2} + 3424 x + 3904$ |
$5$ |
[5,0] |
$11^{4}\cdot 41^{4}$ |
$2$ |
$132.843782685$ |
$132.8437826852893$ |
|
✓ |
|
$C_5$ (as 5T1) |
$[5]$ |
$2$ |
$4$ |
$23210.5470603$ |
| 5.5.45165175441.1 |
$x^{5} - x^{4} - 184 x^{3} + 129 x^{2} + 4551 x - 5419$ |
$5$ |
[5,0] |
$461^{4}$ |
$1$ |
$135.195034302$ |
$135.1950343017928$ |
|
✓ |
|
$C_5$ (as 5T1) |
trivial |
$2$ |
$4$ |
$4946.7233313$ |
| 5.5.58120048561.1 |
$x^{5} - x^{4} - 196 x^{3} - 59 x^{2} + 2019 x - 1377$ |
$5$ |
[5,0] |
$491^{4}$ |
$1$ |
$142.188736054$ |
$142.18873605415627$ |
|
✓ |
|
$C_5$ (as 5T1) |
trivial |
$2$ |
$4$ |
$28434.7104177$ |
| 5.5.73680216481.1 |
$x^{5} - x^{4} - 208 x^{3} + 771 x^{2} + 4143 x - 2083$ |
$5$ |
[5,0] |
$521^{4}$ |
$1$ |
$149.097437236$ |
$149.09743723635626$ |
|
✓ |
|
$C_5$ (as 5T1) |
trivial |
$2$ |
$4$ |
$3171.44786999$ |
| 5.5.85662167761.1 |
$x^{5} - x^{4} - 216 x^{3} - 1147 x^{2} - 805 x + 2629$ |
$5$ |
[5,0] |
$541^{4}$ |
$1$ |
$153.658932626$ |
$153.65893262567562$ |
|
✓ |
|
$C_5$ (as 5T1) |
trivial |
$2$ |
$4$ |
$5591.83636552$ |
| 5.5.106302733681.1 |
$x^{5} - x^{4} - 228 x^{3} - 868 x^{2} + 3056 x + 7552$ |
$5$ |
[5,0] |
$571^{4}$ |
$1$ |
$160.438608482$ |
$160.43860848150953$ |
|
✓ |
|
$C_5$ (as 5T1) |
trivial |
$2$ |
$4$ |
$148439.26957$ |
| 5.5.130466162401.1 |
$x^{5} - x^{4} - 240 x^{3} - 1755 x^{2} - 3731 x - 2399$ |
$5$ |
[5,0] |
$601^{4}$ |
$1$ |
$167.147381576$ |
$167.14738157598725$ |
|
✓ |
|
$C_5$ (as 5T1) |
trivial |
$2$ |
$4$ |
$23153.4060852$ |
| 5.5.158532181921.1 |
$x^{5} - x^{4} - 252 x^{3} - 2095 x^{2} - 5785 x - 5069$ |
$5$ |
[5,0] |
$631^{4}$ |
$1$ |
$173.789481456$ |
$173.78948145596087$ |
|
✓ |
|
$C_5$ (as 5T1) |
$[11]$ |
$2$ |
$4$ |
$478.383345376$ |
| 5.5.168823196161.1 |
$x^{5} - x^{4} - 256 x^{3} + 564 x^{2} + 5328 x + 5120$ |
$5$ |
[5,0] |
$641^{4}$ |
$1$ |
$175.989364729$ |
$175.98936472906092$ |
|
✓ |
|
$C_5$ (as 5T1) |
$[11]$ |
$2$ |
$4$ |
$39805.8132601$ |
| 5.5.190899960241.1 |
$x^{5} - x^{4} - 264 x^{3} + 185 x^{2} + 16837 x - 4851$ |
$5$ |
[5,0] |
$661^{4}$ |
$1$ |
$180.368696867$ |
$180.36869686739456$ |
|
✓ |
|
$C_5$ (as 5T1) |
trivial |
$2$ |
$4$ |
$107708.333686$ |
| 5.5.202716958081.1 |
$x^{5} - x^{4} - 268 x^{3} - 1020 x^{2} + 4128 x - 1024$ |
$5$ |
[5,0] |
$11^{4}\cdot 61^{4}$ |
$2$ |
$182.548393836$ |
$182.5483938364549$ |
|
✓ |
|
$C_5$ (as 5T1) |
$[5]$ |
$2$ |
$4$ |
$25011.6652454$ |
| 5.5.202716958081.2 |
$x^{5} - x^{4} - 268 x^{3} + 2335 x^{2} - 5937 x + 2331$ |
$5$ |
[5,0] |
$11^{4}\cdot 61^{4}$ |
$2$ |
$182.548393836$ |
$182.5483938364549$ |
|
✓ |
|
$C_5$ (as 5T1) |
$[5]$ |
$2$ |
$4$ |
$19885.4936643$ |
| 5.5.202716958081.3 |
$x^{5} - x^{4} - 268 x^{3} - 349 x^{2} + 3457 x + 5015$ |
$5$ |
[5,0] |
$11^{4}\cdot 61^{4}$ |
$2$ |
$182.548393836$ |
$182.5483938364549$ |
|
✓ |
|
$C_5$ (as 5T1) |
$[5]$ |
$2$ |
$4$ |
$4572.95146181$ |
| 5.5.202716958081.4 |
$x^{5} - x^{4} - 268 x^{3} - 349 x^{2} + 7483 x + 13067$ |
$5$ |
[5,0] |
$11^{4}\cdot 61^{4}$ |
$2$ |
$182.548393836$ |
$182.5483938364549$ |
|
✓ |
|
$C_5$ (as 5T1) |
$[5]$ |
$2$ |
$4$ |
$1293.31076803$ |
| 5.5.227988105361.1 |
$x^{5} - x^{4} - 276 x^{3} + 1299 x^{2} + 5329 x - 15581$ |
$5$ |
[5,0] |
$691^{4}$ |
$1$ |
$186.888439574$ |
$186.88843957442577$ |
|
✓ |
|
$C_5$ (as 5T1) |
trivial |
$2$ |
$4$ |
$11543.7370825$ |
| 5.5.241474942801.1 |
$x^{5} - x^{4} - 280 x^{3} - 2047 x^{2} - 3791 x - 1699$ |
$5$ |
[5,0] |
$701^{4}$ |
$1$ |
$189.049013027$ |
$189.04901302748888$ |
|
✓ |
|
$C_5$ (as 5T1) |
trivial |
$2$ |
$4$ |
$11580.5925324$ |
| 5.5.318097128001.1 |
$x^{5} - x^{4} - 300 x^{3} + 2313 x^{2} - 3761 x + 571$ |
$5$ |
[5,0] |
$751^{4}$ |
$1$ |
$199.761573204$ |
$199.7615732040473$ |
|
✓ |
|
$C_5$ (as 5T1) |
trivial |
$2$ |
$4$ |
$11903.3361639$ |
| 5.5.335381132641.1 |
$x^{5} - x^{4} - 304 x^{3} - 2831 x^{2} - 8925 x - 8775$ |
$5$ |
[5,0] |
$761^{4}$ |
$1$ |
$201.886707538$ |
$201.88670753754164$ |
|
✓ |
|
$C_5$ (as 5T1) |
trivial |
$2$ |
$4$ |
$193371.740026$ |
