| 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 |
| 5.1.140625.1 |
$x^{5} - 5 x^{2} - 3$ |
$5$ |
(1, 2) |
$3^{2}\cdot 5^{6}$ |
$2$ |
$10.7056368417$ |
$14.035297835467638$ |
|
|
? |
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$8.89638200899$ |
| 5.1.640625.1 |
$x^{5} + 5 x^{3} - 5 x^{2} + 5 x - 2$ |
$5$ |
(1, 2) |
$5^{6}\cdot 41$ |
$2$ |
$14.4984233388$ |
$51.8863276741943$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$35.7098505245$ |
| 5.1.765625.1 |
$x^{5} - 5 x^{2} + 10 x - 4$ |
$5$ |
(1, 2) |
$5^{6}\cdot 7^{2}$ |
$2$ |
$15.0246104687$ |
$21.43927157742677$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$27.2394058796$ |
| 5.1.1000000.1 |
$x^{5} - 5 x - 12$ |
$5$ |
(1, 2) |
$2^{6}\cdot 5^{6}$ |
$2$ |
$15.8489319246$ |
$22.91954538992328$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$77.3368458859$ |
| 5.1.1000000.2 |
$x^{5} + 20 x - 16$ |
$5$ |
(1, 2) |
$2^{6}\cdot 5^{6}$ |
$2$ |
$15.8489319246$ |
$22.91954538992328$ |
|
|
? |
$A_5$ (as 5T4) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$12.8121862985$ |
| 5.3.1937500.1 |
$x^{5} - 5 x^{3} - 5 x^{2} + 10 x - 3$ |
$5$ |
(3, 1) |
$-\,2^{2}\cdot 5^{6}\cdot 31$ |
$3$ |
$18.0904071858$ |
$71.61904346470169$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$68.1075898869$ |
| 5.1.2750000.1 |
$x^{5} - 10 x^{2} - 4$ |
$5$ |
(1, 2) |
$2^{4}\cdot 5^{6}\cdot 11$ |
$3$ |
$19.4028952365$ |
$67.72214039520378$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$79.0116926447$ |
| 5.3.4671875.1 |
$x^{5} - 15 x^{3} - 30 x^{2} - 25 x - 10$ |
$5$ |
(3, 1) |
$-\,5^{6}\cdot 13\cdot 23$ |
$3$ |
$21.5723889925$ |
$140.1188614638235$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$50.1747617933$ |
| 5.3.4750000.1 |
$x^{5} - 10 x^{2} - 25 x - 4$ |
$5$ |
(3, 1) |
$-\,2^{4}\cdot 5^{6}\cdot 19$ |
$3$ |
$21.6440596384$ |
$79.29384320938603$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$115.370477084$ |
| 5.1.4750000.1 |
$x^{5} + 5 x^{3} - 10 x^{2} - 5 x + 12$ |
$5$ |
(1, 2) |
$2^{4}\cdot 5^{6}\cdot 19$ |
$3$ |
$21.6440596384$ |
$99.9039821865691$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$92.7293617873$ |
| 5.3.4937500.1 |
$x^{5} + 5 x^{3} - 30 x^{2} + 30 x - 2$ |
$5$ |
(3, 1) |
$-\,2^{2}\cdot 5^{6}\cdot 79$ |
$3$ |
$21.8122979665$ |
$114.33026629971943$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$76.4404322175$ |
| 5.3.5062500.1 |
$x^{5} - 15 x^{2} - 15 x - 3$ |
$5$ |
(3, 1) |
$-\,2^{2}\cdot 3^{4}\cdot 5^{6}$ |
$3$ |
$21.9216382743$ |
$39.029052225185055$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$95.4676047335$ |
| 5.1.5562500.1 |
$x^{5} + 5 x^{3} - 5 x^{2} - 10 x - 23$ |
$5$ |
(1, 2) |
$2^{2}\cdot 5^{6}\cdot 89$ |
$3$ |
$22.3384998624$ |
$121.35080810038305$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$81.1073390978$ |
| 5.1.5953125.2 |
$x^{5} + 25 x - 25$ |
$5$ |
(1, 2) |
$3\cdot 5^{6}\cdot 127$ |
$3$ |
$22.6437838362$ |
$158.16977377788047$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$41.3694536199$ |
| 5.3.6109375.1 |
$x^{5} - 15 x^{3} - 5 x^{2} + 45 x - 2$ |
$5$ |
(3, 1) |
$-\,5^{6}\cdot 17\cdot 23$ |
$3$ |
$22.761420215$ |
$160.23204825516905$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$173.73891479$ |
| 5.1.6187500.1 |
$x^{5} + 5 x^{3} + 10 x - 12$ |
$5$ |
(1, 2) |
$2^{2}\cdot 3^{2}\cdot 5^{6}\cdot 11$ |
$4$ |
$22.8193380639$ |
$93.0996334822669$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$174.712111914$ |
| 5.1.6625000.1 |
$x^{5} - 5 x^{3} - 5 x^{2} + 50 x - 57$ |
$5$ |
(1, 2) |
$2^{3}\cdot 5^{6}\cdot 53$ |
$3$ |
$23.1332779782$ |
$166.85680905099417$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$202.220362846$ |
| 5.1.7515625.1 |
$x^{5} - 5 x^{2} - 20 x - 16$ |
$5$ |
(1, 2) |
$5^{6}\cdot 13\cdot 37$ |
$3$ |
$23.7242788764$ |
$177.7188702641205$ |
|
|
|
$S_5$ (as 5T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$42.0622214336$ |
| 5.1.7750000.1 |
$x^{5} + 5 x^{3} - 20 x^{2} - 90$ |
$5$ |
(1, 2) |
$2^{4}\cdot 5^{6}\cdot 31$ |
$3$ |
$23.8704353907$ |
$113.68814493682366$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$198.579492505$ |
| 5.1.8062500.2 |
$x^{5} - 15 x^{3} - 5 x^{2} + 50 x + 65$ |
$5$ |
(1, 2) |
$2^{2}\cdot 3\cdot 5^{6}\cdot 43$ |
$4$ |
$24.0599070677$ |
$146.09741258633204$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$137.198379928$ |
| 5.1.8265625.1 |
$x^{5} - 15 x^{2} - 20 x - 12$ |
$5$ |
(1, 2) |
$5^{6}\cdot 23^{2}$ |
$2$ |
$24.1799355871$ |
$38.86197997441929$ |
|
|
|
$D_{5}$ (as 5T2) |
trivial |
trivial |
$2$ |
$2$ |
$130.02582299$ |
| 5.1.8375000.1 |
$x^{5} - 10 x^{3} - 15 x^{2} - 25 x - 45$ |
$5$ |
(1, 2) |
$2^{3}\cdot 5^{6}\cdot 67$ |
$3$ |
$24.2435918083$ |
$187.60456438746493$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$99.92406158$ |
| 5.1.8453125.1 |
$x^{5} + 5 x^{3} - 15 x^{2} + 10 x + 4$ |
$5$ |
(1, 2) |
$5^{6}\cdot 541$ |
$2$ |
$24.2886545577$ |
$188.47755451130234$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$80.0212171793$ |
| 5.1.8687500.1 |
$x^{5} + 10 x^{3} - 15 x^{2} + 10 x - 22$ |
$5$ |
(1, 2) |
$2^{2}\cdot 5^{6}\cdot 139$ |
$3$ |
$24.4218727217$ |
$191.07259479373897$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$132.80737821$ |
| 5.1.8812500.1 |
$x^{5} + 25 x - 50$ |
$5$ |
(1, 2) |
$2^{2}\cdot 3\cdot 5^{6}\cdot 47$ |
$4$ |
$24.4917504671$ |
$152.74156135696145$ |
|
|
|
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$258.163469853$ |
| 5.3.9234375.1 |
$x^{5} - 5 x^{3} - 20 x^{2} + 20 x + 16$ |
$5$ |
(3, 1) |
$-\,3\cdot 5^{6}\cdot 197$ |
$3$ |
$24.7218804184$ |
$196.99479259631627$ |
|
|
|
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$163.179321759$ |
| 5.3.9671875.1 |
$x^{5} - 5 x^{3} - 10 x^{2} - 5 x + 3$ |
$5$ |
(3, 1) |
$-\,5^{6}\cdot 619$ |
$2$ |
$24.9518146111$ |
$201.6073356134352$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
$[2]$ |
$2$ |
$3$ |
$117.967211309$ |
| 5.1.9828125.1 |
$x^{5} - 5 x - 13$ |
$5$ |
(1, 2) |
$5^{6}\cdot 17\cdot 37$ |
$3$ |
$25.0319183932$ |
$203.229303310938$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$46.1056422217$ |
| 5.3.10484375.1 |
$x^{5} - 25 x^{2} - 5 x + 13$ |
$5$ |
(3, 1) |
$-\,5^{6}\cdot 11\cdot 61$ |
$3$ |
$25.3576211596$ |
$209.90474963390704$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$182.145718478$ |
| 5.3.10562500.1 |
$x^{5} + 5 x^{3} - 25 x^{2} - 40 x - 13$ |
$5$ |
(3, 1) |
$-\,2^{2}\cdot 5^{6}\cdot 13^{2}$ |
$3$ |
$25.395299812$ |
$89.60245373417463$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$290.724774175$ |
| 5.1.10562500.1 |
$x^{5} + 5 x^{3} - 10 x^{2} + 20$ |
$5$ |
(1, 2) |
$2^{2}\cdot 5^{6}\cdot 13^{2}$ |
$3$ |
$25.395299812$ |
$46.37878270056908$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
trivial |
$2$ |
$2$ |
$93.2582062928$ |
| 5.1.10765625.1 |
$x^{5} - 5 x^{3} - 5 x^{2} + 25 x - 32$ |
$5$ |
(1, 2) |
$5^{6}\cdot 13\cdot 53$ |
$3$ |
$25.4922312561$ |
$212.70153133171112$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$127.558581299$ |
| 5.3.11187500.1 |
$x^{5} - 5 x^{3} - 20 x^{2} + 32$ |
$5$ |
(3, 1) |
$-\,2^{2}\cdot 5^{6}\cdot 179$ |
$3$ |
$25.6889651555$ |
$172.09735075438294$ |
|
|
|
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$324.005663862$ |
| 5.3.11312500.2 |
$x^{5} - 20 x^{3} - 15 x^{2} + 95 x + 113$ |
$5$ |
(3, 1) |
$-\,2^{2}\cdot 5^{6}\cdot 181$ |
$3$ |
$25.7461158099$ |
$218.03704561314387$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
$[2]$ |
$2$ |
$3$ |
$120.481389705$ |
| 5.1.11500000.1 |
$x^{5} + 5 x^{3} - 20 x^{2} + 20 x - 46$ |
$5$ |
(1, 2) |
$2^{5}\cdot 5^{6}\cdot 23$ |
$3$ |
$25.8309017813$ |
$138.48835257442275$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$125.809677647$ |
| 5.1.11937500.1 |
$x^{5} - 25 x^{2} + 25 x - 25$ |
$5$ |
(1, 2) |
$2^{2}\cdot 5^{6}\cdot 191$ |
$3$ |
$26.024516935$ |
$223.97919783790627$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$92.3181574788$ |
| 5.3.12250000.1 |
$x^{5} - 10 x^{3} - 56$ |
$5$ |
(3, 1) |
$-\,2^{4}\cdot 5^{6}\cdot 7^{2}$ |
$3$ |
$26.1593662137$ |
$74.71933990356241$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$209.038742294$ |
| 5.1.12750000.1 |
$x^{5} + 5 x^{3} - 10 x^{2} - 30$ |
$5$ |
(1, 2) |
$2^{4}\cdot 3\cdot 5^{6}\cdot 17$ |
$4$ |
$26.3695086141$ |
$145.82078143613396$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$174.970020509$ |
| 5.1.12750000.2 |
$x^{5} - 5 x - 16$ |
$5$ |
(1, 2) |
$2^{4}\cdot 3\cdot 5^{6}\cdot 17$ |
$4$ |
$26.3695086141$ |
$163.67829301687632$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$111.409722648$ |
| 5.3.12796875.1 |
$x^{5} - 10 x^{3} + 40 x - 33$ |
$5$ |
(3, 1) |
$-\,3^{2}\cdot 5^{6}\cdot 7\cdot 13$ |
$4$ |
$26.3888695077$ |
$133.88820808814984$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$165.954182482$ |
| 5.1.13500000.2 |
$x^{5} + 5 x^{3} - 20 x^{2} + 30 x + 2$ |
$5$ |
(1, 2) |
$2^{5}\cdot 3^{3}\cdot 5^{6}$ |
$3$ |
$26.672686084$ |
$104.03771253823282$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$354.819938724$ |
| 5.3.13921875.1 |
$x^{5} - 20 x^{2} + 30 x - 9$ |
$5$ |
(3, 1) |
$-\,3^{4}\cdot 5^{6}\cdot 11$ |
$3$ |
$26.8373448048$ |
$116.28374796987914$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
$[2]$ |
$2$ |
$3$ |
$129.695412252$ |
| 5.3.14750000.1 |
$x^{5} - 10 x^{3} - 20 x^{2} + 10 x + 46$ |
$5$ |
(3, 1) |
$-\,2^{4}\cdot 5^{6}\cdot 59$ |
$3$ |
$27.1492854695$ |
$108.37048274935462$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
$[2]$ |
$2$ |
$3$ |
$142.495907636$ |
| 5.1.15015625.1 |
$x^{5} + 5 x^{3} - 10 x^{2} - 1$ |
$5$ |
(1, 2) |
$5^{6}\cdot 31^{2}$ |
$2$ |
$27.2463720568$ |
$45.11717021725675$ |
|
|
✓ |
$A_5$ (as 5T4) |
$[3]$ |
$[3]$ |
$2$ |
$2$ |
$13.6202131364$ |
| 5.1.15250000.1 |
$x^{5} - 10 x^{3} - 20 x^{2} + 65 x + 44$ |
$5$ |
(1, 2) |
$2^{4}\cdot 5^{6}\cdot 61$ |
$3$ |
$27.3309022401$ |
$142.07824527458476$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$130.385427893$ |
| 5.3.16000000.1 |
$x^{5} - 10 x^{3} + 15 x - 8$ |
$5$ |
(3, 1) |
$-\,2^{10}\cdot 5^{6}$ |
$2$ |
$27.5945932292$ |
$54.512172900649155$ |
|
|
✓ |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$3$ |
$230.937164698$ |
| 5.1.16078125.1 |
$x^{5} + 10 x^{3} - 25 x^{2} + 15 x + 6$ |
$5$ |
(1, 2) |
$3\cdot 5^{6}\cdot 7^{3}$ |
$3$ |
$27.6214885953$ |
$71.034609880671$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$184.634692508$ |
| 5.1.16625000.1 |
$x^{5} - 5 x^{3} - 15 x^{2} + 30 x - 14$ |
$5$ |
(1, 2) |
$2^{3}\cdot 5^{6}\cdot 7\cdot 19$ |
$4$ |
$27.8068843604$ |
$264.3210918506887$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$182.057279995$ |
| 5.1.17562500.1 |
$x^{5} + 5 x^{3} - 45 x^{2} + 50 x - 15$ |
$5$ |
(1, 2) |
$2^{2}\cdot 5^{6}\cdot 281$ |
$3$ |
$28.1136521786$ |
$215.6258524576302$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$123.525442925$ |
| 5.1.17750000.1 |
$x^{5} - 10 x^{3} - 30 x^{2} - 15 x - 46$ |
$5$ |
(1, 2) |
$2^{4}\cdot 5^{6}\cdot 71$ |
$3$ |
$28.1734266069$ |
$193.1235221886073$ |
|
|
? |
$S_5$ (as 5T5) |
trivial |
trivial |
$2$ |
$2$ |
$94.6104077035$ |
