| 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 |
| 5.1.18496.1 |
$x^{5} - x^{4} + 2 x^{2} - 2 x + 2$ |
$5$ |
[1,2] |
$2^{6}\cdot 17^{2}$ |
$2$ |
$7.13535464233$ |
$18.700114874768015$ |
|
|
✓ |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$3.02530540001$ |
| 5.1.42849.1 |
$x^{5} - x^{4} + x^{3} + 2 x^{2} + x - 1$ |
$5$ |
[1,2] |
$3^{4}\cdot 23^{2}$ |
$2$ |
$8.44088800813$ |
$29.138018934862163$ |
|
|
✓ |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$3.0578963607$ |
| 5.1.53824.1 |
$x^{5} - 2 x^{3} - 2 x^{2} + 3 x + 2$ |
$5$ |
[1,2] |
$2^{6}\cdot 29^{2}$ |
$2$ |
$8.834768905$ |
$26.697893241960433$ |
|
|
✓ |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$6.23781662192$ |
| 5.1.70225.1 |
$x^{5} - 2 x^{4} - x^{3} + 3 x^{2} - x + 2$ |
$5$ |
[1,2] |
$5^{2}\cdot 53^{2}$ |
$2$ |
$9.31747743326$ |
$31.550209585176834$ |
|
|
✓ |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$7.58244011162$ |
| 5.1.118336.2 |
$x^{5} - 2 x^{4} + 6 x^{3} - 8 x^{2} + 10 x - 8$ |
$5$ |
[1,2] |
$2^{6}\cdot 43^{2}$ |
$2$ |
$10.3424487385$ |
$34.715543100649214$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$10.7716006519$ |
| 5.1.126025.1 |
$x^{5} - x^{4} + 3 x^{3} - 4 x^{2} + 5 x - 1$ |
$5$ |
[1,2] |
$5^{2}\cdot 71^{2}$ |
$2$ |
$10.4734880427$ |
$38.34045254095357$ |
|
|
✓ |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$6.31955282188$ |
| 5.1.129600.1 |
$x^{5} - 2 x^{3} - 4 x^{2} - 6 x - 4$ |
$5$ |
[1,2] |
$2^{6}\cdot 3^{4}\cdot 5^{2}$ |
$3$ |
$10.5322461457$ |
$35.783817426546634$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$13.4888953709$ |
| 5.1.133225.1 |
$x^{5} - 2 x^{4} + x^{2} + 4 x - 5$ |
$5$ |
[1,2] |
$5^{2}\cdot 73^{2}$ |
$2$ |
$10.5905166121$ |
$39.05712235532912$ |
|
|
✓ |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$4.20349723184$ |
| 5.1.144400.1 |
$x^{5} - x^{4} + 3 x^{3} - 3 x^{2} + 5 x - 1$ |
$5$ |
[1,2] |
$2^{4}\cdot 5^{2}\cdot 19^{2}$ |
$3$ |
$10.7625067947$ |
$41.64016092004265$ |
|
|
✓ |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$8.48532720749$ |
| 5.1.149769.1 |
$x^{5} - 2 x^{4} + x^{3} - 5 x^{2} + x - 2$ |
$5$ |
[1,2] |
$3^{4}\cdot 43^{2}$ |
$2$ |
$10.8413754795$ |
$44.220172685887526$ |
|
|
✓ |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$17.0364698806$ |
| 5.1.162409.1 |
$x^{5} + 2 x^{3} - 5 x^{2} + 2 x - 1$ |
$5$ |
[1,2] |
$13^{2}\cdot 31^{2}$ |
$2$ |
$11.0184883917$ |
$35.58056215005226$ |
|
|
✓ |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$2.5379106436$ |
| 5.1.193600.1 |
$x^{5} + 2 x^{3} - 2 x^{2} - x + 2$ |
$5$ |
[1,2] |
$2^{6}\cdot 5^{2}\cdot 11^{2}$ |
$3$ |
$11.4125073593$ |
$27.42971776263377$ |
|
|
✓ |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$13.3372584057$ |
| 5.1.195364.1 |
$x^{5} - 2 x^{4} - 3 x^{3} + 9 x^{2} - 4 x + 1$ |
$5$ |
[1,2] |
$2^{2}\cdot 13^{2}\cdot 17^{2}$ |
$3$ |
$11.4332291456$ |
$37.840565748474845$ |
|
|
✓ |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$11.3766762967$ |
| 5.1.198025.1 |
$x^{5} - x^{4} + 5 x^{3} - x^{2} + 6 x + 1$ |
$5$ |
[1,2] |
$5^{2}\cdot 89^{2}$ |
$2$ |
$11.46420661$ |
$27.585128172099004$ |
|
|
✓ |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$4.11437022031$ |
| 5.1.210681.1 |
$x^{5} - 2 x^{4} + 4 x^{3} - 5 x^{2} + 4 x - 5$ |
$5$ |
[1,2] |
$3^{6}\cdot 17^{2}$ |
$2$ |
$11.6071360306$ |
$49.54748116432225$ |
|
|
✓ |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$9.37085148477$ |
| 5.1.223729.1 |
$x^{5} - 3 x^{3} - 7 x^{2} - 5 x - 3$ |
$5$ |
[1,2] |
$11^{2}\cdot 43^{2}$ |
$2$ |
$11.7474730207$ |
$32.43366434492542$ |
|
|
✓ |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$6.86734566835$ |
| 5.1.243049.1 |
$x^{5} - x^{2} - 2 x - 3$ |
$5$ |
[1,2] |
$17^{2}\cdot 29^{2}$ |
$2$ |
$11.9436967383$ |
$38.918532796896685$ |
|
|
✓ |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$10.7855048337$ |
| 5.1.243049.2 |
$x^{5} - x^{4} + 5 x^{3} - 3 x^{2} + 4 x - 3$ |
$5$ |
[1,2] |
$17^{2}\cdot 29^{2}$ |
$2$ |
$11.9436967383$ |
$35.60395798495597$ |
|
|
✓ |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$7.68746944439$ |
| 5.1.245025.1 |
$x^{5} - 3 x^{3} - 4 x^{2} + 6 x + 3$ |
$5$ |
[1,2] |
$3^{4}\cdot 5^{2}\cdot 11^{2}$ |
$3$ |
$11.9630544538$ |
$52.105462702620216$ |
|
|
✓ |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$9.83685596131$ |
| 5.1.245025.2 |
$x^{5} - x^{4} - 3 x^{3} - 2 x^{2} + 5 x - 3$ |
$5$ |
[1,2] |
$3^{4}\cdot 5^{2}\cdot 11^{2}$ |
$3$ |
$11.9630544538$ |
$47.852922372050145$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$11.4859992338$ |
| 5.1.261121.1 |
$x^{5} - 5 x^{3} - x^{2} + 9 x + 7$ |
$5$ |
[1,2] |
$7^{2}\cdot 73^{2}$ |
$2$ |
$12.116253747$ |
$31.265121691698095$ |
|
|
✓ |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$5.94845433539$ |
| 5.1.263169.1 |
$x^{5} - x^{4} + x^{3} + 2 x^{2} + x + 5$ |
$5$ |
[1,2] |
$3^{6}\cdot 19^{2}$ |
$2$ |
$12.1352002157$ |
$32.66623641048394$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$10.3600379754$ |
| 5.1.270400.1 |
$x^{5} - 2 x^{4} + 5 x^{3} - 2 x^{2} + 7 x + 4$ |
$5$ |
[1,2] |
$2^{6}\cdot 5^{2}\cdot 13^{2}$ |
$3$ |
$12.201166045$ |
$45.72501934899875$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$10.8919711178$ |
| 5.1.287296.1 |
$x^{5} - x^{4} - x^{3} + 7 x^{2} - 9 x + 5$ |
$5$ |
[1,2] |
$2^{6}\cdot 67^{2}$ |
$2$ |
$12.3499703768$ |
$46.65822308917137$ |
|
|
✓ |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$13.0592140393$ |
| 5.1.287296.2 |
$x^{5} + 2 x^{3} - 4 x^{2} + 6 x - 4$ |
$5$ |
[1,2] |
$2^{6}\cdot 67^{2}$ |
$2$ |
$12.3499703768$ |
$23.15167380558045$ |
|
|
? |
$A_5$ (as 5T4) |
$[3]$ |
$2$ |
$2$ |
$6.22840695088$ |
| 5.1.329476.1 |
$x^{5} - 2 x^{4} - 5 x^{3} + 2 x^{2} + 4 x - 4$ |
$5$ |
[1,2] |
$2^{2}\cdot 7^{2}\cdot 41^{2}$ |
$3$ |
$12.6930139385$ |
$37.1943767206359$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$12.4599937287$ |
| 5.1.341056.1 |
$x^{5} + 2 x^{3} - 4 x^{2} - 2 x + 4$ |
$5$ |
[1,2] |
$2^{6}\cdot 73^{2}$ |
$2$ |
$12.7810089465$ |
$24.166091947189145$ |
|
|
? |
$A_5$ (as 5T4) |
$[3]$ |
$2$ |
$2$ |
$5.82992888324$ |
| 5.1.342225.1 |
$x^{5} - x^{4} + x^{3} + 3 x^{2} - 9$ |
$5$ |
[1,2] |
$3^{4}\cdot 5^{2}\cdot 13^{2}$ |
$3$ |
$12.7897585693$ |
$58.24388936725177$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$10.2907932998$ |
| 5.1.363609.1 |
$x^{5} - 3 x^{3} - 3 x^{2} + 9 x - 9$ |
$5$ |
[1,2] |
$3^{4}\cdot 67^{2}$ |
$2$ |
$12.945741323$ |
$29.49027790468186$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$11.7316074152$ |
| 5.1.364816.1 |
$x^{5} - 2 x^{3} - 2 x^{2} + 5 x - 6$ |
$5$ |
[1,2] |
$2^{4}\cdot 151^{2}$ |
$2$ |
$12.9543246108$ |
$56.71282667135762$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$21.7496055702$ |
| 5.1.379456.1 |
$x^{5} - x^{4} + 4 x^{3} - 8 x^{2} + x + 7$ |
$5$ |
[1,2] |
$2^{6}\cdot 7^{2}\cdot 11^{2}$ |
$3$ |
$13.0566657057$ |
$37.01312923532268$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$23.1120215585$ |
| 5.1.408321.1 |
$x^{5} - x^{4} + x^{3} - 9 x + 12$ |
$5$ |
[1,2] |
$3^{4}\cdot 71^{2}$ |
$2$ |
$13.249526047$ |
$61.775134027123485$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$31.706564963$ |
| 5.1.426409.1 |
$x^{5} + 3 x^{3} - 6 x^{2} + 2 x - 1$ |
$5$ |
[1,2] |
$653^{2}$ |
$1$ |
$13.3648864263$ |
$25.553864678361276$ |
|
|
✓ |
$A_5$ (as 5T4) |
$[3]$ |
$2$ |
$2$ |
$3.08752737307$ |
| 5.1.430336.1 |
$x^{5} - 2 x^{4} + 8 x^{3} - 12 x^{2} + 17 x - 14$ |
$5$ |
[1,2] |
$2^{8}\cdot 41^{2}$ |
$2$ |
$13.38941294$ |
$47.56080854749077$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$34.0338134529$ |
| 5.1.444889.1 |
$x^{5} - x^{4} + 2 x^{3} - 3 x^{2} - 6 x + 8$ |
$5$ |
[1,2] |
$23^{2}\cdot 29^{2}$ |
$2$ |
$13.4787722016$ |
$43.55294795488584$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$22.5890483863$ |
| 5.1.446224.1 |
$x^{5} - x^{4} - 5 x^{3} + 5 x^{2} + 5 x - 9$ |
$5$ |
[1,2] |
$2^{4}\cdot 167^{2}$ |
$2$ |
$13.4868517906$ |
$60.65142044657117$ |
|
|
✓ |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$25.267441499$ |
| 5.1.462400.1 |
$x^{5} - x^{4} - x^{3} - 5 x^{2} + 9 x - 1$ |
$5$ |
[1,2] |
$2^{6}\cdot 5^{2}\cdot 17^{2}$ |
$3$ |
$13.583245969$ |
$54.67946760043995$ |
|
|
✓ |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$13.702877058$ |
| 5.1.465124.1 |
$x^{5} - x^{4} + 5 x^{3} + 2 x^{2} - 10 x - 6$ |
$5$ |
[1,2] |
$2^{2}\cdot 11^{2}\cdot 31^{2}$ |
$3$ |
$13.5992121802$ |
$43.714881030456596$ |
|
|
✓ |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$23.4142361411$ |
| 5.1.484416.1 |
$x^{5} - 2 x^{4} + 8 x^{3} - 16 x^{2} + 28 x - 8$ |
$5$ |
[1,2] |
$2^{6}\cdot 3^{2}\cdot 29^{2}$ |
$3$ |
$13.7101970218$ |
$46.24210755012524$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$28.446179221$ |
| 5.1.498436.1 |
$x^{5} + x^{3} - 5 x^{2} - 4 x - 7$ |
$5$ |
[1,2] |
$2^{2}\cdot 353^{2}$ |
$2$ |
$13.7886542057$ |
$29.824558022304043$ |
|
|
✓ |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$19.4037049149$ |
| 5.1.529984.1 |
$x^{5} + 6 x^{3} - 10 x^{2} + 7 x - 2$ |
$5$ |
[1,2] |
$2^{6}\cdot 7^{2}\cdot 13^{2}$ |
$3$ |
$13.9589435743$ |
$41.373562242822544$ |
|
|
✓ |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$21.5394082921$ |
| 5.1.544644.1 |
$x^{5} + x^{3} - 3 x^{2} + 3$ |
$5$ |
[1,2] |
$2^{2}\cdot 3^{4}\cdot 41^{2}$ |
$3$ |
$14.0353273004$ |
$43.97848506856695$ |
|
|
✓ |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$22.4404676633$ |
| 5.1.544644.2 |
$x^{5} - 2 x^{4} + x^{3} + 5 x^{2} - 10 x - 13$ |
$5$ |
[1,2] |
$2^{2}\cdot 3^{4}\cdot 41^{2}$ |
$3$ |
$14.0353273004$ |
$68.00132350455397$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$31.2508258439$ |
| 5.1.570025.1 |
$x^{5} - 3 x^{3} - x^{2} + x - 3$ |
$5$ |
[1,2] |
$5^{2}\cdot 151^{2}$ |
$2$ |
$14.1637672229$ |
$35.93093151785668$ |
|
|
✓ |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$13.5718074228$ |
| 5.1.588289.1 |
$x^{5} - 2 x^{4} - x^{3} + 4 x^{2} + 2 x - 15$ |
$5$ |
[1,2] |
$13^{2}\cdot 59^{2}$ |
$2$ |
$14.2533892501$ |
$54.643647855672945$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$15.4944157807$ |
| 5.1.613089.1 |
$x^{5} - 2 x^{4} + 4 x^{3} - 3 x^{2} + 6 x - 3$ |
$5$ |
[1,2] |
$3^{6}\cdot 29^{2}$ |
$2$ |
$14.3715862238$ |
$40.35722529423499$ |
|
|
✓ |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$12.911326464$ |
| 5.1.616225.1 |
$x^{5} - x^{4} - 5 x^{3} + 6 x^{2} + 13 x - 1$ |
$5$ |
[1,2] |
$5^{2}\cdot 157^{2}$ |
$2$ |
$14.3862586003$ |
$36.6378372470484$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$8.56015957299$ |
| 5.1.617796.1 |
$x^{5} + 3 x^{3} - 8 x^{2} + 12 x - 12$ |
$5$ |
[1,2] |
$2^{2}\cdot 3^{2}\cdot 131^{2}$ |
$3$ |
$14.3935863783$ |
$70.91881793671696$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$34.3942284531$ |
| 5.1.627264.1 |
$x^{5} - x^{4} - 4 x^{3} + 9 x - 9$ |
$5$ |
[1,2] |
$2^{6}\cdot 3^{4}\cdot 11^{2}$ |
$3$ |
$14.4374360195$ |
$40.58850068501063$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$34.873840981$ |
| 5.1.627264.2 |
$x^{5} - x^{4} - 5 x^{3} + 11 x^{2} - 11 x + 11$ |
$5$ |
[1,2] |
$2^{6}\cdot 3^{4}\cdot 11^{2}$ |
$3$ |
$14.4374360195$ |
$60.52969095636233$ |
|
|
? |
$A_5$ (as 5T4) |
trivial |
$2$ |
$2$ |
$36.2130131039$ |
