| 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 $p$ |
| 4.2.12844.1 |
$x^{4} - x^{3} + 3 x^{2} - 3 x - 4$ |
$4$ |
(2, 1) |
$-\,2^{2}\cdot 13^{2}\cdot 19$ |
$3$ |
$10.6457208554$ |
$24.947965821847426$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$5.39417571756$ |
$2$ |
|
| 4.0.21125.1 |
$x^{4} - x^{3} + 16 x^{2} - 16 x + 61$ |
$4$ |
(0, 2) |
$5^{3}\cdot 13^{2}$ |
$2$ |
$12.0558872978$ |
$12.055887297809578$ |
✓ |
✓ |
|
$C_4$ (as 4T1) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$0.962423650119$ |
$0$ |
|
| 4.2.29744.1 |
$x^{4} - 2 x^{3} + 4 x^{2} + 10 x - 1$ |
$4$ |
(2, 1) |
$-\,2^{4}\cdot 11\cdot 13^{2}$ |
$3$ |
$13.1325735901$ |
$26.84538769583832$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$7.39412389028$ |
$2$ |
|
| 4.2.46475.1 |
$x^{4} - x^{3} + 3 x^{2} + 23 x - 121$ |
$4$ |
(2, 1) |
$-\,5^{2}\cdot 11\cdot 13^{2}$ |
$3$ |
$14.6826636335$ |
$26.739483914241877$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$4.49005765234$ |
$2$ |
|
| 4.0.66248.1 |
$x^{4} - x^{3} - 15 x^{2} + 19 x + 88$ |
$4$ |
(0, 2) |
$2^{3}\cdot 7^{2}\cdot 13^{2}$ |
$3$ |
$16.0432810968$ |
$26.981475126464083$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$16.413248255$ |
$0$ |
|
| 4.2.73684.1 |
$x^{4} - x^{3} + x^{2} + 11 x + 4$ |
$4$ |
(2, 1) |
$-\,2^{2}\cdot 13^{2}\cdot 109$ |
$3$ |
$16.4756781114$ |
$75.28612089887484$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$23.511704336$ |
$2$ |
|
| 4.2.75712.1 |
$x^{4} - 2 x^{3} + 7 x^{2} + 20 x - 82$ |
$4$ |
(2, 1) |
$-\,2^{6}\cdot 7\cdot 13^{2}$ |
$3$ |
$16.5878912569$ |
$26.981475126464083$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$14.4662034891$ |
$2$ |
|
| 4.2.80275.1 |
$x^{4} - 2 x^{3} + 8 x^{2} - 7 x - 199$ |
$4$ |
(2, 1) |
$-\,5^{2}\cdot 13^{2}\cdot 19$ |
$3$ |
$16.8323626188$ |
$35.14256678161116$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$3.45350051843$ |
$2$ |
|
| 4.2.95823.1 |
$x^{4} - 3 x^{2} - 13 x - 27$ |
$4$ |
(2, 1) |
$-\,3^{4}\cdot 7\cdot 13^{2}$ |
$3$ |
$17.59411559$ |
$41.27455210028946$ |
|
|
✓ |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$18.0468588271$ |
$2$ |
|
| 4.0.100048.1 |
$x^{4} - 2 x^{3} + 12 x^{2} + 2 x + 27$ |
$4$ |
(0, 2) |
$2^{4}\cdot 13^{2}\cdot 37$ |
$3$ |
$17.7849276517$ |
$49.235029196678006$ |
|
|
✓ |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$10.028708122$ |
$0$ |
|
| 4.0.102245.1 |
$x^{4} - x^{3} - 8 x^{2} + 22 x + 55$ |
$4$ |
(0, 2) |
$5\cdot 11^{2}\cdot 13^{2}$ |
$3$ |
$17.8817706277$ |
$26.739483914241877$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$9.33073008291$ |
$0$ |
|
| 4.2.117455.1 |
$x^{4} + 9 x^{2} - 13 x + 4$ |
$4$ |
(2, 1) |
$-\,5\cdot 13^{2}\cdot 139$ |
$3$ |
$18.5126196009$ |
$95.05261700763425$ |
|
|
✓ |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$13.4419336231$ |
$2$ |
|
| 4.0.117793.1 |
$x^{4} - 2 x^{3} + 5 x^{2} + 9 x + 4$ |
$4$ |
(0, 2) |
$13^{2}\cdot 17\cdot 41$ |
$3$ |
$18.525923684$ |
$95.1892851112981$ |
|
|
✓ |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$8.30020939733$ |
$0$ |
|
| 4.2.125567.1 |
$x^{4} - 2 x^{3} + 5 x^{2} + 9 x - 9$ |
$4$ |
(2, 1) |
$-\,13^{2}\cdot 743$ |
$2$ |
$18.8243019109$ |
$98.28021163998376$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$13.1856386891$ |
$2$ |
|
| 4.0.127764.1 |
$x^{4} + 12 x^{2} - 26 x + 36$ |
$4$ |
(0, 2) |
$2^{2}\cdot 3^{3}\cdot 7\cdot 13^{2}$ |
$4$ |
$18.9061075901$ |
$54.556791795880414$ |
|
|
|
$S_4$ (as 4T5) |
$[10]$ |
$[10]$ |
$2$ |
$1$ |
$4.87787537326$ |
$0$ |
|
| 4.2.130975.1 |
$x^{4} - x^{3} + 3 x^{2} - 42 x - 316$ |
$4$ |
(2, 1) |
$-\,5^{2}\cdot 13^{2}\cdot 31$ |
$3$ |
$19.0237925657$ |
$44.88875137492688$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$10.0385054146$ |
$2$ |
|
| 4.0.133172.2 |
$x^{4} - 4 x^{2} - 26 x + 56$ |
$4$ |
(0, 2) |
$2^{2}\cdot 13^{2}\cdot 197$ |
$3$ |
$19.1030727905$ |
$80.33253150225966$ |
|
|
✓ |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$23.9229314074$ |
$0$ |
|
| 4.2.135200.1 |
$x^{4} - 2 x^{3} - 2 x^{2} - 10 x - 27$ |
$4$ |
(2, 1) |
$-\,2^{5}\cdot 5^{2}\cdot 13^{2}$ |
$3$ |
$19.1753885545$ |
$42.17078354197091$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$28.3274332282$ |
$2$ |
|
| 4.2.136552.1 |
$x^{4} - x^{3} + x^{2} + 24 x + 4$ |
$4$ |
(2, 1) |
$-\,2^{3}\cdot 13^{2}\cdot 101$ |
$3$ |
$19.2231482981$ |
$102.48902380255166$ |
|
|
✓ |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$11.3375316424$ |
$2$ |
|
| 4.2.137228.1 |
$x^{4} - 4 x^{2} - 26 x + 4$ |
$4$ |
(2, 1) |
$-\,2^{2}\cdot 7\cdot 13^{2}\cdot 29$ |
$4$ |
$19.2468952839$ |
$81.54669399396361$ |
|
|
✓ |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$29.5685385831$ |
$2$ |
|
| 4.2.146016.1 |
$x^{4} - 2 x^{3} - 9 x^{2} - 16 x + 38$ |
$4$ |
(2, 1) |
$-\,2^{5}\cdot 3^{3}\cdot 13^{2}$ |
$3$ |
$19.5479001398$ |
$51.96047724584012$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$36.8237572363$ |
$2$ |
|
| 4.0.150748.1 |
$x^{4} - x^{3} - x^{2} - x + 14$ |
$4$ |
(0, 2) |
$2^{2}\cdot 13^{2}\cdot 223$ |
$3$ |
$19.7043852378$ |
$107.68472500777443$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$33.6055848558$ |
$0$ |
|
| 4.2.153452.1 |
$x^{4} - 2 x^{3} - 2 x^{2} - 36 x - 1$ |
$4$ |
(2, 1) |
$-\,2^{2}\cdot 13^{2}\cdot 227$ |
$3$ |
$19.7921575$ |
$86.23255786812508$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$26.8882189606$ |
$2$ |
|
| 4.0.173225.1 |
$x^{4} - x^{3} + 42 x^{2} - 29 x + 451$ |
$4$ |
(0, 2) |
$5^{2}\cdot 13^{2}\cdot 41$ |
$3$ |
$20.4010557431$ |
$51.62363799656123$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[10]$ |
$[10]$ |
$2$ |
$1$ |
$0.962423650119$ |
$0$ |
|
| 4.4.190125.1 |
$x^{4} - x^{3} - 49 x^{2} + 49 x + 451$ |
$4$ |
(4, 0) |
$3^{2}\cdot 5^{3}\cdot 13^{2}$ |
$3$ |
$20.8814093301$ |
$20.88140933013045$ |
|
✓ |
|
$C_4$ (as 4T1) |
$[2]$ |
$[2, 2]$ |
$2$ |
$3$ |
$12.0903797544$ |
$3$ |
|
| 4.0.190801.1 |
$x^{4} - x^{2} - 13 x + 23$ |
$4$ |
(0, 2) |
$13^{2}\cdot 1129$ |
$2$ |
$20.8999458857$ |
$121.1486689980538$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$8.97494534049$ |
$0$ |
|
| 4.2.198068.1 |
$x^{4} - x^{3} - 7 x^{2} - 24 x + 4$ |
$4$ |
(2, 1) |
$-\,2^{2}\cdot 13^{2}\cdot 293$ |
$3$ |
$21.0961681825$ |
$123.43419299367578$ |
|
|
✓ |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$21.6618221183$ |
$2$ |
|
| 4.2.198744.1 |
$x^{4} - x^{3} - 7 x^{2} + 2 x - 74$ |
$4$ |
(2, 1) |
$-\,2^{3}\cdot 3\cdot 7^{2}\cdot 13^{2}$ |
$4$ |
$21.114145334$ |
$64.63622593542183$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$25.7505976594$ |
$2$ |
|
| 4.2.203983.1 |
$x^{4} - x^{3} - 2 x^{2} - 7 x + 10$ |
$4$ |
(2, 1) |
$-\,13^{2}\cdot 17\cdot 71$ |
$3$ |
$21.2519357216$ |
$125.26372180324198$ |
|
|
✓ |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$15.528070615$ |
$2$ |
|
| 4.2.214968.1 |
$x^{4} - x^{3} - 2 x^{2} + 6 x - 16$ |
$4$ |
(2, 1) |
$-\,2^{3}\cdot 3\cdot 13^{2}\cdot 53$ |
$4$ |
$21.5324503251$ |
$128.59237924542808$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$55.0989452329$ |
$2$ |
|
| 4.2.222235.1 |
$x^{4} - x^{3} + 3 x^{2} + 23 x + 9$ |
$4$ |
(2, 1) |
$-\,5\cdot 13^{2}\cdot 263$ |
$3$ |
$21.7121641822$ |
$130.7478489306803$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$21.1886237151$ |
$2$ |
|
| 4.2.222911.1 |
$x^{4} - x^{3} + x^{2} - 2 x - 9$ |
$4$ |
(2, 1) |
$-\,13^{2}\cdot 1319$ |
$2$ |
$21.728656533$ |
$130.9465539829132$ |
|
|
✓ |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$17.9596587264$ |
$2$ |
|
| 4.0.227305.1 |
$x^{4} - 2 x^{3} + 11 x^{2} + 3 x + 25$ |
$4$ |
(0, 2) |
$5\cdot 13^{2}\cdot 269$ |
$3$ |
$21.8349522863$ |
$132.23085872821065$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$18.9028410359$ |
$0$ |
|
| 4.2.230347.1 |
$x^{4} - x^{3} - 2 x^{2} + 6 x - 29$ |
$4$ |
(2, 1) |
$-\,13^{2}\cdot 29\cdot 47$ |
$3$ |
$21.9076422394$ |
$133.11273417671202$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$8.91337596107$ |
$2$ |
|
| 4.0.231868.1 |
$x^{4} - x^{3} + 24 x^{2} - 46 x + 296$ |
$4$ |
(0, 2) |
$2^{2}\cdot 7^{3}\cdot 13^{2}$ |
$3$ |
$21.9437175204$ |
$31.03310292619014$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$32.0043535364$ |
$0$ |
|
| 4.0.232037.1 |
$x^{4} - x^{3} - 14 x^{2} - x + 79$ |
$4$ |
(0, 2) |
$13^{2}\cdot 1373$ |
$2$ |
$21.9477149188$ |
$133.60014970051492$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$17.7149003359$ |
$0$ |
|
| 4.0.233896.2 |
$x^{4} - 2 x^{3} - 6 x^{2} - 6 x + 61$ |
$4$ |
(0, 2) |
$2^{3}\cdot 13^{2}\cdot 173$ |
$3$ |
$21.9915428331$ |
$134.13426109685773$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$40.6215931559$ |
$0$ |
|
| 4.0.240825.1 |
$x^{4} - 2 x^{3} + 5 x^{2} + 35 x + 30$ |
$4$ |
(0, 2) |
$3\cdot 5^{2}\cdot 13^{2}\cdot 19$ |
$4$ |
$22.1526350192$ |
$79.59560843688025$ |
|
|
✓ |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$31.5255219266$ |
$0$ |
|
| 4.0.242684.2 |
$x^{4} - x^{3} + 18 x^{2} - 4 x + 120$ |
$4$ |
(0, 2) |
$2^{2}\cdot 13^{2}\cdot 359$ |
$3$ |
$22.1952625206$ |
$136.63088962602856$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$62.8879426961$ |
$0$ |
|
| 4.2.249275.1 |
$x^{4} - x^{3} - 10 x^{2} + 62 x - 641$ |
$4$ |
(2, 1) |
$-\,5^{2}\cdot 13^{2}\cdot 59$ |
$3$ |
$22.3444506223$ |
$61.927376821564145$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$7.34838386968$ |
$2$ |
|
| 4.2.250120.1 |
$x^{4} - 2 x^{3} - 14 x^{2} + 2 x + 53$ |
$4$ |
(2, 1) |
$-\,2^{3}\cdot 5\cdot 13^{2}\cdot 37$ |
$4$ |
$22.3633625737$ |
$138.70832707519762$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$24.7005390707$ |
$2$ |
|
| 4.0.264992.1 |
$x^{4} - 13 x^{2} + 338$ |
$4$ |
(0, 2) |
$2^{5}\cdot 7^{2}\cdot 13^{2}$ |
$3$ |
$22.6886257121$ |
$38.157568056677825$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$11.0957346659$ |
$0$ |
|
| 4.2.266175.1 |
$x^{4} - 2 x^{3} + 5 x^{2} + 35 x - 35$ |
$4$ |
(2, 1) |
$-\,3^{2}\cdot 5^{2}\cdot 7\cdot 13^{2}$ |
$4$ |
$22.7139055571$ |
$48.312701924169914$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2, 2]$ |
$2$ |
$2$ |
$20.8495830347$ |
$1$ |
|
| 4.2.267020.1 |
$x^{4} - 4 x^{2} - 26 x - 48$ |
$4$ |
(2, 1) |
$-\,2^{2}\cdot 5\cdot 13^{2}\cdot 79$ |
$4$ |
$22.7319110453$ |
$113.75143595761922$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$49.9982061067$ |
$2$ |
|
| 4.2.271583.1 |
$x^{4} - x^{3} + 5 x^{2} + 9 x - 62$ |
$4$ |
(2, 1) |
$-\,13^{2}\cdot 1607$ |
$2$ |
$22.8284090241$ |
$144.53719244540486$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$95.8029187864$ |
$2$ |
|
| 4.0.273780.1 |
$x^{4} - 2 x^{3} - 6 x^{2} - 6 x + 48$ |
$4$ |
(0, 2) |
$2^{2}\cdot 3^{4}\cdot 5\cdot 13^{2}$ |
$4$ |
$22.8744378452$ |
$55.37388762967983$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$41.6899810831$ |
$0$ |
|
| 4.2.283075.1 |
$x^{4} - x^{3} - 10 x^{2} + 10 x + 35$ |
$4$ |
(2, 1) |
$-\,5^{2}\cdot 13^{2}\cdot 67$ |
$3$ |
$23.0661641842$ |
$86.29568498932618$ |
|
|
✓ |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$10.7311743847$ |
$2$ |
|
| 4.2.286624.1 |
$x^{4} - 9 x^{2} - 26 x - 22$ |
$4$ |
(2, 1) |
$-\,2^{5}\cdot 13^{2}\cdot 53$ |
$3$ |
$23.1381236778$ |
$104.9952379872535$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$31.2066224897$ |
$2$ |
|
| 4.0.288652.1 |
$x^{4} - x^{3} - x^{2} + 12 x + 14$ |
$4$ |
(0, 2) |
$2^{2}\cdot 7\cdot 13^{2}\cdot 61$ |
$4$ |
$23.1789438136$ |
$149.01006677402705$ |
|
|
✓ |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$26.8463156707$ |
$0$ |
|
| 4.2.293384.1 |
$x^{4} - x^{3} - 7 x^{2} + 15 x + 4$ |
$4$ |
(2, 1) |
$-\,2^{3}\cdot 7\cdot 13^{2}\cdot 31$ |
$4$ |
$23.2733610176$ |
$150.22649566571138$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$69.6488225938$ |
$2$ |
|
