| 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 |
| 4.2.3751.1 |
$x^{4} - x^{3} - 2 x^{2} - 3 x - 2$ |
$4$ |
[2,1] |
$-\,11^{2}\cdot 31$ |
$2$ |
$7.82594454307$ |
$18.466185312619388$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$3.26843086484$ |
| 4.0.14157.1 |
$x^{4} - x^{3} + 20 x^{2} - 14 x + 97$ |
$4$ |
[0,2] |
$3^{2}\cdot 11^{2}\cdot 13$ |
$3$ |
$10.9079416982$ |
$20.71231517720798$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$6$ |
$1$ |
$3.64556543445$ |
| 4.2.18392.2 |
$x^{4} - x^{3} - 4 x^{2} + 9 x - 7$ |
$4$ |
[2,1] |
$-\,2^{3}\cdot 11^{2}\cdot 19$ |
$3$ |
$11.6454758626$ |
$40.890096600521744$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$10.7388833007$ |
| 4.0.22869.1 |
$x^{4} - x^{3} - 24 x^{2} + 8 x + 163$ |
$4$ |
[0,2] |
$3^{3}\cdot 7\cdot 11^{2}$ |
$3$ |
$12.2973573557$ |
$20.0025932455872$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$6$ |
$1$ |
$6.86628528057$ |
| 4.0.32912.1 |
$x^{4} - 5 x^{2} - 22 x + 130$ |
$4$ |
[0,2] |
$2^{4}\cdot 11^{2}\cdot 17$ |
$3$ |
$13.4690997296$ |
$27.349588662354687$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$4$ |
$1$ |
$14.4933145906$ |
| 4.0.38236.1 |
$x^{4} - x^{3} + 5 x^{2} - x + 12$ |
$4$ |
[0,2] |
$2^{2}\cdot 11^{2}\cdot 79$ |
$3$ |
$13.983571689$ |
$58.957611891934704$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$2$ |
$1$ |
$16.3233351416$ |
| 4.0.38841.1 |
$x^{4} - x^{2} - 11 x + 14$ |
$4$ |
[0,2] |
$3\cdot 11^{2}\cdot 107$ |
$3$ |
$14.0385612346$ |
$59.42221806698232$ |
|
|
✓ |
$S_4$ (as 4T5) |
$[2]$ |
$2$ |
$1$ |
$6.50631032194$ |
| 4.2.44407.1 |
$x^{4} - x^{3} - 2 x^{2} + 8 x - 24$ |
$4$ |
[2,1] |
$-\,11^{2}\cdot 367$ |
$2$ |
$14.5165314269$ |
$63.53739056650029$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$20.7845791175$ |
| 4.0.48884.1 |
$x^{4} - 2 x^{3} + 4 x^{2} + 8 x + 5$ |
$4$ |
[0,2] |
$2^{2}\cdot 11^{2}\cdot 101$ |
$3$ |
$14.8693397185$ |
$52.910722664375015$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$2$ |
$1$ |
$6.87712668609$ |
| 4.2.50336.1 |
$x^{4} - 2 x^{3} - 8 x^{2} - 2 x + 23$ |
$4$ |
[2,1] |
$-\,2^{5}\cdot 11^{2}\cdot 13$ |
$3$ |
$14.9785466117$ |
$47.83304297240559$ |
|
|
|
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$30.3711821169$ |
| 4.2.55660.1 |
$x^{4} - x^{3} - 2 x^{2} + 8 x - 2$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 5\cdot 11^{2}\cdot 23$ |
$4$ |
$15.3598084781$ |
$56.45883683033179$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$24.0809803421$ |
| 4.2.61347.1 |
$x^{4} - x^{3} - 4 x^{2} + 20 x - 29$ |
$4$ |
[2,1] |
$-\,3\cdot 11^{2}\cdot 13^{2}$ |
$3$ |
$15.7379562041$ |
$20.71231517720798$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$8.71117497458$ |
| 4.0.61952.1 |
$x^{4} - 22 x^{2} + 242$ |
$4$ |
[0,2] |
$2^{9}\cdot 11^{2}$ |
$2$ |
$15.7766151939$ |
$22.311503175611666$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$4$ |
$1$ |
$10.5293385917$ |
| 4.0.62073.1 |
$x^{4} - x^{3} + 42 x^{2} - 25 x + 427$ |
$4$ |
[0,2] |
$3^{3}\cdot 11^{2}\cdot 19$ |
$3$ |
$15.7843129836$ |
$32.95445123721052$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$6$ |
$1$ |
$19.7821637041$ |
| 4.0.66429.1 |
$x^{4} - 2 x^{3} + 40 x^{2} - 39 x + 471$ |
$4$ |
[0,2] |
$3^{2}\cdot 11^{2}\cdot 61$ |
$3$ |
$16.0542280819$ |
$44.86646854834911$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$6$ |
$1$ |
$17.7248549642$ |
| 4.2.71148.1 |
$x^{4} - x^{3} - 10 x^{2} + 12 x + 12$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 3\cdot 7^{2}\cdot 11^{2}$ |
$4$ |
$16.3320489947$ |
$33.36893354677306$ |
|
|
|
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$36.4238542156$ |
| 4.2.78892.1 |
$x^{4} - x^{3} - 5 x^{2} - 7 x - 6$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 11^{2}\cdot 163$ |
$3$ |
$16.7593913185$ |
$67.21664142846632$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$45.3430588187$ |
| 4.0.79376.1 |
$x^{4} - 27 x^{2} - 22 x + 317$ |
$4$ |
[0,2] |
$2^{4}\cdot 11^{2}\cdot 41$ |
$3$ |
$16.7850369808$ |
$42.473521163190604$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$4$ |
$1$ |
$4.27253589211$ |
| 4.0.79497.1 |
$x^{4} - x^{3} - 46 x^{2} + 19 x + 559$ |
$4$ |
[0,2] |
$3^{2}\cdot 11^{2}\cdot 73$ |
$3$ |
$16.791430064$ |
$49.08156476723211$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$6$ |
$1$ |
$14.0447162792$ |
| 4.2.84216.1 |
$x^{4} - x^{3} - 2 x^{2} - 3 x - 13$ |
$4$ |
[2,1] |
$-\,2^{3}\cdot 3\cdot 11^{2}\cdot 29$ |
$4$ |
$17.0352555332$ |
$87.49857141690943$ |
|
|
|
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$29.963880384$ |
| 4.2.85547.1 |
$x^{4} - x^{3} + 12 x^{2} + x - 21$ |
$4$ |
[2,1] |
$-\,7\cdot 11^{2}\cdot 101$ |
$3$ |
$17.1021690907$ |
$88.1873006730561$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$47.7952382354$ |
| 4.0.91476.3 |
$x^{4} - x^{3} + 12 x^{2} - 10 x + 34$ |
$4$ |
[0,2] |
$2^{2}\cdot 3^{3}\cdot 7\cdot 11^{2}$ |
$4$ |
$17.3910895538$ |
$50.18494935401794$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$2$ |
$1$ |
$22.9959407274$ |
| 4.2.93291.1 |
$x^{4} - 4 x^{2} - 11 x - 7$ |
$4$ |
[2,1] |
$-\,3\cdot 11^{2}\cdot 257$ |
$3$ |
$17.4767203529$ |
$92.09234495874236$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$14.6578308934$ |
| 4.0.95348.1 |
$x^{4} - 2 x^{3} - 2 x^{2} - 8 x + 27$ |
$4$ |
[0,2] |
$2^{2}\cdot 11^{2}\cdot 197$ |
$3$ |
$17.5722711864$ |
$73.89518137364831$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$2$ |
$1$ |
$20.0870471459$ |
| 4.0.100672.5 |
$x^{4} - 2 x^{3} - 20 x^{2} - 12 x + 410$ |
$4$ |
[0,2] |
$2^{6}\cdot 11^{2}\cdot 13$ |
$3$ |
$17.812594203$ |
$33.823069050575526$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$4$ |
$1$ |
$17.5746639695$ |
| 4.2.104423.1 |
$x^{4} - 9 x^{2} - 11 x + 1$ |
$4$ |
[2,1] |
$-\,11^{2}\cdot 863$ |
$2$ |
$17.9762476083$ |
$97.43202758846806$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$19.9754305614$ |
| 4.2.106843.3 |
$x^{4} - x^{3} - 6 x^{2} + 10 x + 1$ |
$4$ |
[2,1] |
$-\,11^{2}\cdot 883$ |
$2$ |
$18.0795042819$ |
$98.55455342093535$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$10.0781169517$ |
| 4.2.117491.2 |
$x^{4} + 2 x^{2} - 11 x - 10$ |
$4$ |
[2,1] |
$-\,11^{2}\cdot 971$ |
$2$ |
$18.514037969$ |
$103.34892355511015$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$48.3842012218$ |
| 4.2.118580.1 |
$x^{4} - x^{3} - 10 x^{2} - 21 x + 1$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 5\cdot 7^{2}\cdot 11^{2}$ |
$4$ |
$18.5567903619$ |
$54.276274940985765$ |
|
|
|
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$35.9122418049$ |
| 4.0.118701.3 |
$x^{4} - x^{3} + 53 x^{2} - 47 x + 823$ |
$4$ |
[0,2] |
$3^{2}\cdot 11^{2}\cdot 109$ |
$3$ |
$18.5615224266$ |
$59.9749947894954$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$6$ |
$1$ |
$7.30718973567$ |
| 4.2.121484.2 |
$x^{4} - x^{3} - 4 x^{2} + 20 x + 4$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 11^{2}\cdot 251$ |
$3$ |
$18.6693746384$ |
$83.41033531595164$ |
|
|
|
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$39.3028789888$ |
| 4.0.121968.1 |
$x^{4} - 55 x^{2} + 847$ |
$4$ |
[0,2] |
$2^{4}\cdot 3^{2}\cdot 7\cdot 11^{2}$ |
$4$ |
$18.6879419161$ |
$42.988370520409354$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$6$ |
$1$ |
$8.19157443492$ |
| 4.0.121968.2 |
$x^{4} + 55 x^{2} + 847$ |
$4$ |
[0,2] |
$2^{4}\cdot 3^{2}\cdot 7\cdot 11^{2}$ |
$4$ |
$18.6879419161$ |
$42.988370520409354$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$6$ |
$1$ |
$29.557940266$ |
| 4.2.123904.3 |
$x^{4} - 22 x^{2} - 121$ |
$4$ |
[2,1] |
$-\,2^{10}\cdot 11^{2}$ |
$2$ |
$18.7616630393$ |
$22.311503175611666$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$18.5605618471$ |
| 4.0.125840.1 |
$x^{4} - 2 x^{3} - 37 x^{2} + 38 x + 482$ |
$4$ |
[0,2] |
$2^{4}\cdot 5\cdot 11^{2}\cdot 13$ |
$4$ |
$18.8345252376$ |
$53.47896782848375$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$4$ |
$1$ |
$31.4485054972$ |
| 4.0.125840.2 |
$x^{4} - 5 x^{2} - 44 x + 493$ |
$4$ |
[0,2] |
$2^{4}\cdot 5\cdot 11^{2}\cdot 13$ |
$4$ |
$18.8345252376$ |
$53.47896782848375$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$4$ |
$1$ |
$8.70471524085$ |
| 4.2.126808.1 |
$x^{4} - x^{3} - 2 x^{2} + 19 x - 13$ |
$4$ |
[2,1] |
$-\,2^{3}\cdot 11^{2}\cdot 131$ |
$3$ |
$18.8706414633$ |
$107.36852425175638$ |
|
|
|
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$29.7860829623$ |
| 4.4.131648.2 |
$x^{4} - 2 x^{3} - 27 x^{2} + 6 x + 119$ |
$4$ |
[4,0] |
$2^{6}\cdot 11^{2}\cdot 17$ |
$3$ |
$19.0481835106$ |
$38.67815921162743$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$18.5531440848$ |
| 4.2.136367.1 |
$x^{4} - x^{3} - 5 x^{2} - 7 x - 28$ |
$4$ |
[2,1] |
$-\,7^{2}\cdot 11^{2}\cdot 23$ |
$3$ |
$19.2166341302$ |
$42.08325082500163$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$2$ |
$2$ |
$19.5886195559$ |
| 4.2.139876.1 |
$x^{4} - x^{3} + x^{2} + 23 x - 32$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 11^{2}\cdot 17^{2}$ |
$3$ |
$19.3390796058$ |
$27.349588662354687$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$60.7186558486$ |
| 4.0.140481.1 |
$x^{4} - x^{3} - 57 x^{2} + 8 x + 988$ |
$4$ |
[0,2] |
$3^{3}\cdot 11^{2}\cdot 43$ |
$3$ |
$19.3599574076$ |
$49.57600322676523$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$6$ |
$1$ |
$26.8660145155$ |
| 4.0.141328.1 |
$x^{4} - 2 x^{3} - 15 x^{2} + 16 x + 548$ |
$4$ |
[0,2] |
$2^{4}\cdot 11^{2}\cdot 73$ |
$3$ |
$19.3890733351$ |
$56.674509261219015$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$4$ |
$1$ |
$34.0961892558$ |
| 4.2.145200.1 |
$x^{4} - 2 x^{3} - 2 x^{2} - 30 x + 38$ |
$4$ |
[2,1] |
$-\,2^{4}\cdot 3\cdot 5^{2}\cdot 11^{2}$ |
$4$ |
$19.5205322075$ |
$37.70844594279965$ |
|
|
|
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$38.6892672277$ |
| 4.2.149435.1 |
$x^{4} - x^{3} + 5 x^{2} - x - 21$ |
$4$ |
[2,1] |
$-\,5\cdot 11^{2}\cdot 13\cdot 19$ |
$4$ |
$19.6613385759$ |
$116.55470818461174$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$25.5989057097$ |
| 4.4.152944.1 |
$x^{4} - 2 x^{3} - 13 x^{2} - 8 x + 5$ |
$4$ |
[4,0] |
$2^{4}\cdot 11^{2}\cdot 79$ |
$3$ |
$19.775756733$ |
$83.37865434270333$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$3$ |
$30.31571763$ |
| 4.2.156332.1 |
$x^{4} - x^{3} + 5 x^{2} + 21 x - 10$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 11^{2}\cdot 17\cdot 19$ |
$4$ |
$19.884376194$ |
$94.62028841930767$ |
|
|
|
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$60.3977342802$ |
| 4.2.156816.1 |
$x^{4} - 3 x^{2} - 22 x + 27$ |
$4$ |
[2,1] |
$-\,2^{4}\cdot 3^{4}\cdot 11^{2}$ |
$3$ |
$19.8997487421$ |
$40.58850068501063$ |
|
|
|
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$32.7073012653$ |
| 4.4.157300.1 |
$x^{4} - x^{3} - 13 x^{2} - 3 x + 20$ |
$4$ |
[4,0] |
$2^{2}\cdot 5^{2}\cdot 11^{2}\cdot 13$ |
$4$ |
$19.9150857468$ |
$55.5053295346095$ |
|
|
|
$S_4$ (as 4T5) |
trivial |
$2$ |
$3$ |
$81.9335571775$ |
| 4.2.160083.2 |
$x^{4} - x^{3} + 6 x^{2} + 26 x - 17$ |
$4$ |
[2,1] |
$-\,3^{3}\cdot 7^{2}\cdot 11^{2}$ |
$3$ |
$20.0025932456$ |
$20.0025932455872$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$2$ |
$10.7580905384$ |
| 4.2.163471.1 |
$x^{4} - x^{3} - 6 x^{2} - x + 12$ |
$4$ |
[2,1] |
$-\,7\cdot 11^{2}\cdot 193$ |
$3$ |
$20.1075973425$ |
$121.90570126126177$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$49.6704564254$ |
