| 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 |
| 4.0.117.1 |
$x^{4} - x^{3} - x^{2} + x + 1$ |
$4$ |
[0,2] |
$3^{2}\cdot 13$ |
$2$ |
$3.28886816799$ |
$6.244997998398398$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$6$ |
$1$ |
$0.543535072498$ |
| 4.0.189.1 |
$x^{4} - x^{3} + 2 x + 1$ |
$4$ |
[0,2] |
$3^{3}\cdot 7$ |
$2$ |
$3.70779275107$ |
$6.03100878451909$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$6$ |
$1$ |
$0.862554627662$ |
| 4.0.272.1 |
$x^{4} + x^{2} - 2 x + 1$ |
$4$ |
[0,2] |
$2^{4}\cdot 17$ |
$2$ |
$4.06108636974$ |
$8.246211251235321$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$4$ |
$1$ |
$0.732857675974$ |
| 4.2.275.1 |
$x^{4} - x^{3} + 2 x - 1$ |
$4$ |
[2,1] |
$-\,5^{2}\cdot 11$ |
$2$ |
$4.07223819929$ |
$7.416198487095663$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$0.369184373575$ |
| 4.0.320.1 |
$x^{4} - 2 x^{3} + 2$ |
$4$ |
[0,2] |
$2^{6}\cdot 5$ |
$2$ |
$4.22948505376$ |
$6.324555320336759$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$4$ |
$1$ |
$1.06127506191$ |
| 4.0.333.1 |
$x^{4} - x^{3} - 2 x^{2} + 3$ |
$4$ |
[0,2] |
$3^{2}\cdot 37$ |
$2$ |
$4.27180144563$ |
$10.535653752852738$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$6$ |
$1$ |
$1.46078161311$ |
| 4.0.392.1 |
$x^{4} - x^{3} + x + 1$ |
$4$ |
[0,2] |
$2^{3}\cdot 7^{2}$ |
$2$ |
$4.44960558625$ |
$7.483314773547883$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$1$ |
$0.632974319201$ |
| 4.2.400.1 |
$x^{4} - x^{2} - 1$ |
$4$ |
[2,1] |
$-\,2^{4}\cdot 5^{2}$ |
$2$ |
$4.472135955$ |
$6.324555320336759$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$0.51069810943$ |
| 4.0.432.1 |
$x^{4} - 3 x^{2} + 3$ |
$4$ |
[0,2] |
$2^{4}\cdot 3^{3}$ |
$2$ |
$4.55901411391$ |
$6.4474195909412515$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$6$ |
$1$ |
$1.66288589106$ |
| 4.2.448.1 |
$x^{4} - 2 x^{3} + x^{2} - 2 x + 1$ |
$4$ |
[2,1] |
$-\,2^{6}\cdot 7$ |
$2$ |
$4.60065326758$ |
$7.483314773547883$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$0.557886846205$ |
| 4.2.475.1 |
$x^{4} - 2 x^{3} + 2 x^{2} - x - 1$ |
$4$ |
[2,1] |
$-\,5^{2}\cdot 19$ |
$2$ |
$4.66845742379$ |
$9.746794344808963$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$0.57693147741$ |
| 4.2.507.1 |
$x^{4} - x^{3} - x^{2} - x + 1$ |
$4$ |
[2,1] |
$-\,3\cdot 13^{2}$ |
$2$ |
$4.74517233601$ |
$6.244997998398398$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$0.649395711926$ |
| 4.0.512.1 |
$x^{4} - 2 x^{2} + 2$ |
$4$ |
[0,2] |
$2^{9}$ |
$1$ |
$4.75682846001$ |
$6.727171322029716$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$4$ |
$1$ |
$1.52857091948$ |
| 4.0.513.1 |
$x^{4} - x^{3} - 3 x^{2} + 2 x + 4$ |
$4$ |
[0,2] |
$3^{3}\cdot 19$ |
$2$ |
$4.75914943092$ |
$9.93614090235369$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$6$ |
$1$ |
$1.96497837511$ |
| 4.0.549.1 |
$x^{4} - 2 x^{3} - 2 x^{2} + 3 x + 3$ |
$4$ |
[0,2] |
$3^{2}\cdot 61$ |
$2$ |
$4.84053189512$ |
$13.527749258468683$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$6$ |
$1$ |
$2.11437619251$ |
| 4.0.605.1 |
$x^{4} - x^{3} + x^{2} + x + 1$ |
$4$ |
[0,2] |
$5\cdot 11^{2}$ |
$2$ |
$4.95951083803$ |
$7.416198487095663$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$1$ |
$0.767197218251$ |
| 4.0.656.1 |
$x^{4} - 2 x^{3} - x^{2} + 2 x + 2$ |
$4$ |
[0,2] |
$2^{4}\cdot 41$ |
$2$ |
$5.06087906887$ |
$12.806248474865697$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$4$ |
$1$ |
$2.42610665212$ |
| 4.0.657.1 |
$x^{4} - x^{3} + 5 x^{2} - 2 x + 4$ |
$4$ |
[0,2] |
$3^{2}\cdot 73$ |
$2$ |
$5.06280665599$ |
$14.798648586948742$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$6$ |
$1$ |
$2.0335456547$ |
| 4.4.725.1 |
$x^{4} - x^{3} - 3 x^{2} + x + 1$ |
$4$ |
[4,0] |
$5^{2}\cdot 29$ |
$2$ |
$5.18900992827$ |
$12.041594578792296$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$0.825068847935$ |
| 4.2.775.1 |
$x^{4} - x^{3} - 3 x - 1$ |
$4$ |
[2,1] |
$-\,5^{2}\cdot 31$ |
$2$ |
$5.27625073458$ |
$12.449899597988733$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$0.867905309463$ |
| 4.0.832.1 |
$x^{4} - 2 x^{3} - 2 x + 5$ |
$4$ |
[0,2] |
$2^{6}\cdot 13$ |
$2$ |
$5.37069922857$ |
$10.198039027185569$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$4$ |
$1$ |
$2.13862208632$ |
| 4.0.837.1 |
$x^{4} - x^{3} - 3 x^{2} - x + 7$ |
$4$ |
[0,2] |
$3^{3}\cdot 31$ |
$2$ |
$5.37875006697$ |
$12.691758156532355$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$6$ |
$1$ |
$2.41883810412$ |
| 4.0.873.1 |
$x^{4} - x^{3} - 4 x^{2} + x + 7$ |
$4$ |
[0,2] |
$3^{2}\cdot 97$ |
$2$ |
$5.43567598422$ |
$17.05872210923198$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$6$ |
$1$ |
$2.42800256046$ |
| 4.0.981.1 |
$x^{4} - x^{3} - 4 x^{2} + 4 x + 7$ |
$4$ |
[0,2] |
$3^{2}\cdot 109$ |
$2$ |
$5.59650958426$ |
$18.083141320025124$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$6$ |
$1$ |
$2.15221875719$ |
| 4.0.1008.1 |
$x^{4} - 5 x^{2} + 7$ |
$4$ |
[0,2] |
$2^{4}\cdot 3^{2}\cdot 7$ |
$3$ |
$5.63462649452$ |
$12.96148139681572$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$6$ |
$1$ |
$3.39588318368$ |
| 4.0.1008.2 |
$x^{4} + 5 x^{2} + 7$ |
$4$ |
[0,2] |
$2^{4}\cdot 3^{2}\cdot 7$ |
$3$ |
$5.63462649452$ |
$12.96148139681572$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$6$ |
$1$ |
$2.41611328691$ |
| 4.2.1024.1 |
$x^{4} - 2 x^{2} - 1$ |
$4$ |
[2,1] |
$-\,2^{10}$ |
$1$ |
$5.65685424949$ |
$6.727171322029716$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$1.34724203432$ |
| 4.0.1025.1 |
$x^{4} - x^{3} + 3 x^{2} - 2 x + 4$ |
$4$ |
[0,2] |
$5^{2}\cdot 41$ |
$2$ |
$5.65823481195$ |
$14.317821063276353$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$1$ |
$0.962423650119$ |
| 4.0.1040.1 |
$x^{4} - 3 x^{2} - 2 x + 5$ |
$4$ |
[0,2] |
$2^{4}\cdot 5\cdot 13$ |
$3$ |
$5.67882302887$ |
$16.1245154965971$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$4$ |
$1$ |
$1.8522660627$ |
| 4.0.1040.2 |
$x^{4} + x^{2} - 4 x + 4$ |
$4$ |
[0,2] |
$2^{4}\cdot 5\cdot 13$ |
$3$ |
$5.67882302887$ |
$16.1245154965971$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$4$ |
$1$ |
$3.46864904298$ |
| 4.0.1088.1 |
$x^{4} - 2 x^{3} + x^{2} - 2 x + 3$ |
$4$ |
[0,2] |
$2^{6}\cdot 17$ |
$2$ |
$5.74324342205$ |
$11.661903789690601$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$1$ |
$1.17996602392$ |
| 4.0.1088.2 |
$x^{4} - 2 x^{3} + 5 x^{2} - 4 x + 2$ |
$4$ |
[0,2] |
$2^{6}\cdot 17$ |
$2$ |
$5.74324342205$ |
$11.661903789690601$ |
✓ |
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$1$ |
$1.76274717404$ |
| 4.2.1156.1 |
$x^{4} - x^{3} - 2 x^{2} - x + 1$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 17^{2}$ |
$2$ |
$5.83095189485$ |
$8.246211251235321$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$1.53512616922$ |
| 4.0.1161.1 |
$x^{4} - x^{3} + 6 x^{2} - x + 7$ |
$4$ |
[0,2] |
$3^{3}\cdot 43$ |
$2$ |
$5.83724678892$ |
$14.947727391693533$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$6$ |
$1$ |
$3.48142350173$ |
| 4.0.1168.1 |
$x^{4} - x^{2} - 4 x + 5$ |
$4$ |
[0,2] |
$2^{4}\cdot 73$ |
$2$ |
$5.84602557138$ |
$17.08800749063506$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$4$ |
$1$ |
$1.8902413596$ |
| 4.0.1197.1 |
$x^{4} - 2 x^{3} - 4 x^{2} + 5 x + 7$ |
$4$ |
[0,2] |
$3^{2}\cdot 7\cdot 19$ |
$3$ |
$5.8819799204$ |
$19.974984355438178$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$6$ |
$1$ |
$2.3192389338$ |
| 4.0.1197.2 |
$x^{4} - x^{3} - 5 x^{2} + 3 x + 9$ |
$4$ |
[0,2] |
$3^{2}\cdot 7\cdot 19$ |
$3$ |
$5.8819799204$ |
$19.974984355438178$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$6$ |
$1$ |
$3.57713438377$ |
| 4.0.1280.1 |
$x^{4} - 4 x^{2} + 5$ |
$4$ |
[0,2] |
$2^{8}\cdot 5$ |
$2$ |
$5.98139512488$ |
$8.94427190999916$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$4$ |
$1$ |
$2.93870348874$ |
| 4.2.1323.1 |
$x^{4} - x^{3} - 3 x^{2} - x + 1$ |
$4$ |
[2,1] |
$-\,3^{3}\cdot 7^{2}$ |
$2$ |
$6.03100878452$ |
$6.03100878451909$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$1.35144993247$ |
| 4.0.1372.1 |
$x^{4} - x^{3} + 3 x^{2} - 4 x + 2$ |
$4$ |
[0,2] |
$2^{2}\cdot 7^{3}$ |
$2$ |
$6.08609220723$ |
$8.607034141317701$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$1$ |
$1.48602212488$ |
| 4.2.1375.1 |
$x^{4} - x^{3} + x^{2} + 4 x - 4$ |
$4$ |
[2,1] |
$-\,5^{3}\cdot 11$ |
$2$ |
$6.08941642815$ |
$11.08980336897316$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$1.33061932583$ |
| 4.0.1413.1 |
$x^{4} - x^{3} + 7 x^{2} - 3 x + 9$ |
$4$ |
[0,2] |
$3^{2}\cdot 157$ |
$2$ |
$6.13105963586$ |
$21.702534414210707$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$6$ |
$1$ |
$3.89262683935$ |
| 4.0.1421.1 |
$x^{4} - 2 x^{3} + 2 x^{2} - x + 2$ |
$4$ |
[0,2] |
$7^{2}\cdot 29$ |
$2$ |
$6.13971934619$ |
$14.247806848775006$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$1$ |
$2.22757871637$ |
| 4.0.1424.1 |
$x^{4} - 2 x^{3} - x^{2} + 2 x + 5$ |
$4$ |
[0,2] |
$2^{4}\cdot 89$ |
$2$ |
$6.14295731128$ |
$18.867962264113206$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$4$ |
$1$ |
$2.40938537636$ |
| 4.2.1472.2 |
$x^{4} - 2 x^{3} + 3 x^{2} - 2 x - 1$ |
$4$ |
[2,1] |
$-\,2^{6}\cdot 23$ |
$2$ |
$6.19408202936$ |
$13.564659966250536$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$1.25951480215$ |
| 4.2.1475.1 |
$x^{4} - x^{3} - x^{2} + 5 x - 5$ |
$4$ |
[2,1] |
$-\,5^{2}\cdot 59$ |
$2$ |
$6.19723557236$ |
$17.175564037317667$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$1.23477697451$ |
| 4.0.1525.1 |
$x^{4} - 2 x^{3} + 6 x^{2} - 5 x + 5$ |
$4$ |
[0,2] |
$5^{2}\cdot 61$ |
$2$ |
$6.24909980553$ |
$17.46424919657298$ |
✓ |
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$1$ |
$0.962423650119$ |
| 4.0.1552.1 |
$x^{4} - 2 x^{3} - 3 x^{2} + 4 x + 5$ |
$4$ |
[0,2] |
$2^{4}\cdot 97$ |
$2$ |
$6.27657798543$ |
$19.697715603592208$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$4$ |
$1$ |
$2.23185135275$ |
| 4.0.1568.1 |
$x^{4} - x^{2} + 2$ |
$4$ |
[0,2] |
$2^{5}\cdot 7^{2}$ |
$2$ |
$6.29269256729$ |
$10.583005244258363$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$1$ |
$2.25676792993$ |
| 4.2.1600.1 |
$x^{4} - 2 x^{2} - 4$ |
$4$ |
[2,1] |
$-\,2^{6}\cdot 5^{2}$ |
$2$ |
$6.32455532034$ |
$8.94427190999916$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$1.41413886912$ |
