| 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 |
| 4.2.8303.1 |
$x^{4} - x^{3} - 3 x^{2} + 4 x - 3$ |
$4$ |
[2,1] |
$-\,19^{2}\cdot 23$ |
$2$ |
$9.54572149934$ |
$20.904544960366874$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$[2]$ |
$2$ |
$2$ |
$5.92225322223$ |
| 4.2.37544.1 |
$x^{4} - x^{3} - 7 x^{2} + 6 x - 2$ |
$4$ |
[2,1] |
$-\,2^{3}\cdot 13\cdot 19^{2}$ |
$3$ |
$13.9198685883$ |
$44.45222154178574$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$[2]$ |
$2$ |
$2$ |
$18.3683901949$ |
| 4.2.50179.1 |
$x^{4} - x^{3} - 6 x^{2} - 4 x - 3$ |
$4$ |
[2,1] |
$-\,19^{2}\cdot 139$ |
$2$ |
$14.9668532541$ |
$51.39066063011839$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$[2]$ |
$2$ |
$2$ |
$14.2395800589$ |
| 4.0.53428.1 |
$x^{4} - x^{3} + 11 x^{2} - 3 x + 28$ |
$4$ |
[0,2] |
$2^{2}\cdot 19^{2}\cdot 37$ |
$3$ |
$15.2034527707$ |
$42.088585105134996$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$9.82956667631$ |
| 4.2.62092.1 |
$x^{4} - x^{3} - 8 x^{2} + 16 x - 10$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 19^{2}\cdot 43$ |
$3$ |
$15.7855207049$ |
$45.37302056870605$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$[2]$ |
$2$ |
$2$ |
$27.9891467159$ |
| 4.2.63175.1 |
$x^{4} - 9 x^{2} - 19 x - 13$ |
$4$ |
[2,1] |
$-\,5^{2}\cdot 7\cdot 19^{2}$ |
$3$ |
$15.853907233$ |
$33.7214175938676$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$[2]$ |
$2$ |
$2$ |
$18.5182063138$ |
| 4.0.114076.1 |
$x^{4} - x^{3} - 9 x^{2} + 7 x + 30$ |
$4$ |
[0,2] |
$2^{2}\cdot 19^{2}\cdot 79$ |
$3$ |
$18.3780137082$ |
$77.48548251124207$ |
|
|
|
$S_4$ (as 4T5) |
$[10]$ |
$[10]$ |
$2$ |
$1$ |
$6.12001722064$ |
| 4.0.141512.1 |
$x^{4} - x^{3} + 25 x^{2} - 29 x + 176$ |
$4$ |
[0,2] |
$2^{3}\cdot 7^{2}\cdot 19^{2}$ |
$3$ |
$19.3953810891$ |
$32.61901286060018$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$19.6368660741$ |
| 4.2.161728.1 |
$x^{4} - 2 x^{3} - 9 x^{2} - 28 x - 146$ |
$4$ |
[2,1] |
$-\,2^{6}\cdot 7\cdot 19^{2}$ |
$3$ |
$20.0537826677$ |
$32.61901286060018$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$[2]$ |
$2$ |
$2$ |
$34.6148301792$ |
| 4.0.184832.1 |
$x^{4} - 38 x^{2} + 722$ |
$4$ |
[0,2] |
$2^{9}\cdot 19^{2}$ |
$2$ |
$20.7345345489$ |
$29.323059968612448$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2]$ |
$4$ |
$1$ |
$14.6014292147$ |
| 4.2.202160.1 |
$x^{4} - 2 x^{3} - 18 x - 14$ |
$4$ |
[2,1] |
$-\,2^{4}\cdot 5\cdot 7\cdot 19^{2}$ |
$4$ |
$21.2042935161$ |
$57.89119097686938$ |
|
|
|
$S_4$ (as 4T5) |
trivial |
$[2]$ |
$2$ |
$2$ |
$45.24402894$ |
| 4.0.203604.1 |
$x^{4} - x^{3} + 10 x^{2} - 12 x + 30$ |
$4$ |
[0,2] |
$2^{2}\cdot 3\cdot 19^{2}\cdot 47$ |
$4$ |
$21.2420573229$ |
$82.16238181392218$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$42.5066943927$ |
| 4.4.224181.1 |
$x^{4} - x^{3} - 9 x^{2} + 7 x + 11$ |
$4$ |
[4,0] |
$3^{3}\cdot 19^{2}\cdot 23$ |
$3$ |
$21.7595395215$ |
$75.31512172212854$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$[2]$ |
$2$ |
$3$ |
$40.0556736477$ |
| 4.0.236816.1 |
$x^{4} - 47 x^{2} - 38 x + 937$ |
$4$ |
[0,2] |
$2^{4}\cdot 19^{2}\cdot 41$ |
$3$ |
$22.0598604267$ |
$55.82114294781145$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2]$ |
$4$ |
$1$ |
$8.32777665757$ |
| 4.2.248368.1 |
$x^{4} - 2 x^{3} + 4 x^{2} + 16 x - 12$ |
$4$ |
[2,1] |
$-\,2^{4}\cdot 19^{2}\cdot 43$ |
$3$ |
$22.3240974699$ |
$64.1671410540975$ |
|
|
✓ |
$S_4$ (as 4T5) |
$[2]$ |
$[2, 2]$ |
$2$ |
$2$ |
$28.5855875254$ |
| 4.2.270028.1 |
$x^{4} - x^{3} - 8 x^{2} - 22 x + 66$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 11\cdot 17\cdot 19^{2}$ |
$4$ |
$22.7956615299$ |
$94.62028841930767$ |
|
|
|
$S_4$ (as 4T5) |
trivial |
$[2]$ |
$2$ |
$2$ |
$101.8513642$ |
| 4.2.278331.1 |
$x^{4} + 14 x^{2} - 19 x - 46$ |
$4$ |
[2,1] |
$-\,3\cdot 19^{2}\cdot 257$ |
$3$ |
$22.9689104731$ |
$121.03305333668155$ |
|
|
|
$S_4$ (as 4T5) |
trivial |
$[2]$ |
$2$ |
$2$ |
$93.8025589619$ |
| 4.2.281580.1 |
$x^{4} - x^{3} + 11 x^{2} - 3 x - 48$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 3\cdot 5\cdot 13\cdot 19^{2}$ |
$5$ |
$23.0356489308$ |
$96.62305614976691$ |
|
|
|
$S_4$ (as 4T5) |
trivial |
$[2]$ |
$2$ |
$2$ |
$86.3294937323$ |
| 4.2.282663.1 |
$x^{4} - x^{3} - 7 x - 8$ |
$4$ |
[2,1] |
$-\,3^{3}\cdot 19^{2}\cdot 29$ |
$3$ |
$23.0577667181$ |
$53.507756306084765$ |
|
|
✓ |
$S_4$ (as 4T5) |
$[2]$ |
$[2, 2]$ |
$2$ |
$2$ |
$28.3443899978$ |
| 4.0.300352.1 |
$x^{4} - 2 x^{3} - 36 x^{2} - 20 x + 1202$ |
$4$ |
[0,2] |
$2^{6}\cdot 13\cdot 19^{2}$ |
$3$ |
$23.4103351935$ |
$44.45222154178574$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2]$ |
$4$ |
$1$ |
$26.4756010078$ |
| 4.2.309016.1 |
$x^{4} - x^{3} - 11 x^{2} + 8 x - 12$ |
$4$ |
[2,1] |
$-\,2^{3}\cdot 19^{2}\cdot 107$ |
$3$ |
$23.5773636324$ |
$127.53038853543887$ |
|
|
|
$S_4$ (as 4T5) |
trivial |
$[2]$ |
$2$ |
$2$ |
$76.619770961$ |
| 4.2.311904.1 |
$x^{4} - 2 x^{3} - 18 x - 33$ |
$4$ |
[2,1] |
$-\,2^{5}\cdot 3^{3}\cdot 19^{2}$ |
$3$ |
$23.6322589135$ |
$62.81715390210758$ |
|
|
|
$S_4$ (as 4T5) |
trivial |
$[2]$ |
$2$ |
$2$ |
$117.293335961$ |
| 4.0.322012.1 |
$x^{4} - x^{3} - 13 x^{2} + 9 x + 100$ |
$4$ |
[0,2] |
$2^{2}\cdot 19^{2}\cdot 223$ |
$3$ |
$23.8214401722$ |
$130.18448448259878$ |
|
|
|
$S_4$ (as 4T5) |
$[6]$ |
$[6]$ |
$2$ |
$1$ |
$19.1268267148$ |
| 4.2.342228.1 |
$x^{4} - x^{3} - 3 x^{2} + 4 x - 22$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 3\cdot 19^{2}\cdot 79$ |
$4$ |
$24.186826251$ |
$134.20879255846094$ |
|
|
|
$S_4$ (as 4T5) |
trivial |
$[2]$ |
$2$ |
$2$ |
$98.4469924429$ |
| 4.2.369664.1 |
$x^{4} - 38 x^{2} - 361$ |
$4$ |
[2,1] |
$-\,2^{10}\cdot 19^{2}$ |
$2$ |
$24.6576560119$ |
$29.323059968612448$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$[2]$ |
$2$ |
$2$ |
$25.7386280851$ |
| 4.0.375440.1 |
$x^{4} - 2 x^{3} - 65 x^{2} + 66 x + 1450$ |
$4$ |
[0,2] |
$2^{4}\cdot 5\cdot 13\cdot 19^{2}$ |
$4$ |
$24.7534157011$ |
$70.28513356322232$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2]$ |
$4$ |
$1$ |
$55.9869773839$ |
| 4.0.375440.2 |
$x^{4} - 9 x^{2} - 76 x + 1469$ |
$4$ |
[0,2] |
$2^{4}\cdot 5\cdot 13\cdot 19^{2}$ |
$4$ |
$24.7534157011$ |
$70.28513356322232$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2]$ |
$4$ |
$1$ |
$14.120594555$ |
| 4.0.397461.1 |
$x^{4} + 2 x^{2} - 19 x + 20$ |
$4$ |
[0,2] |
$3\cdot 19^{2}\cdot 367$ |
$3$ |
$25.1086654539$ |
$144.63402089411744$ |
|
|
✓ |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$44.9142927786$ |
| 4.2.428507.1 |
$x^{4} - x^{3} - 13 x^{2} + 9 x + 43$ |
$4$ |
[2,1] |
$-\,19^{2}\cdot 1187$ |
$2$ |
$25.585239118$ |
$150.17656275198203$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$[2]$ |
$2$ |
$2$ |
$24.8489860895$ |
| 4.2.434283.1 |
$x^{4} - x^{3} + 12 x - 27$ |
$4$ |
[2,1] |
$-\,3\cdot 19^{2}\cdot 401$ |
$3$ |
$25.6710248617$ |
$151.1853167473614$ |
|
|
|
$S_4$ (as 4T5) |
trivial |
$[2]$ |
$2$ |
$2$ |
$70.0120626201$ |
| 4.0.453777.1 |
$x^{4} - x^{3} + 20 x^{2} - 17 x + 42$ |
$4$ |
[0,2] |
$3\cdot 19^{2}\cdot 419$ |
$3$ |
$25.9543776702$ |
$154.54125662747796$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$46.4842327191$ |
| 4.2.467856.1 |
$x^{4} - 9 x^{2} - 38 x - 51$ |
$4$ |
[2,1] |
$-\,2^{4}\cdot 3^{4}\cdot 19^{2}$ |
$3$ |
$26.1533936612$ |
$53.34374068187387$ |
|
|
|
$S_4$ (as 4T5) |
trivial |
$[2]$ |
$2$ |
$2$ |
$62.610670351$ |
| 4.0.470744.1 |
$x^{4} - x^{3} + 6 x^{2} - 10 x + 24$ |
$4$ |
[0,2] |
$2^{3}\cdot 19^{2}\cdot 163$ |
$3$ |
$26.1936607453$ |
$157.40393895960798$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$94.8914928755$ |
| 4.2.479047.1 |
$x^{4} - 2 x^{3} - 5 x^{2} - 13 x - 29$ |
$4$ |
[2,1] |
$-\,19^{2}\cdot 1327$ |
$2$ |
$26.3084057442$ |
$158.78601953572613$ |
|
|
|
$S_4$ (as 4T5) |
trivial |
$[2]$ |
$2$ |
$2$ |
$96.8762769239$ |
| 4.2.482296.1 |
$x^{4} - 2 x^{3} - 6 x^{2} - 12 x - 40$ |
$4$ |
[2,1] |
$-\,2^{3}\cdot 19^{2}\cdot 167$ |
$3$ |
$26.3529000593$ |
$159.32357013323548$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$[2]$ |
$2$ |
$2$ |
$47.8495263175$ |
| 4.4.485545.1 |
$x^{4} - x^{3} - 13 x^{2} - 10 x + 5$ |
$4$ |
[4,0] |
$5\cdot 19^{2}\cdot 269$ |
$3$ |
$26.3971701361$ |
$159.85931314752983$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$[2]$ |
$2$ |
$3$ |
$86.7633163685$ |
| 4.2.489155.1 |
$x^{4} - 2 x^{3} - 6 x^{2} - 31 x - 97$ |
$4$ |
[2,1] |
$-\,5\cdot 19^{2}\cdot 271$ |
$3$ |
$26.446099299$ |
$160.45248517863473$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$[2]$ |
$2$ |
$2$ |
$33.1616808459$ |
| 4.2.489516.1 |
$x^{4} - x^{3} - 7 x^{2} - 13 x - 2$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 3\cdot 19^{2}\cdot 113$ |
$4$ |
$26.4509773033$ |
$127.39820628543306$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$[2]$ |
$2$ |
$2$ |
$108.715482518$ |
| 4.0.512981.1 |
$x^{4} - 2 x^{3} - 8 x^{2} + 9 x + 652$ |
$4$ |
[0,2] |
$7^{2}\cdot 19^{2}\cdot 29$ |
$3$ |
$26.7624161717$ |
$62.10475022089695$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$22.7846936748$ |
| 4.0.514064.1 |
$x^{4} - 47 x^{2} - 76 x + 2020$ |
$4$ |
[0,2] |
$2^{4}\cdot 19^{2}\cdot 89$ |
$3$ |
$26.7765301344$ |
$82.24354077980836$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2]$ |
$4$ |
$1$ |
$75.2253513241$ |
| 4.2.516952.1 |
$x^{4} - x^{3} + x^{2} - 17 x + 4$ |
$4$ |
[2,1] |
$-\,2^{3}\cdot 19^{2}\cdot 179$ |
$3$ |
$26.8140586499$ |
$164.9484768041221$ |
|
|
|
$S_4$ (as 4T5) |
trivial |
$[2]$ |
$2$ |
$2$ |
$224.122334233$ |
| 4.2.531392.1 |
$x^{4} - 2 x^{3} - 6 x^{2} - 12 x - 2$ |
$4$ |
[2,1] |
$-\,2^{6}\cdot 19^{2}\cdot 23$ |
$3$ |
$26.999377614$ |
$59.12698199637793$ |
|
|
✓ |
$S_4$ (as 4T5) |
$[2]$ |
$[2, 2]$ |
$2$ |
$2$ |
$38.7532689099$ |
| 4.2.531392.2 |
$x^{4} - 2 x^{3} - 27 x^{2} + 28 x - 526$ |
$4$ |
[2,1] |
$-\,2^{6}\cdot 19^{2}\cdot 23$ |
$3$ |
$26.999377614$ |
$59.12698199637793$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$[2]$ |
$2$ |
$2$ |
$83.0084463089$ |
| 4.0.538612.2 |
$x^{4} - x^{3} + 8 x^{2} - 30 x + 26$ |
$4$ |
[0,2] |
$2^{2}\cdot 19^{2}\cdot 373$ |
$3$ |
$27.090623854$ |
$133.6342806364068$ |
|
|
✓ |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$30.330708404$ |
| 4.0.560272.1 |
$x^{4} - 85 x^{2} - 38 x + 2210$ |
$4$ |
[0,2] |
$2^{4}\cdot 19^{2}\cdot 97$ |
$3$ |
$27.3589691497$ |
$85.86035173466273$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2]$ |
$4$ |
$1$ |
$69.6956011917$ |
| 4.0.566048.1 |
$x^{4} + 19 x^{2} + 722$ |
$4$ |
[0,2] |
$2^{5}\cdot 7^{2}\cdot 19^{2}$ |
$3$ |
$27.4292109836$ |
$46.130250378683186$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$22.0229962439$ |
| 4.0.567853.1 |
$x^{4} - 6 x^{2} - 19 x + 85$ |
$4$ |
[0,2] |
$11^{2}\cdot 13\cdot 19^{2}$ |
$3$ |
$27.4510512835$ |
$77.73386588917877$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$14.5187969295$ |
| 4.2.646912.1 |
$x^{4} + 18 x^{2} - 76 x - 622$ |
$4$ |
[2,1] |
$-\,2^{8}\cdot 7\cdot 19^{2}$ |
$3$ |
$28.3603314255$ |
$46.130250378683186$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2, 2]$ |
$2$ |
$2$ |
$19.4104871964$ |
| 4.0.652688.1 |
$x^{4} - 2 x^{3} - 65 x^{2} + 66 x + 2533$ |
$4$ |
[0,2] |
$2^{4}\cdot 19^{2}\cdot 113$ |
$3$ |
$28.4234248775$ |
$92.67146270562476$ |
|
|
|
$D_{4}$ (as 4T3) |
$[10]$ |
$[10]$ |
$4$ |
$1$ |
$5.315574948$ |
| 4.0.654493.1 |
$x^{4} - 2 x^{3} + 30 x^{2} - 29 x + 842$ |
$4$ |
[0,2] |
$7^{2}\cdot 19^{2}\cdot 37$ |
$3$ |
$28.443055682$ |
$70.14983962918234$ |
|
|
|
$D_{4}$ (as 4T3) |
$[10]$ |
$[10]$ |
$2$ |
$1$ |
$5.44487429969$ |
