| 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 |
| 4.2.1203079.1 |
$x^{4} - x^{3} - 3 x^{2} - 23 x - 62$ |
$4$ |
[2,1] |
$-\,31\cdot 197^{2}$ |
$2$ |
$33.1187194722$ |
$78.14729681825213$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$39.2755762981$ |
| 4.0.4540653.1 |
$x^{4} - x^{3} - 344 x^{2} + 246 x + 31557$ |
$4$ |
[0,2] |
$3^{2}\cdot 13\cdot 197^{2}$ |
$3$ |
$46.1614644893$ |
$87.6527238595584$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2]$ |
$6$ |
$1$ |
$129.461094843$ |
| 4.0.4851125.1 |
$x^{4} - x^{3} + 246 x^{2} - 246 x + 12251$ |
$4$ |
[0,2] |
$5^{3}\cdot 197^{2}$ |
$2$ |
$46.9310873285$ |
$46.9310873285213$ |
✓ |
✓ |
|
$C_4$ (as 4T1) |
$[26]$ |
$[26]$ |
$2$ |
$1$ |
$0.962423650119$ |
| 4.0.7334901.1 |
$x^{4} - x^{3} + 444 x^{2} - 148 x + 50863$ |
$4$ |
[0,2] |
$3^{3}\cdot 7\cdot 197^{2}$ |
$3$ |
$52.0413512096$ |
$84.64924211658628$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2]$ |
$6$ |
$1$ |
$75.8875564519$ |
| 4.2.9896295.1 |
$x^{4} - x^{3} - x^{2} - 24 x - 15$ |
$4$ |
[2,1] |
$-\,3\cdot 5\cdot 17\cdot 197^{2}$ |
$4$ |
$56.087768062798226$ |
$224.13165773714343$ |
|
|
✓ |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$252.38274521091657$ |
| 4.2.10672475.1 |
$x^{4} - x^{3} + 49 x^{2} + 345 x - 26755$ |
$4$ |
[2,1] |
$-\,5^{2}\cdot 11\cdot 197^{2}$ |
$3$ |
$57.1565868339$ |
$104.09130607308182$ |
|
|
? |
$D_{4}$ (as 4T3) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$73.4581840635$ |
| 4.2.10982947.1 |
$x^{4} - x^{3} - 28 x^{2} + 88 x - 136$ |
$4$ |
[2,1] |
$-\,197^{2}\cdot 283$ |
$2$ |
$57.5678118112$ |
$236.1164966706054$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2, 2]$ |
$2$ |
$2$ |
$324.54416698999574$ |
| 4.2.10982947.2 |
$x^{4} - x^{3} + 6 x^{2} - 126 x - 81$ |
$4$ |
[2,1] |
$-\,197^{2}\cdot 283$ |
$2$ |
$57.5678118112$ |
$236.1164966706054$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2, 2]$ |
$2$ |
$2$ |
$99.78620864613316$ |
| 4.2.16765488.1 |
$x^{4} - 2 x^{3} - 42 x^{2} - 154 x - 178$ |
$4$ |
[2,1] |
$-\,2^{4}\cdot 3^{3}\cdot 197^{2}$ |
$3$ |
$63.9888123745$ |
$113.52100794287168$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$256.234299174$ |
| 4.0.16765488.1 |
$x^{4} - 591 x^{2} + 116427$ |
$4$ |
[0,2] |
$2^{4}\cdot 3^{3}\cdot 197^{2}$ |
$3$ |
$63.9888123745$ |
$90.4938463000974$ |
|
|
|
$D_{4}$ (as 4T3) |
$[14]$ |
$[14]$ |
$6$ |
$1$ |
$34.8177590578$ |
| 4.2.17075960.1 |
$x^{4} - x^{3} + 18 x^{2} - 132 x + 88$ |
$4$ |
[2,1] |
$-\,2^{3}\cdot 5\cdot 11\cdot 197^{2}$ |
$4$ |
$64.28302156705452$ |
$294.41467354736244$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$734.2573331651118$ |
| 4.2.17502859.1 |
$x^{4} - x^{3} - 11 x^{2} - 19 x - 33$ |
$4$ |
[2,1] |
$-\,11\cdot 41\cdot 197^{2}$ |
$3$ |
$64.6810778711539$ |
$298.0721389194233$ |
|
|
✓ |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$170.66101527352376$ |
| 4.0.18356657.1 |
$x^{4} - x^{3} + 40 x^{2} - 143 x + 158$ |
$4$ |
[0,2] |
$11\cdot 43\cdot 197^{2}$ |
$3$ |
$65.45583965295621$ |
$305.2556305787004$ |
|
|
? |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$137.40937540555322$ |
| 4.2.19676163.1 |
$x^{4} - x^{3} + 48 x^{2} - 344 x - 7153$ |
$4$ |
[2,1] |
$-\,3\cdot 13^{2}\cdot 197^{2}$ |
$3$ |
$66.6016675331$ |
$87.6527238595584$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$154.675354188$ |
| 4.0.19909017.1 |
$x^{4} - x^{3} - 738 x^{2} + 443 x + 138331$ |
$4$ |
[0,2] |
$3^{3}\cdot 19\cdot 197^{2}$ |
$3$ |
$66.7978454087$ |
$139.4603833287107$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2]$ |
$6$ |
$1$ |
$179.481029413$ |
| 4.2.20141871.1 |
$x^{4} - x^{3} - 26 x^{2} + 87 x - 114$ |
$4$ |
[2,1] |
$-\,3\cdot 173\cdot 197^{2}$ |
$3$ |
$66.99230989791619$ |
$319.75459339937555$ |
|
|
? |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$177.2412074796543$ |
| 4.2.21733040.1 |
$x^{4} - 2 x^{3} - 56 x^{2} - 140 x - 25$ |
$4$ |
[2,1] |
$-\,2^{4}\cdot 5\cdot 7\cdot 197^{2}$ |
$4$ |
$68.27789443943404$ |
$186.40982419416795$ |
|
|
? |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$207.05079448968954$ |
| 4.0.23479445.1 |
$x^{4} - x^{3} - 146 x^{2} + 344 x + 12153$ |
$4$ |
[0,2] |
$5\cdot 11^{2}\cdot 197^{2}$ |
$3$ |
$69.6100517687$ |
$104.09130607308182$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$152.65249156$ |
| 4.2.23595872.1 |
$x^{4} - 2 x^{3} - 32 x^{2} - 164 x - 1156$ |
$4$ |
[2,1] |
$-\,2^{5}\cdot 19\cdot 197^{2}$ |
$3$ |
$69.69618522085375$ |
$244.72024844707886$ |
|
|
? |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$397.50284943773624$ |
| 4.0.24100389.1 |
$x^{4} + 24 x^{2} - 197 x + 735$ |
$4$ |
[0,2] |
$3^{3}\cdot 23\cdot 197^{2}$ |
$3$ |
$70.06578839194334$ |
$242.5149381534379$ |
|
|
? |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$130.62405873267417$ |
| 4.2.25148232.2 |
$x^{4} - x^{3} - 15 x^{2} - 17 x + 92$ |
$4$ |
[2,1] |
$-\,2^{3}\cdot 3^{4}\cdot 197^{2}$ |
$3$ |
$70.8152617179$ |
$171.76701937848316$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$1236.4300927250763$ |
| 4.0.27049873.2 |
$x^{4} - x^{3} + 15 x^{2} - 32 x + 39$ |
$4$ |
[0,2] |
$17\cdot 41\cdot 197^{2}$ |
$3$ |
$72.11760700607702$ |
$370.55229050702144$ |
|
|
✓ |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$175.87951781152566$ |
| 4.0.29339604.1 |
$x^{4} - x^{3} - 60 x^{2} + 104 x + 1360$ |
$4$ |
[0,2] |
$2^{2}\cdot 3^{3}\cdot 7\cdot 197^{2}$ |
$4$ |
$73.59758468481016$ |
$212.37835896173453$ |
|
|
? |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$505.65411814317895$ |
| 4.2.30076975.1 |
$x^{4} - x^{3} + 49 x^{2} - 640 x - 75020$ |
$4$ |
[2,1] |
$-\,5^{2}\cdot 31\cdot 197^{2}$ |
$3$ |
$74.0557080676$ |
$174.7426679434648$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$149.080665214$ |
| 4.0.30465065.1 |
$x^{4} - x^{3} + 67 x^{2} - 58 x + 15$ |
$4$ |
[0,2] |
$5\cdot 157\cdot 197^{2}$ |
$3$ |
$74.29345015606711$ |
$393.24928480545265$ |
|
|
? |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$409.08447095093356$ |
| 4.2.33492167.1 |
$x^{4} - 49 x^{2} - 197 x - 237$ |
$4$ |
[2,1] |
$-\,197^{2}\cdot 863$ |
$2$ |
$76.07392288884505$ |
$412.32390180536464$ |
|
|
✓ |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$189.1010154784856$ |
| 4.2.33647403.1 |
$x^{4} - x^{3} - 45 x^{2} - 199 x + 595$ |
$4$ |
[2,1] |
$-\,3\cdot 17^{2}\cdot 197^{2}$ |
$3$ |
$76.16192063326771$ |
$160.7285479973713$ |
|
|
? |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$361.43093059689727$ |
| 4.2.35238572.1 |
$x^{4} - x^{3} + 35 x^{2} - 633 x + 1764$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 197^{2}\cdot 227$ |
$3$ |
$77.04679457503622$ |
$335.68559525320364$ |
|
|
? |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$363.867659022148$ |
| 4.0.36480460.1 |
$x^{4} - 2 x^{3} + 78 x^{2} + 120 x + 448$ |
$4$ |
[0,2] |
$2^{2}\cdot 5\cdot 47\cdot 197^{2}$ |
$4$ |
$77.71682976294016$ |
$430.32545822900136$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$995.3121657700098$ |
| 4.2.37411876.1 |
$x^{4} - x^{3} - 3 x^{2} - 220 x + 726$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 197^{2}\cdot 241$ |
$3$ |
$78.20821459620754$ |
$435.7843503385591$ |
|
|
? |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$538.2803848134149$ |
| 4.2.37683539.1 |
$x^{4} - x^{3} + 61 x^{2} - 252 x - 324$ |
$4$ |
[2,1] |
$-\,197^{2}\cdot 971$ |
$2$ |
$78.34980511557036$ |
$437.3636930519039$ |
|
|
? |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$559.4422574231659$ |
| 4.2.37722348.1 |
$x^{4} - x^{3} + 51 x^{2} - 247 x - 1046$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 3^{5}\cdot 197^{2}$ |
$3$ |
$78.369969782$ |
$166.9713956089313$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$557.6370543399253$ |
| 4.2.37722348.4 |
$x^{4} - x^{3} + 54 x^{2} - 150 x + 42$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 3^{5}\cdot 197^{2}$ |
$3$ |
$78.369969782$ |
$166.9713956089313$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$615.4469664262067$ |
| 4.0.38537337.1 |
$x^{4} - x^{3} - 51 x^{2} + x + 986$ |
$4$ |
[0,2] |
$3\cdot 197^{2}\cdot 331$ |
$3$ |
$78.78987749131204$ |
$442.29062843338653$ |
|
|
? |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$329.1506177428737$ |
| 4.2.38653764.1 |
$x^{4} - x^{3} - 15 x^{2} + 180 x + 486$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 3\cdot 83\cdot 197^{2}$ |
$4$ |
$78.8493191612676$ |
$442.958237309117$ |
|
|
? |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$823.8957906457066$ |
| 4.0.39429944.2 |
$x^{4} - x^{3} + 31 x^{2} - 40 x + 24$ |
$4$ |
[0,2] |
$2^{3}\cdot 127\cdot 197^{2}$ |
$3$ |
$79.24220286880366$ |
$447.38350438969024$ |
|
|
? |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$290.714014357187$ |
| 4.2.41409203.1 |
$x^{4} - x^{3} - x^{2} - 24 x - 212$ |
$4$ |
[2,1] |
$-\,11\cdot 97\cdot 197^{2}$ |
$3$ |
$80.21844108805695$ |
$458.47464488235335$ |
|
|
? |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$628.3556827519099$ |
| 4.2.41913720.1 |
$x^{4} - 2 x^{3} + 39 x^{2} + 356 x - 1018$ |
$4$ |
[2,1] |
$-\,2^{3}\cdot 3^{3}\cdot 5\cdot 197^{2}$ |
$4$ |
$80.46167180534508$ |
$319.8192294503278$ |
|
|
? |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$471.88704107334075$ |
| 4.0.42224192.1 |
$x^{4} - 2 x^{3} + 493 x^{2} - 98 x + 41407$ |
$4$ |
[0,2] |
$2^{6}\cdot 17\cdot 197^{2}$ |
$3$ |
$80.6102627832$ |
$163.682619724881$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[78]$ |
$[78]$ |
$2$ |
$1$ |
$1.76274717404$ |
| 4.0.42224192.2 |
$x^{4} - 2 x^{3} - 293 x^{2} - 100 x + 41506$ |
$4$ |
[0,2] |
$2^{6}\cdot 17\cdot 197^{2}$ |
$3$ |
$80.6102627832$ |
$163.682619724881$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$440.192576466$ |
| 4.2.43000372.1 |
$x^{4} - x^{3} + 64 x^{2} - 549 x + 385$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 197^{2}\cdot 277$ |
$3$ |
$80.97818773580164$ |
$467.2001712328453$ |
|
|
? |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$387.6053146820535$ |
| 4.4.43660125.1 |
$x^{4} - x^{3} - 739 x^{2} + 739 x + 108781$ |
$4$ |
[4,0] |
$3^{2}\cdot 5^{3}\cdot 197^{2}$ |
$3$ |
$81.2870277075$ |
$81.28702770745083$ |
|
✓ |
|
$C_4$ (as 4T1) |
$[2]$ |
$[2, 2]$ |
$2$ |
$3$ |
$153.101560249$ |
| 4.2.44513923.1 |
$x^{4} - 2 x^{3} + 30 x^{2} + 365 x - 2006$ |
$4$ |
[2,1] |
$-\,31\cdot 37\cdot 197^{2}$ |
$3$ |
$81.68154946754612$ |
$475.35144893015735$ |
|
|
? |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$487.35419169822256$ |
| 4.2.47657452.1 |
$x^{4} - x^{3} - 89 x^{2} + 217 x + 2764$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 197^{2}\cdot 307$ |
$3$ |
$83.08692854093526$ |
$390.3812628100689$ |
|
|
? |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$1011.2772595188136$ |
| 4.2.48550059.1 |
$x^{4} - x^{3} - 76 x^{2} + 112 x + 1315$ |
$4$ |
[2,1] |
$-\,3^{2}\cdot 139\cdot 197^{2}$ |
$3$ |
$83.47327259924576$ |
$286.61646847311476$ |
|
|
? |
$S_4$ (as 4T5) |
$[2]$ |
$[2, 2]$ |
$2$ |
$2$ |
$93.49025922249555$ |
| 4.2.48860531.1 |
$x^{4} - x^{3} + 34 x^{2} - 337 x + 491$ |
$4$ |
[2,1] |
$-\,197^{2}\cdot 1259$ |
$2$ |
$83.60640423848407$ |
$498.019075939868$ |
|
|
? |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$756.7710095737158$ |
| 4.2.50141228.1 |
$x^{4} - x^{3} + 65 x^{2} - 57 x - 494$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 17\cdot 19\cdot 197^{2}$ |
$4$ |
$84.14895779337319$ |
$400.42486517662877$ |
|
|
? |
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$763.4893659321219$ |
| 4.2.50451700.1 |
$x^{4} - x^{3} + 6 x^{2} - 126 x + 116$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 5^{2}\cdot 13\cdot 197^{2}$ |
$4$ |
$84.27891796092341$ |
$295.9475764198457$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$1031.713368383188$ |
| 4.0.50606936.1 |
$x^{4} - x^{3} + 59 x^{2} - 251 x + 552$ |
$4$ |
[0,2] |
$2^{3}\cdot 163\cdot 197^{2}$ |
$3$ |
$84.34367322802291$ |
$506.84119800979084$ |
|
|
|
$S_4$ (as 4T5) |
$[18]$ |
$[18]$ |
$2$ |
$1$ |
$122.26469382460319$ |
| 4.2.51344307.1 |
$x^{4} - x^{3} - 150 x^{2} - 442 x - 7349$ |
$4$ |
[2,1] |
$-\,3^{3}\cdot 7^{2}\cdot 197^{2}$ |
$3$ |
$84.6492421166$ |
$84.64924211658628$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2, 2]$ |
$2$ |
$2$ |
$118.900565545$ |
