| 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 $p$ |
| 4.4.3524845.1 |
$x^{4} - x^{3} - 33 x^{2} + 50 x + 8$ |
$4$ |
(4, 0) |
$5\cdot 89^{3}$ |
$2$ |
$43.3296325482$ |
$64.79291322178058$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$260.008334664$ |
$4$ |
$89$ |
| 4.0.6344721.1 |
$x^{4} - x^{3} + 56 x^{2} + 139 x + 1165$ |
$4$ |
(0, 2) |
$3^{2}\cdot 89^{3}$ |
$2$ |
$50.188374772$ |
$50.18837477204371$ |
✓ |
✓ |
|
$C_4$ (as 4T1) |
$[10]$ |
$[10]$ |
$2$ |
$1$ |
$13.815512558$ |
$0$ |
$89$ |
| 4.0.11984473.1 |
$x^{4} - x^{3} + 56 x^{2} + 228 x + 720$ |
$4$ |
(0, 2) |
$17\cdot 89^{3}$ |
$2$ |
$58.8375709925$ |
$119.47222879314523$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[86]$ |
$[86]$ |
$2$ |
$1$ |
$13.815512558$ |
$0$ |
$89$ |
| 4.2.14099380.1 |
$x^{4} - x^{3} - 33 x^{2} - 395 x - 1772$ |
$4$ |
(2, 1) |
$-\,2^{2}\cdot 5\cdot 89^{3}$ |
$3$ |
$61.2773540024$ |
$129.58582644356116$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2, 4]$ |
$[2, 4]$ |
$2$ |
$2$ |
$127.572998353$ |
$2$ |
$89$ |
| 4.2.14099380.2 |
$x^{4} - x^{3} - 33 x^{2} - 128 x - 170$ |
$4$ |
(2, 1) |
$-\,2^{2}\cdot 5\cdot 89^{3}$ |
$3$ |
$61.2773540024$ |
$129.58582644356116$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$2$ |
$82.6323315228$ |
$2$ |
$89$ |
| 4.4.17624225.1 |
$x^{4} - 2 x^{3} - 43 x^{2} + 44 x + 39$ |
$4$ |
(4, 0) |
$5^{2}\cdot 89^{3}$ |
$2$ |
$64.7929132218$ |
$64.79291322178058$ |
|
|
|
$D_{4}$ (as 4T3) |
$[4]$ |
$[8]$ |
$2$ |
$3$ |
$229.362116899$ |
$3$ |
$89$ |
| 4.2.25378884.1 |
$x^{4} - 801$ |
$4$ |
(2, 1) |
$-\,2^{2}\cdot 3^{2}\cdot 89^{3}$ |
$3$ |
$70.9770802761$ |
$100.37674954408742$ |
|
|
|
$D_{4}$ (as 4T3) |
$[10]$ |
$[2, 10]$ |
$2$ |
$2$ |
$168.427156715$ |
$1$ |
$89$ |
| 4.2.28198760.1 |
$x^{4} - x^{3} - 33 x^{2} + 317 x - 1060$ |
$4$ |
(2, 1) |
$-\,2^{3}\cdot 5\cdot 89^{3}$ |
$3$ |
$72.8714653682$ |
$183.26203324781025$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2, 14]$ |
$[2, 14]$ |
$2$ |
$2$ |
$70.3129307989$ |
$2$ |
$89$ |
| 4.2.28198760.2 |
$x^{4} - x^{3} + 56 x^{2} + 317 x + 97$ |
$4$ |
(2, 1) |
$-\,2^{3}\cdot 5\cdot 89^{3}$ |
$3$ |
$72.8714653682$ |
$183.26203324781025$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2, 2]$ |
$[2, 4]$ |
$2$ |
$2$ |
$117.615600097$ |
$1$ |
$89$ |
| 4.0.28198760.1 |
$x^{4} + 89 x^{2} + 890$ |
$4$ |
(0, 2) |
$2^{3}\cdot 5\cdot 89^{3}$ |
$3$ |
$72.8714653682$ |
$183.26203324781025$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[2, 10]$ |
$[2, 10]$ |
$2$ |
$1$ |
$13.815512558$ |
$0$ |
$89$ |
| 4.0.28198760.2 |
$x^{4} - x^{3} + 145 x^{2} + 139 x + 6416$ |
$4$ |
(0, 2) |
$2^{3}\cdot 5\cdot 89^{3}$ |
$3$ |
$72.8714653682$ |
$183.26203324781025$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[2, 24]$ |
$[2, 24]$ |
$2$ |
$1$ |
$13.815512558$ |
$0$ |
$89$ |
| 4.2.33133543.1 |
$x^{4} - x^{3} - 33 x^{2} - 306 x - 1060$ |
$4$ |
(2, 1) |
$-\,47\cdot 89^{3}$ |
$2$ |
$75.8694558909$ |
$198.6513102785702$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$136.221973724$ |
$2$ |
$89$ |
| 4.0.34543481.1 |
$x^{4} - x^{3} + 145 x^{2} + 317 x + 5170$ |
$4$ |
(0, 2) |
$7^{2}\cdot 89^{3}$ |
$2$ |
$76.6640087999$ |
$76.66400879990078$ |
✓ |
✓ |
|
$C_4$ (as 4T1) |
$[218]$ |
$[218]$ |
$2$ |
$1$ |
$13.815512558$ |
$0$ |
$89$ |
| 4.0.37363357.1 |
$x^{4} - 2 x^{3} + 46 x^{2} - 45 x + 306$ |
$4$ |
(0, 2) |
$53\cdot 89^{3}$ |
$2$ |
$78.1828454381$ |
$210.95044204720455$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[66]$ |
$[66]$ |
$2$ |
$1$ |
$13.815512558$ |
$0$ |
$89$ |
| 4.2.38773295.1 |
$x^{4} - x^{3} + 56 x^{2} - 484 x - 704$ |
$4$ |
(2, 1) |
$-\,5\cdot 11\cdot 89^{3}$ |
$3$ |
$78.9102060401$ |
$214.89378223070364$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$2$ |
$689.0995578168763$ |
$2$ |
$89$ |
| 4.2.38773295.2 |
$x^{4} - 2 x^{3} - 43 x^{2} + 44 x - 317$ |
$4$ |
(2, 1) |
$-\,5\cdot 11\cdot 89^{3}$ |
$3$ |
$78.9102060401$ |
$214.89378223070364$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$2$ |
$63.28222558410435$ |
$2$ |
$89$ |
| 4.0.40183233.1 |
$x^{4} - x^{3} - 33 x^{2} - 39 x + 720$ |
$4$ |
(0, 2) |
$3\cdot 19\cdot 89^{3}$ |
$3$ |
$79.617991745$ |
$218.7660537718847$ |
|
|
|
$S_4$ (as 4T5) |
$[8]$ |
$[8]$ |
$2$ |
$1$ |
$135.93801982088496$ |
$0$ |
$89$ |
| 4.2.45118016.1 |
$x^{4} - 356 x - 1869$ |
$4$ |
(2, 1) |
$-\,2^{6}\cdot 89^{3}$ |
$2$ |
$81.9572728074$ |
$115.90508673931703$ |
|
|
|
$S_4$ (as 4T5) |
$[8]$ |
$[8]$ |
$2$ |
$2$ |
$186.017244445$ |
$2$ |
$89$ |
| 4.2.47937892.1 |
$x^{4} + 89 x^{2} - 6052$ |
$4$ |
(2, 1) |
$-\,2^{2}\cdot 17\cdot 89^{3}$ |
$3$ |
$83.2088908747$ |
$238.94445758629047$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2, 2]$ |
$2$ |
$2$ |
$336.73294139245064$ |
$1$ |
$89$ |
| 4.2.47937892.2 |
$x^{4} - x^{3} - 33 x^{2} + 228 x - 526$ |
$4$ |
(2, 1) |
$-\,2^{2}\cdot 17\cdot 89^{3}$ |
$3$ |
$83.2088908747$ |
$238.94445758629047$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2, 2]$ |
$2$ |
$2$ |
$189.6479992409217$ |
$1$ |
$89$ |
| 4.2.50052799.1 |
$x^{4} - x^{3} - 33 x^{2} + 406 x - 1772$ |
$4$ |
(2, 1) |
$-\,71\cdot 89^{3}$ |
$2$ |
$84.111831985$ |
$244.1584050846206$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$106.875473637$ |
$2$ |
$89$ |
| 4.2.50757768.1 |
$x^{4} - x^{3} + 56 x^{2} - 395 x + 97$ |
$4$ |
(2, 1) |
$-\,2^{3}\cdot 3^{2}\cdot 89^{3}$ |
$3$ |
$84.4064488664$ |
$141.9541605521758$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2, 2]$ |
$2$ |
$2$ |
$315.285724259$ |
$1$ |
$89$ |
| 4.4.50757768.1 |
$x^{4} - x^{3} - 211 x^{2} + 673 x + 5170$ |
$4$ |
(4, 0) |
$2^{3}\cdot 3^{2}\cdot 89^{3}$ |
$3$ |
$84.4064488664$ |
$141.9541605521758$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2, 2]$ |
$2$ |
$3$ |
$1488.35498025$ |
$3$ |
$89$ |
| 4.2.55692551.1 |
$x^{4} - x^{3} + 145 x^{2} + 762 x - 1060$ |
$4$ |
(2, 1) |
$-\,79\cdot 89^{3}$ |
$2$ |
$86.3871761337$ |
$257.54673622371917$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$411.61353804$ |
$2$ |
$89$ |
| 4.2.55692551.2 |
$x^{4} - x^{3} - 33 x^{2} + 50 x + 275$ |
$4$ |
(2, 1) |
$-\,79\cdot 89^{3}$ |
$2$ |
$86.3871761337$ |
$257.54673622371917$ |
|
|
|
$S_4$ (as 4T5) |
$[4]$ |
$[4]$ |
$2$ |
$2$ |
$128.746214167$ |
$2$ |
$89$ |
| 4.0.56397520.1 |
$x^{4} + 89 x^{2} + 1780$ |
$4$ |
(0, 2) |
$2^{4}\cdot 5\cdot 89^{3}$ |
$3$ |
$86.6592650965$ |
$129.58582644356116$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[2, 2, 18]$ |
$[2, 2, 18]$ |
$2$ |
$1$ |
$13.815512558$ |
$0$ |
$89$ |
| 4.2.69791931.1 |
$x^{4} - 2 x^{3} - 132 x^{2} + 133 x - 584$ |
$4$ |
(2, 1) |
$-\,3^{2}\cdot 11\cdot 89^{3}$ |
$3$ |
$91.4010749958$ |
$166.4560079566077$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2, 2]$ |
$2$ |
$2$ |
$400.382081705$ |
$1$ |
$89$ |
| 4.2.75431683.1 |
$x^{4} - 2 x^{3} + 46 x^{2} - 45 x - 584$ |
$4$ |
(2, 1) |
$-\,89^{3}\cdot 107$ |
$2$ |
$93.1941066119$ |
$299.7328849502087$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$491.896768125$ |
$2$ |
$107$ |
| 4.0.76841621.1 |
$x^{4} - 2 x^{3} + 224 x^{2} - 223 x + 662$ |
$4$ |
(0, 2) |
$89^{3}\cdot 109$ |
$2$ |
$93.6265734768$ |
$302.52115787508336$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[38]$ |
$[38]$ |
$2$ |
$1$ |
$13.815512558$ |
$0$ |
$109$ |
| 4.0.88121125.1 |
$x^{4} - x^{3} + 56 x^{2} - 1196 x + 4191$ |
$4$ |
(0, 2) |
$5^{3}\cdot 89^{3}$ |
$2$ |
$96.888003818$ |
$96.8880038179619$ |
✓ |
✓ |
|
$C_4$ (as 4T1) |
$[2, 2, 40]$ |
$[2, 2, 40]$ |
$2$ |
$1$ |
$6.09356467444$ |
$0$ |
$89$ |
| 4.0.88121125.2 |
$x^{4} - x^{3} + 56 x^{2} + 584 x + 5971$ |
$4$ |
(0, 2) |
$5^{3}\cdot 89^{3}$ |
$2$ |
$96.888003818$ |
$96.8880038179619$ |
✓ |
✓ |
|
$C_4$ (as 4T1) |
$[4, 4, 4]$ |
$[4, 4, 4]$ |
$2$ |
$1$ |
$6.09356467444$ |
$0$ |
$89$ |
| 4.2.92350939.1 |
$x^{4} - x^{3} - 122 x^{2} + 1207 x - 12541$ |
$4$ |
(2, 1) |
$-\,89^{3}\cdot 131$ |
$2$ |
$98.030299367$ |
$331.64858814511473$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$431.81318956$ |
$2$ |
$131$ |
| 4.2.95875784.1 |
$x^{4} - 178 x^{2} - 12104$ |
$4$ |
(2, 1) |
$-\,2^{3}\cdot 17\cdot 89^{3}$ |
$3$ |
$98.9526050597$ |
$337.9184925724148$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2, 2]$ |
$2$ |
$2$ |
$2040.2860750432321$ |
$1$ |
$89$ |
| 4.2.95875784.2 |
$x^{4} + 89 x^{2} - 3026$ |
$4$ |
(2, 1) |
$-\,2^{3}\cdot 17\cdot 89^{3}$ |
$3$ |
$98.9526050597$ |
$337.9184925724148$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2, 2]$ |
$2$ |
$2$ |
$1006.988363539413$ |
$1$ |
$89$ |
| 4.4.95875784.1 |
$x^{4} - x^{3} - 122 x^{2} - 395 x + 275$ |
$4$ |
(4, 0) |
$2^{3}\cdot 17\cdot 89^{3}$ |
$3$ |
$98.9526050597$ |
$337.9184925724148$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2, 2]$ |
$2$ |
$3$ |
$984.085660387$ |
$3$ |
$89$ |
| 4.4.95875784.2 |
$x^{4} - x^{3} - 122 x^{2} + 139 x + 2411$ |
$4$ |
(4, 0) |
$2^{3}\cdot 17\cdot 89^{3}$ |
$3$ |
$98.9526050597$ |
$337.9184925724148$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2, 2]$ |
$2$ |
$3$ |
$346.136000296$ |
$3$ |
$89$ |
| 4.0.101515536.1 |
$x^{4} - 2 x^{3} + 46 x^{2} + 222 x + 573$ |
$4$ |
(0, 2) |
$2^{4}\cdot 3^{2}\cdot 89^{3}$ |
$3$ |
$100.376749544$ |
$100.37674954408742$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2, 60]$ |
$[2, 60]$ |
$2$ |
$1$ |
$24.3823247249$ |
$0$ |
$89$ |
| 4.4.101515536.1 |
$x^{4} - 267 x^{2} + 12816$ |
$4$ |
(4, 0) |
$2^{4}\cdot 3^{2}\cdot 89^{3}$ |
$3$ |
$100.376749544$ |
$100.37674954408742$ |
|
✓ |
|
$C_4$ (as 4T1) |
$[2]$ |
$[2, 2, 2]$ |
$2$ |
$3$ |
$1789.59887096$ |
$2$ |
$89$ |
| 4.0.110680133.1 |
$x^{4} - x^{3} + 145 x^{2} + 406 x + 4280$ |
$4$ |
(0, 2) |
$89^{3}\cdot 157$ |
$2$ |
$102.569306251$ |
$363.0716435611943$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[58]$ |
$[58]$ |
$2$ |
$1$ |
$13.815512558$ |
$0$ |
$157$ |
| 4.2.112795040.1 |
$x^{4} + 89 x^{2} - 14240$ |
$4$ |
(2, 1) |
$-\,2^{5}\cdot 5\cdot 89^{3}$ |
$3$ |
$103.055814634$ |
$259.1716528871223$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2, 2]$ |
$[2, 2, 2]$ |
$2$ |
$2$ |
$399.4585274867451$ |
$1$ |
$89$ |
| 4.2.112795040.2 |
$x^{4} + 267 x^{2} - 890$ |
$4$ |
(2, 1) |
$-\,2^{5}\cdot 5\cdot 89^{3}$ |
$3$ |
$103.055814634$ |
$259.1716528871223$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2, 2]$ |
$[2, 2, 2]$ |
$2$ |
$2$ |
$211.7790844811927$ |
$1$ |
$89$ |
| 4.4.112795040.1 |
$x^{4} - 89 x^{2} + 890$ |
$4$ |
(4, 0) |
$2^{5}\cdot 5\cdot 89^{3}$ |
$3$ |
$103.055814634$ |
$259.1716528871223$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2, 2]$ |
$[2, 2, 2]$ |
$2$ |
$3$ |
$569.4615367142848$ |
$3$ |
$89$ |
| 4.4.112795040.2 |
$x^{4} - 178 x^{2} + 3560$ |
$4$ |
(4, 0) |
$2^{5}\cdot 5\cdot 89^{3}$ |
$3$ |
$103.055814634$ |
$259.1716528871223$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2, 2]$ |
$[2, 2, 2]$ |
$2$ |
$3$ |
$386.4580880256414$ |
$3$ |
$89$ |
| 4.4.119139761.1 |
$x^{4} - x^{3} - 300 x^{2} - 573 x + 13625$ |
$4$ |
(4, 0) |
$13^{2}\cdot 89^{3}$ |
$2$ |
$104.475433331$ |
$104.47543333142721$ |
|
✓ |
|
$C_4$ (as 4T1) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$423.752088707$ |
$4$ |
$89$ |
| 4.4.121959637.1 |
$x^{4} - x^{3} - 300 x^{2} + 851 x + 13625$ |
$4$ |
(4, 0) |
$89^{3}\cdot 173$ |
$2$ |
$105.088218744$ |
$381.1233494425073$ |
|
|
|
$D_{4}$ (as 4T3) |
$[6]$ |
$[6]$ |
$2$ |
$3$ |
$529.178678524$ |
$4$ |
$173$ |
| 4.2.131829203.1 |
$x^{4} - x^{3} + 56 x^{2} - 1285 x - 15923$ |
$4$ |
(2, 1) |
$-\,11\cdot 17\cdot 89^{3}$ |
$3$ |
$107.152647666$ |
$396.2445557743577$ |
|
|
|
$D_{4}$ (as 4T3) |
$[6]$ |
$[2, 6]$ |
$2$ |
$2$ |
$298.6780868986754$ |
$1$ |
$89$ |
| 4.2.131829203.2 |
$x^{4} - x^{3} - 211 x^{2} - 1018 x - 4976$ |
$4$ |
(2, 1) |
$-\,11\cdot 17\cdot 89^{3}$ |
$3$ |
$107.152647666$ |
$396.2445557743577$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2, 2]$ |
$2$ |
$2$ |
$1264.448905380041$ |
$1$ |
$89$ |
| 4.0.132534172.1 |
$x^{4} - x^{3} + 56 x^{2} + 50 x + 1432$ |
$4$ |
(0, 2) |
$2^{2}\cdot 47\cdot 89^{3}$ |
$3$ |
$107.295613491$ |
$397.3026205571404$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[2, 70]$ |
$[2, 70]$ |
$2$ |
$1$ |
$13.815512557961274$ |
$0$ |
$89$ |
| 4.4.132534172.1 |
$x^{4} - 267 x^{2} + 16732$ |
$4$ |
(4, 0) |
$2^{2}\cdot 47\cdot 89^{3}$ |
$3$ |
$107.295613491$ |
$397.3026205571404$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2, 2]$ |
$2$ |
$3$ |
$2992.059788808588$ |
$3$ |
$89$ |
| 4.2.138173924.1 |
$x^{4} - 4361$ |
$4$ |
(2, 1) |
$-\,2^{2}\cdot 7^{2}\cdot 89^{3}$ |
$3$ |
$108.419280991$ |
$153.32801759980157$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$[2, 2]$ |
$2$ |
$2$ |
$757.755023381$ |
$1$ |
$89$ |
