| 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 $p$ |
| 4.0.13771804.1 |
$x^{4} + 151$ |
$4$ |
(0, 2) |
$2^{2}\cdot 151^{3}$ |
$2$ |
$60.9182906005$ |
$86.15147276382733$ |
|
|
|
$D_{4}$ (as 4T3) |
$[21]$ |
$[21]$ |
$2$ |
$1$ |
$8.88889750369$ |
$0$ |
$151$ |
| 4.0.27543608.1 |
$x^{4} - x^{3} + 57 x^{2} - 387 x + 1034$ |
$4$ |
(0, 2) |
$2^{3}\cdot 151^{3}$ |
$2$ |
$72.4444646159$ |
$121.83658120102092$ |
|
|
|
$D_{4}$ (as 4T3) |
$[7]$ |
$[7]$ |
$2$ |
$1$ |
$129.908481881$ |
$0$ |
$151$ |
| 4.0.37872461.1 |
$x^{4} - x^{3} + 57 x^{2} + 66 x + 128$ |
$4$ |
(0, 2) |
$11\cdot 151^{3}$ |
$2$ |
$78.447820425$ |
$142.8660551470689$ |
|
|
|
$D_{4}$ (as 4T3) |
$[7]$ |
$[7]$ |
$2$ |
$1$ |
$78.4991747442$ |
$0$ |
$151$ |
| 4.0.65416069.1 |
$x^{4} - 2 x^{3} - 74 x^{2} + 75 x + 4464$ |
$4$ |
(0, 2) |
$19\cdot 151^{3}$ |
$2$ |
$89.9334203256$ |
$187.76278180736003$ |
|
|
|
$D_{4}$ (as 4T3) |
$[7]$ |
$[7]$ |
$2$ |
$1$ |
$99.3926924016$ |
$0$ |
$151$ |
| 4.0.68859020.1 |
$x^{4} - x^{3} + 57 x^{2} + 217 x + 430$ |
$4$ |
(0, 2) |
$2^{2}\cdot 5\cdot 151^{3}$ |
$3$ |
$91.0940916036$ |
$192.6405494616396$ |
|
|
|
$D_{4}$ (as 4T3) |
$[14]$ |
$[14]$ |
$2$ |
$1$ |
$118.59781086$ |
$0$ |
$151$ |
| 4.0.68859020.2 |
$x^{4} - x^{3} + 57 x^{2} - 840 x + 4658$ |
$4$ |
(0, 2) |
$2^{2}\cdot 5\cdot 151^{3}$ |
$3$ |
$91.0940916036$ |
$192.6405494616396$ |
|
|
|
$D_{4}$ (as 4T3) |
$[14]$ |
$[14]$ |
$2$ |
$1$ |
$36.8370970425$ |
$0$ |
$151$ |
| 4.0.106731481.1 |
$x^{4} - x^{3} - 94 x^{2} + 519 x + 5715$ |
$4$ |
(0, 2) |
$31\cdot 151^{3}$ |
$2$ |
$101.641984061$ |
$239.83554992987953$ |
|
|
|
$D_{4}$ (as 4T3) |
$[21]$ |
$[21]$ |
$2$ |
$1$ |
$37.5556981859$ |
$0$ |
$151$ |
| 4.0.110174432.1 |
$x^{4} + 151 x^{2} + 7550$ |
$4$ |
(0, 2) |
$2^{5}\cdot 151^{3}$ |
$2$ |
$102.451944379$ |
$172.30294552765466$ |
|
|
|
$D_{4}$ (as 4T3) |
$[42]$ |
$[42]$ |
$2$ |
$1$ |
$18.5888776843$ |
$0$ |
$151$ |
| 4.0.123946236.1 |
$x^{4} + 1359$ |
$4$ |
(0, 2) |
$2^{2}\cdot 3^{2}\cdot 151^{3}$ |
$3$ |
$105.51357443$ |
$149.21872797383526$ |
|
|
|
$D_{4}$ (as 4T3) |
$[14]$ |
$[14]$ |
$2$ |
$1$ |
$246.001042671$ |
$0$ |
$151$ |
| 4.0.148046893.1 |
$x^{4} - x^{3} + 57 x^{2} - 991 x + 6470$ |
$4$ |
(0, 2) |
$43\cdot 151^{3}$ |
$2$ |
$110.306174797$ |
$282.46649321343796$ |
|
|
|
$D_{4}$ (as 4T3) |
$[7]$ |
$[7]$ |
$2$ |
$1$ |
$229.260325498$ |
$0$ |
$151$ |
| 4.0.161818697.1 |
$x^{4} - 2 x^{3} + 77 x^{2} - 76 x + 11108$ |
$4$ |
(0, 2) |
$47\cdot 151^{3}$ |
$2$ |
$112.786514323$ |
$295.31237029232904$ |
|
|
|
$D_{4}$ (as 4T3) |
$[63]$ |
$[63]$ |
$2$ |
$1$ |
$64.0057733079$ |
$0$ |
$151$ |
| 4.2.165261648.1 |
$x^{4} - 2 x^{3} - 74 x^{2} - 378 x - 519$ |
$4$ |
(2, 1) |
$-\,2^{4}\cdot 3\cdot 151^{3}$ |
$3$ |
$113.38171448205759$ |
$211.0271488606594$ |
|
|
? |
$S_4$ (as 4T5) |
trivial |
$[2]$ |
$2$ |
$2$ |
$795.246353395955$ |
$1$ |
$151$ |
| 4.0.203134109.1 |
$x^{4} - x^{3} + 208 x^{2} - 85 x + 7225$ |
$4$ |
(0, 2) |
$59\cdot 151^{3}$ |
$2$ |
$119.38388658$ |
$330.8710093462453$ |
|
|
|
$D_{4}$ (as 4T3) |
$[7]$ |
$[7]$ |
$2$ |
$1$ |
$376.339223603$ |
$0$ |
$151$ |
| 4.0.203134109.2 |
$x^{4} - x^{3} - 94 x^{2} + 66 x + 5715$ |
$4$ |
(0, 2) |
$59\cdot 151^{3}$ |
$2$ |
$119.38388658$ |
$330.8710093462453$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$[2]$ |
$2$ |
$1$ |
$312.7961341783113$ |
$0$ |
$151$ |
| 4.0.220348864.1 |
$x^{4} + 604$ |
$4$ |
(0, 2) |
$2^{6}\cdot 151^{3}$ |
$2$ |
$121.836581201$ |
$172.30294552765466$ |
|
|
|
$D_{4}$ (as 4T3) |
$[14]$ |
$[14]$ |
$2$ |
$1$ |
$142.656513019$ |
$0$ |
$151$ |
| 4.2.306422639.1 |
$x^{4} - x^{3} - 94 x^{2} + 519 x - 778$ |
$4$ |
(2, 1) |
$-\,89\cdot 151^{3}$ |
$2$ |
$132.306204873$ |
$406.3756842764177$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$[2]$ |
$2$ |
$2$ |
$1242.8011773636524$ |
$1$ |
$151$ |
| 4.0.344295100.1 |
$x^{4} + 3775$ |
$4$ |
(0, 2) |
$2^{2}\cdot 5^{2}\cdot 151^{3}$ |
$3$ |
$136.217438856$ |
$192.6405494616396$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2, 42]$ |
$[2, 42]$ |
$2$ |
$1$ |
$51.950126919$ |
$0$ |
$151$ |
| 4.0.354623953.1 |
$x^{4} - x^{3} - 94 x^{2} + 368 x + 4960$ |
$4$ |
(0, 2) |
$103\cdot 151^{3}$ |
$2$ |
$137.227773377$ |
$437.17097762653964$ |
|
|
|
$D_{4}$ (as 4T3) |
$[7]$ |
$[7]$ |
$2$ |
$1$ |
$1182.69814786$ |
$0$ |
$151$ |
| 4.0.437254777.1 |
$x^{4} - x^{3} - 245 x^{2} - 387 x + 21872$ |
$4$ |
(0, 2) |
$127\cdot 151^{3}$ |
$2$ |
$144.605110182$ |
$485.4388954700718$ |
|
|
|
$D_{4}$ (as 4T3) |
$[21]$ |
$[21]$ |
$2$ |
$1$ |
$249.535566155$ |
$0$ |
$151$ |
| 4.0.478570189.1 |
$x^{4} - 2 x^{3} + 228 x^{2} - 227 x + 32852$ |
$4$ |
(0, 2) |
$139\cdot 151^{3}$ |
$2$ |
$147.906210625$ |
$507.8554420436319$ |
|
|
|
$D_{4}$ (as 4T3) |
$[21]$ |
$[21]$ |
$2$ |
$1$ |
$164.647381748$ |
$0$ |
$151$ |
| 4.0.495784944.1 |
$x^{4} + 151 x^{2} + 151$ |
$4$ |
(0, 2) |
$2^{4}\cdot 3^{2}\cdot 151^{3}$ |
$3$ |
$149.218727974$ |
$211.0271488606594$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[76]$ |
$[76]$ |
$2$ |
$1$ |
$10.0078025198$ |
$0$ |
$151$ |
| 4.4.495784944.1 |
$x^{4} - 151 x^{2} + 151$ |
$4$ |
(4, 0) |
$2^{4}\cdot 3^{2}\cdot 151^{3}$ |
$3$ |
$149.218727974$ |
$211.0271488606594$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$[2, 2]$ |
$2$ |
$3$ |
$1217.18362046$ |
$2$ |
$151$ |
| 4.0.550872160.1 |
$x^{4} + 302 x^{2} + 24160$ |
$4$ |
(0, 2) |
$2^{5}\cdot 5\cdot 151^{3}$ |
$3$ |
$153.20139016$ |
$385.2810989232792$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2, 14]$ |
$[2, 14]$ |
$2$ |
$1$ |
$65.82669535301129$ |
$0$ |
$151$ |
| 4.0.574972817.1 |
$x^{4} - 2 x^{3} + 77 x^{2} - 76 x + 1595$ |
$4$ |
(0, 2) |
$151^{3}\cdot 167$ |
$2$ |
$154.850220552$ |
$556.6611930330406$ |
|
|
|
$D_{4}$ (as 4T3) |
$[259]$ |
$[259]$ |
$2$ |
$1$ |
$5.05556362066$ |
$0$ |
$167$ |
| 4.2.623174131.1 |
$x^{4} - x^{3} + 208 x^{2} - 538 x - 9083$ |
$4$ |
(2, 1) |
$-\,151^{3}\cdot 181$ |
$2$ |
$157.998278189$ |
$579.5247628331216$ |
|
|
|
$S_4$ (as 4T5) |
trivial |
$[2]$ |
$2$ |
$2$ |
$639.7404276225905$ |
$1$ |
$181$ |
| 4.0.657603641.1 |
$x^{4} - 2 x^{3} + 77 x^{2} - 76 x + 45083$ |
$4$ |
(0, 2) |
$151^{3}\cdot 191$ |
$2$ |
$160.136765521$ |
$595.3185209492705$ |
|
|
|
$D_{4}$ (as 4T3) |
$[7]$ |
$[7]$ |
$2$ |
$1$ |
$124.04465646$ |
$0$ |
$191$ |
| 4.0.674818396.1 |
$x^{4} + 7399$ |
$4$ |
(0, 2) |
$2^{2}\cdot 7^{2}\cdot 151^{3}$ |
$3$ |
$161.174647224$ |
$227.93537201504154$ |
|
|
|
$D_{4}$ (as 4T3) |
$[28]$ |
$[28]$ |
$2$ |
$1$ |
$121.27763197450287$ |
$0$ |
$151$ |
| 4.2.678261347.1 |
$x^{4} - 1963 x + 2869$ |
$4$ |
(2, 1) |
$-\,151^{3}\cdot 197$ |
$2$ |
$161.379834969$ |
$604.5967712238396$ |
|
|
|
$S_4$ (as 4T5) |
trivial |
$[2]$ |
$2$ |
$2$ |
$851.7742177782276$ |
$1$ |
$197$ |
| 4.0.740234465.1 |
$x^{4} - 2 x^{3} + 77 x^{2} - 76 x + 2048$ |
$4$ |
(0, 2) |
$5\cdot 43\cdot 151^{3}$ |
$3$ |
$164.946204044$ |
$631.6142801912303$ |
|
|
|
$D_{4}$ (as 4T3) |
$[14]$ |
$[14]$ |
$2$ |
$1$ |
$447.1933449502414$ |
$0$ |
$151$ |
| 4.0.767778073.1 |
$x^{4} - x^{3} - 94 x^{2} - 840 x + 9792$ |
$4$ |
(0, 2) |
$151^{3}\cdot 223$ |
$2$ |
$166.459630486$ |
$643.2579198581537$ |
|
|
|
$D_{4}$ (as 4T3) |
$[7]$ |
$[7]$ |
$2$ |
$1$ |
$1632.8928351$ |
$0$ |
$223$ |
| 4.0.781549877.1 |
$x^{4} - x^{3} + 57 x^{2} - 1142 x + 8584$ |
$4$ |
(0, 2) |
$151^{3}\cdot 227$ |
$2$ |
$167.201117122$ |
$649.0014081029527$ |
|
|
|
$D_{4}$ (as 4T3) |
$[7]$ |
$[7]$ |
$2$ |
$1$ |
$455.50491938$ |
$0$ |
$227$ |
| 4.0.798764632.1 |
$x^{4} + 302 x^{2} + 35032$ |
$4$ |
(0, 2) |
$2^{3}\cdot 29\cdot 151^{3}$ |
$3$ |
$168.114319387$ |
$656.1100693053232$ |
|
|
|
$D_{4}$ (as 4T3) |
$[28]$ |
$[28]$ |
$2$ |
$1$ |
$71.43473311719755$ |
$0$ |
$151$ |
| 4.0.822865289.1 |
$x^{4} - x^{3} + 208 x^{2} - 236 x + 7376$ |
$4$ |
(0, 2) |
$151^{3}\cdot 239$ |
$2$ |
$169.368322346$ |
$665.9347239014834$ |
|
|
|
$D_{4}$ (as 4T3) |
$[7]$ |
$[7]$ |
$2$ |
$1$ |
$1165.35701815$ |
$0$ |
$239$ |
| 4.0.864180701.1 |
$x^{4} - 2 x^{3} - 74 x^{2} + 75 x + 2350$ |
$4$ |
(0, 2) |
$151^{3}\cdot 251$ |
$2$ |
$171.455389356$ |
$682.4480092108661$ |
|
|
|
$D_{4}$ (as 4T3) |
$[7]$ |
$[7]$ |
$2$ |
$1$ |
$684.274051958$ |
$0$ |
$251$ |
| 4.2.953697427.1 |
$x^{4} - x^{3} - 245 x^{2} - 1897 x - 4553$ |
$4$ |
(2, 1) |
$-\,151^{3}\cdot 277$ |
$2$ |
$175.732728748$ |
$716.9231346258965$ |
|
|
|
$S_4$ (as 4T5) |
trivial |
$[2]$ |
$2$ |
$2$ |
$1299.871590559207$ |
$1$ |
$277$ |
| 4.0.1015670545.1 |
$x^{4} - 2 x^{3} + 77 x^{2} - 76 x + 2803$ |
$4$ |
(0, 2) |
$5\cdot 59\cdot 151^{3}$ |
$3$ |
$178.520549295$ |
$739.8500686821726$ |
|
|
|
$D_{4}$ (as 4T3) |
$[14]$ |
$[14]$ |
$2$ |
$1$ |
$70.20171513763444$ |
$0$ |
$151$ |
| 4.0.1046657104.1 |
$x^{4} + 302 x^{2} + 71725$ |
$4$ |
(0, 2) |
$2^{4}\cdot 19\cdot 151^{3}$ |
$3$ |
$179.866840651$ |
$375.52556361472006$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2, 42]$ |
$[2, 42]$ |
$2$ |
$1$ |
$38.86135090892486$ |
$0$ |
$151$ |
| 4.0.1056985957.1 |
$x^{4} - x^{3} + 57 x^{2} + 1274 x + 11000$ |
$4$ |
(0, 2) |
$151^{3}\cdot 307$ |
$2$ |
$180.308958302$ |
$754.7478737347625$ |
|
|
|
$D_{4}$ (as 4T3) |
$[35]$ |
$[35]$ |
$2$ |
$1$ |
$185.117168339$ |
$0$ |
$307$ |
| 4.0.1070757761.1 |
$x^{4} - x^{3} + 208 x^{2} - 2501 x + 45881$ |
$4$ |
(0, 2) |
$151^{3}\cdot 311$ |
$2$ |
$180.893435847$ |
$759.6488854507203$ |
|
|
|
$D_{4}$ (as 4T3) |
$[7]$ |
$[7]$ |
$2$ |
$1$ |
$112.765293922$ |
$0$ |
$311$ |
| 4.0.1101744320.1 |
$x^{4} + 302 x^{2} + 48320$ |
$4$ |
(0, 2) |
$2^{6}\cdot 5\cdot 151^{3}$ |
$3$ |
$182.188183207$ |
$385.2810989232792$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2, 14]$ |
$[2, 14]$ |
$2$ |
$1$ |
$80.18677055552365$ |
$0$ |
$151$ |
| 4.0.1101744320.2 |
$x^{4} - 302 x^{2} + 48320$ |
$4$ |
(0, 2) |
$2^{6}\cdot 5\cdot 151^{3}$ |
$3$ |
$182.188183207$ |
$385.2810989232792$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2, 140]$ |
$[2, 140]$ |
$2$ |
$1$ |
$9.176783406681798$ |
$0$ |
$151$ |
| 4.0.1139616781.1 |
$x^{4} - x^{3} + 208 x^{2} - 840 x + 11000$ |
$4$ |
(0, 2) |
$151^{3}\cdot 331$ |
$2$ |
$183.734075695$ |
$783.694334841974$ |
|
|
|
$D_{4}$ (as 4T3) |
$[7]$ |
$[7]$ |
$2$ |
$1$ |
$939.28515237$ |
$0$ |
$331$ |
| 4.2.1160274487.1 |
$x^{4} - x^{3} - 245 x^{2} - 2350 x - 7875$ |
$4$ |
(2, 1) |
$-\,151^{3}\cdot 337$ |
$2$ |
$184.561106687$ |
$790.7654044357711$ |
|
|
|
$S_4$ (as 4T5) |
trivial |
$[2]$ |
$2$ |
$2$ |
$7046.492423563955$ |
$1$ |
$337$ |
| 4.0.1194703997.1 |
$x^{4} - 2 x^{3} - 74 x^{2} + 75 x + 3256$ |
$4$ |
(0, 2) |
$151^{3}\cdot 347$ |
$2$ |
$185.915277494$ |
$802.4120609144094$ |
|
|
|
$D_{4}$ (as 4T3) |
$[7]$ |
$[7]$ |
$2$ |
$1$ |
$638.834399236$ |
$0$ |
$347$ |
| 4.2.1270448919.1 |
$x^{4} - 2 x^{3} - 225 x^{2} + 226 x - 3539$ |
$4$ |
(2, 1) |
$-\,3^{2}\cdot 41\cdot 151^{3}$ |
$3$ |
$188.794484272$ |
$477.7330268840818$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$[2]$ |
$2$ |
$2$ |
$3062.7851461135115$ |
$1$ |
$151$ |
| 4.0.1318650233.1 |
$x^{4} - x^{3} - 396 x^{2} - 1293 x + 62189$ |
$4$ |
(0, 2) |
$151^{3}\cdot 383$ |
$2$ |
$190.560289518$ |
$843.0087792160282$ |
|
|
|
$D_{4}$ (as 4T3) |
$[7]$ |
$[7]$ |
$2$ |
$1$ |
$139.791304321$ |
$0$ |
$383$ |
| 4.0.1335864988.1 |
$x^{4} - x^{3} - 396 x^{2} + 1727 x + 62189$ |
$4$ |
(0, 2) |
$2^{2}\cdot 97\cdot 151^{3}$ |
$3$ |
$191.179200847$ |
$848.4936046662455$ |
|
|
|
$D_{4}$ (as 4T3) |
$[84]$ |
$[84]$ |
$2$ |
$1$ |
$36.846858076409475$ |
$0$ |
$151$ |
| 4.4.1349636792.1 |
$x^{4} - x^{3} - 94 x^{2} + 217 x + 883$ |
$4$ |
(4, 0) |
$2^{3}\cdot 7^{2}\cdot 151^{3}$ |
$3$ |
$191.67003723697027$ |
$445.8372972785733$ |
|
|
? |
$S_4$ (as 4T5) |
trivial |
$[2, 2]$ |
$2$ |
$3$ |
$4988.150096770002$ |
$2$ |
$151$ |
| 4.0.1401281057.1 |
$x^{4} - 2 x^{3} + 77 x^{2} - 76 x + 3860$ |
$4$ |
(0, 2) |
$11\cdot 37\cdot 151^{3}$ |
$3$ |
$193.477876765$ |
$869.0202871001097$ |
|
|
|
$D_{4}$ (as 4T3) |
$[14]$ |
$[14]$ |
$2$ |
$1$ |
$1073.7553756137652$ |
$0$ |
$151$ |
| 4.2.1449482371.1 |
$x^{4} - 2 x^{3} - 74 x^{2} - 2643 x - 16072$ |
$4$ |
(2, 1) |
$-\,151^{3}\cdot 421$ |
$2$ |
$195.120650165$ |
$883.8402153666548$ |
|
|
|
$S_4$ (as 4T5) |
trivial |
$[2]$ |
$2$ |
$2$ |
$26022.886244733763$ |
$1$ |
$421$ |
