| 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 |
| 4.4.1125.1 |
$x^{4} - x^{3} - 4 x^{2} + 4 x + 1$ |
$4$ |
[4,0] |
$3^{2}\cdot 5^{3}$ |
$2$ |
$5.79146092644$ |
$5.791460926441346$ |
|
✓ |
✓ |
$C_4$ (as 4T1) |
trivial |
$2$ |
$3$ |
$1.16545519432$ |
| 4.2.1791.1 |
$x^{4} - x^{3} - x^{2} - 2 x + 1$ |
$4$ |
[2,1] |
$-\,3^{2}\cdot 199$ |
$2$ |
$6.50539836897$ |
$24.43358344574123$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$2.01913849925$ |
| 4.2.2412.1 |
$x^{4} - x^{3} - x^{2} + x - 2$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 3^{2}\cdot 67$ |
$3$ |
$7.00800375508$ |
$22.50529408956344$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$3.44842241827$ |
| 4.0.2448.1 |
$x^{4} - x^{2} - 6 x + 10$ |
$4$ |
[0,2] |
$2^{4}\cdot 3^{2}\cdot 17$ |
$3$ |
$7.03400792631$ |
$14.2828568570857$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$4$ |
$1$ |
$3.23198305835$ |
| 4.2.2736.1 |
$x^{4} - 2 x^{3} + 2 x^{2} + 2 x - 2$ |
$4$ |
[2,1] |
$-\,2^{4}\cdot 3^{2}\cdot 19$ |
$3$ |
$7.23234314192$ |
$16.948805249221287$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$2.67531471285$ |
| 4.2.2763.1 |
$x^{4} - 4 x^{2} - 3 x + 1$ |
$4$ |
[2,1] |
$-\,3^{2}\cdot 307$ |
$2$ |
$7.25012044064$ |
$30.347981810987037$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$1.81949527695$ |
| 4.0.2880.1 |
$x^{4} - 2 x^{3} - 4 x^{2} + 2 x + 13$ |
$4$ |
[0,2] |
$2^{6}\cdot 3^{2}\cdot 5$ |
$3$ |
$7.32568300297$ |
$10.954451150103322$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
$[2]$ |
$4$ |
$1$ |
$2.4529137425$ |
| 4.2.3303.1 |
$x^{4} - x^{2} - 3 x + 1$ |
$4$ |
[2,1] |
$-\,3^{2}\cdot 367$ |
$2$ |
$7.58101129019$ |
$33.18132004607411$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$2.87147261682$ |
| 4.2.3411.1 |
$x^{4} - x^{3} - 4 x^{2} - 2 x + 1$ |
$4$ |
[2,1] |
$-\,3^{2}\cdot 379$ |
$2$ |
$7.6422357332$ |
$33.71943060017473$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$1.8206171549$ |
| 4.0.3528.1 |
$x^{4} - x^{3} + 5 x^{2} - 5 x + 4$ |
$4$ |
[0,2] |
$2^{3}\cdot 3^{2}\cdot 7^{2}$ |
$3$ |
$7.70694294903$ |
$12.96148139681572$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$1$ |
$2.79876781094$ |
| 4.2.3600.1 |
$x^{4} - 3 x^{2} - 9$ |
$4$ |
[2,1] |
$-\,2^{4}\cdot 3^{2}\cdot 5^{2}$ |
$3$ |
$7.74596669241$ |
$10.954451150103322$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$2.36074219749$ |
| 4.0.3636.1 |
$x^{4} - x^{3} - x^{2} + x + 4$ |
$4$ |
[0,2] |
$2^{2}\cdot 3^{2}\cdot 101$ |
$3$ |
$7.76525941143$ |
$27.631723729009256$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$2$ |
$1$ |
$1.95638710674$ |
| 4.2.3816.1 |
$x^{4} - x^{3} - x^{2} - 2 x - 2$ |
$4$ |
[2,1] |
$-\,2^{3}\cdot 3^{2}\cdot 53$ |
$3$ |
$7.85962981609$ |
$35.66510900025401$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$3.57917436453$ |
| 4.2.3951.1 |
$x^{4} - x^{3} + 2 x^{2} + x - 2$ |
$4$ |
[2,1] |
$-\,3^{2}\cdot 439$ |
$2$ |
$7.92823943378$ |
$36.29049462324811$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$3.18478426488$ |
| 4.2.4032.1 |
$x^{4} - 2 x^{3} - x^{2} - 4 x - 2$ |
$4$ |
[2,1] |
$-\,2^{6}\cdot 3^{2}\cdot 7$ |
$3$ |
$7.96856520746$ |
$12.96148139681572$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$4.93352004952$ |
| 4.0.4257.1 |
$x^{4} - x^{3} + 5 x^{2} - 2 x + 1$ |
$4$ |
[0,2] |
$3^{2}\cdot 11\cdot 43$ |
$3$ |
$8.07748039384$ |
$37.66961640367472$ |
|
|
✓ |
$S_4$ (as 4T5) |
$[2]$ |
$2$ |
$1$ |
$1.5123335985$ |
| 4.2.4275.1 |
$x^{4} - 2 x^{3} + x - 11$ |
$4$ |
[2,1] |
$-\,3^{2}\cdot 5^{2}\cdot 19$ |
$3$ |
$8.08600545097$ |
$16.881943016134134$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$1.83134528682$ |
| 4.0.4608.1 |
$x^{4} - 6 x^{2} + 18$ |
$4$ |
[0,2] |
$2^{9}\cdot 3^{2}$ |
$2$ |
$8.23906857563$ |
$11.651802520975762$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$4$ |
$1$ |
$2.91403538772$ |
| 4.0.5904.1 |
$x^{4} - 7 x^{2} - 6 x + 25$ |
$4$ |
[0,2] |
$2^{4}\cdot 3^{2}\cdot 41$ |
$3$ |
$8.76569967825$ |
$22.181073012818835$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$4$ |
$1$ |
$2.89310593284$ |
| 4.0.6525.1 |
$x^{4} - x^{3} + 8 x^{2} - 2 x + 19$ |
$4$ |
[0,2] |
$3^{2}\cdot 5^{2}\cdot 29$ |
$3$ |
$8.98762883674$ |
$20.85665361461421$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$1$ |
$0.962423650119$ |
| 4.0.6849.2 |
$x^{4} - x^{3} + 2 x^{2} - 5 x + 4$ |
$4$ |
[0,2] |
$3^{2}\cdot 761$ |
$2$ |
$9.09718007653$ |
$47.78074926160116$ |
|
|
✓ |
$S_4$ (as 4T5) |
$[2]$ |
$2$ |
$1$ |
$1.64286804459$ |
| 4.2.6975.1 |
$x^{4} - x^{3} - x^{2} + 10 x - 20$ |
$4$ |
[2,1] |
$-\,3^{2}\cdot 5^{2}\cdot 31$ |
$3$ |
$9.13873434576$ |
$21.563858652847824$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$4.02528237098$ |
| 4.0.7065.1 |
$x^{4} - x^{2} - 3 x + 4$ |
$4$ |
[0,2] |
$3^{2}\cdot 5\cdot 157$ |
$3$ |
$9.16807255407$ |
$48.52834223420371$ |
|
|
✓ |
$S_4$ (as 4T5) |
$[2]$ |
$2$ |
$1$ |
$1.79922408268$ |
| 4.2.7947.1 |
$x^{4} - 4 x^{2} - 3 x - 2$ |
$4$ |
[2,1] |
$-\,3^{2}\cdot 883$ |
$2$ |
$9.44171317869$ |
$51.468436929831086$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$8.22939789308$ |
| 4.2.8676.1 |
$x^{4} - x^{3} + 2 x^{2} - 5 x + 1$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 3^{2}\cdot 241$ |
$3$ |
$9.65116822864$ |
$53.777318638995006$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$6.07758213603$ |
| 4.2.9216.1 |
$x^{4} - 6 x^{2} - 9$ |
$4$ |
[2,1] |
$-\,2^{10}\cdot 3^{2}$ |
$2$ |
$9.79795897113$ |
$11.651802520975762$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$5.13670764475$ |
| 4.4.9225.1 |
$x^{4} - x^{3} - 10 x^{2} + 7 x + 19$ |
$4$ |
[4,0] |
$3^{2}\cdot 5^{2}\cdot 41$ |
$3$ |
$9.80035017545$ |
$24.79919353527449$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$5.14912489678$ |
| 4.0.9360.1 |
$x^{4} - 2 x^{3} - 9 x^{2} + 10 x + 34$ |
$4$ |
[0,2] |
$2^{4}\cdot 3^{2}\cdot 5\cdot 13$ |
$4$ |
$9.83601001319$ |
$27.92848008753788$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$4$ |
$1$ |
$6.65026233206$ |
| 4.0.9360.2 |
$x^{4} - x^{2} - 12 x + 37$ |
$4$ |
[0,2] |
$2^{4}\cdot 3^{2}\cdot 5\cdot 13$ |
$4$ |
$9.83601001319$ |
$27.92848008753788$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$4$ |
$1$ |
$3.20082011047$ |
| 4.0.9684.1 |
$x^{4} - x^{3} + 2 x^{2} + 4 x + 4$ |
$4$ |
[0,2] |
$2^{2}\cdot 3^{2}\cdot 269$ |
$3$ |
$9.92004620963$ |
$45.09448496801272$ |
|
|
✓ |
$S_4$ (as 4T5) |
$[2]$ |
$2$ |
$1$ |
$3.7465536516$ |
| 4.2.9783.1 |
$x^{4} - 2 x^{3} - x^{2} - x + 4$ |
$4$ |
[2,1] |
$-\,3^{2}\cdot 1087$ |
$2$ |
$9.94530286774$ |
$57.105166141076936$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$5.50097259769$ |
| 4.4.9792.1 |
$x^{4} - 2 x^{3} - 7 x^{2} + 2 x + 7$ |
$4$ |
[4,0] |
$2^{6}\cdot 3^{2}\cdot 17$ |
$3$ |
$9.94758940723$ |
$20.199009876724155$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$4.9482532611$ |
| 4.2.9972.1 |
$x^{4} - 2 x^{3} + 5 x^{2} + 2 x - 2$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 3^{2}\cdot 277$ |
$3$ |
$9.99299263797$ |
$57.654141221598294$ |
|
|
|
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$5.80347995925$ |
| 4.2.10296.1 |
$x^{4} - x^{2} - 6 x + 4$ |
$4$ |
[2,1] |
$-\,2^{3}\cdot 3^{2}\cdot 11\cdot 13$ |
$4$ |
$10.0731925005$ |
$58.58327406350724$ |
|
|
|
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$6.83369049492$ |
| 4.2.10404.1 |
$x^{4} - x^{3} - x^{2} + 7 x - 2$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 3^{2}\cdot 17^{2}$ |
$3$ |
$10.0995049384$ |
$14.2828568570857$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$13.5401509297$ |
| 4.2.11052.1 |
$x^{4} - x^{3} + 2 x^{2} - 8 x + 4$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 3^{2}\cdot 307$ |
$3$ |
$10.253218656$ |
$48.1744182518726$ |
|
|
|
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$9.29510911926$ |
| 4.2.11403.1 |
$x^{4} - 2 x^{3} + 2 x^{2} + 5 x + 1$ |
$4$ |
[2,1] |
$-\,3^{2}\cdot 7\cdot 181$ |
$3$ |
$10.3336745828$ |
$61.652250567193406$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$2.89391381106$ |
| 4.0.11520.1 |
$x^{4} - 12 x^{2} + 45$ |
$4$ |
[0,2] |
$2^{8}\cdot 3^{2}\cdot 5$ |
$3$ |
$10.3600802564$ |
$15.491933384829668$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$4$ |
$1$ |
$3.96677405983$ |
| 4.0.11736.1 |
$x^{4} - x^{3} + 2 x^{2} - 8 x + 16$ |
$4$ |
[0,2] |
$2^{3}\cdot 3^{2}\cdot 163$ |
$3$ |
$10.4083053621$ |
$62.545983084447556$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$2$ |
$1$ |
$6.4982274041$ |
| 4.2.12267.1 |
$x^{4} + 2 x^{2} - 3 x - 2$ |
$4$ |
[2,1] |
$-\,3^{2}\cdot 29\cdot 47$ |
$3$ |
$10.5240909181$ |
$63.94528911499267$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$11.1791931639$ |
| 4.2.12375.1 |
$x^{4} - x^{3} - 4 x^{2} - 11 x - 29$ |
$4$ |
[2,1] |
$-\,3^{2}\cdot 5^{3}\cdot 11$ |
$3$ |
$10.547178642$ |
$19.208102881010017$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$2$ |
$2.58290495535$ |
| 4.2.12780.1 |
$x^{4} - x^{3} - 4 x^{2} - 2 x - 2$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 3^{2}\cdot 5\cdot 71$ |
$4$ |
$10.6324344385$ |
$51.803782065367386$ |
|
|
✓ |
$S_4$ (as 4T5) |
trivial |
$2$ |
$2$ |
$10.8924556597$ |
| 4.0.12789.1 |
$x^{4} - 2 x^{3} + x + 16$ |
$4$ |
[0,2] |
$3^{2}\cdot 7^{2}\cdot 29$ |
$3$ |
$10.6343058518$ |
$24.677925358506133$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$1$ |
$4.16348864333$ |
| 4.0.12816.1 |
$x^{4} - 7 x^{2} - 12 x + 52$ |
$4$ |
[0,2] |
$2^{4}\cdot 3^{2}\cdot 89$ |
$3$ |
$10.6399141719$ |
$32.68026927673638$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$4$ |
$1$ |
$6.8691516537$ |
| 4.0.14112.1 |
$x^{4} + 3 x^{2} + 18$ |
$4$ |
[0,2] |
$2^{5}\cdot 3^{2}\cdot 7^{2}$ |
$3$ |
$10.899263243$ |
$18.33030277982336$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$1$ |
$4.1885322481$ |
| 4.2.14400.1 |
$x^{4} - 6 x^{2} - 36$ |
$4$ |
[2,1] |
$-\,2^{6}\cdot 3^{2}\cdot 5^{2}$ |
$3$ |
$10.9544511501$ |
$15.491933384829668$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$3.81771716986$ |
| 4.0.15948.1 |
$x^{4} - x^{3} - x^{2} + x + 16$ |
$4$ |
[0,2] |
$2^{2}\cdot 3^{2}\cdot 443$ |
$3$ |
$11.2376772991$ |
$72.91090453423274$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$2$ |
$1$ |
$7.21349052837$ |
| 4.2.16128.1 |
$x^{4} + 2 x^{2} - 12 x - 14$ |
$4$ |
[2,1] |
$-\,2^{8}\cdot 3^{2}\cdot 7$ |
$3$ |
$11.269252989$ |
$18.33030277982336$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$2$ |
$3.69166169185$ |
| 4.0.16245.1 |
$x^{4} - x^{3} + 2 x^{2} - 8 x + 7$ |
$4$ |
[0,2] |
$3^{2}\cdot 5\cdot 19^{2}$ |
$3$ |
$11.2896357212$ |
$16.881943016134134$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$1$ |
$1.90284734441$ |
| 4.0.16272.1 |
$x^{4} - 2 x^{3} - 9 x^{2} + 10 x + 61$ |
$4$ |
[0,2] |
$2^{4}\cdot 3^{2}\cdot 113$ |
$3$ |
$11.2943237847$ |
$36.823905279043935$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$4$ |
$1$ |
$3.4148483592$ |
