| 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 |
| 4.0.3136.1 |
$x^{4} - 2 x^{3} + 2 x^{2} + 2$ |
$4$ |
[0,2] |
$2^{6}\cdot 7^{2}$ |
$2$ |
$7.48331477355$ |
$10.350079527967589$ |
|
|
✓ |
$A_4$ (as 4T4) |
trivial |
$2$ |
$1$ |
$2.89814944536$ |
| 4.0.4225.1 |
$x^{4} - x^{3} - 3 x + 4$ |
$4$ |
[0,2] |
$5^{2}\cdot 13^{2}$ |
$2$ |
$8.0622577483$ |
$12.362716315674692$ |
|
|
✓ |
$A_4$ (as 4T4) |
$[2]$ |
$2$ |
$1$ |
$1.5729532878$ |
| 4.0.5184.1 |
$x^{4} - 2 x^{3} + 6 x^{2} - 4 x + 2$ |
$4$ |
[0,2] |
$2^{6}\cdot 3^{4}$ |
$2$ |
$8.48528137424$ |
$12.237893415933033$ |
|
|
✓ |
$A_4$ (as 4T4) |
trivial |
$2$ |
$1$ |
$4.74604040898$ |
| 4.0.8281.1 |
$x^{4} - x^{3} + 5 x^{2} - 4 x + 3$ |
$4$ |
[0,2] |
$7^{2}\cdot 13^{2}$ |
$2$ |
$9.53939201417$ |
$13.193814370085985$ |
|
|
✓ |
$A_4$ (as 4T4) |
$[2]$ |
$2$ |
$1$ |
$2.66193075$ |
| 4.0.10816.1 |
$x^{4} - 2 x^{3} + 2 x^{2} + 4 x + 2$ |
$4$ |
[0,2] |
$2^{6}\cdot 13^{2}$ |
$2$ |
$10.1980390272$ |
$15.637736649622886$ |
|
|
✓ |
$A_4$ (as 4T4) |
trivial |
$2$ |
$1$ |
$4.96532021813$ |
| 4.0.15376.1 |
$x^{4} + 7 x^{2} - 2 x + 14$ |
$4$ |
[0,2] |
$2^{4}\cdot 31^{2}$ |
$2$ |
$11.1355287257$ |
$19.736544806437948$ |
|
|
|
$A_4$ (as 4T4) |
$[4]$ |
$2$ |
$1$ |
$2.92897443712$ |
| 4.0.17689.1 |
$x^{4} + 3 x^{2} - 7 x + 4$ |
$4$ |
[0,2] |
$7^{2}\cdot 19^{2}$ |
$2$ |
$11.5325625947$ |
$18.838721275076466$ |
|
|
✓ |
$A_4$ (as 4T4) |
$[4]$ |
$2$ |
$1$ |
$2.03622616194$ |
| 4.0.23104.1 |
$x^{4} - 2 x^{3} + 10 x^{2} - 8 x + 2$ |
$4$ |
[0,2] |
$2^{6}\cdot 19^{2}$ |
$2$ |
$12.3288280059$ |
$20.13944017607579$ |
|
|
✓ |
$A_4$ (as 4T4) |
trivial |
$2$ |
$1$ |
$7.30653189653$ |
| 4.0.23409.1 |
$x^{4} - x^{3} + 6 x^{2} - 5 x + 8$ |
$4$ |
[0,2] |
$3^{4}\cdot 17^{2}$ |
$2$ |
$12.3693168769$ |
$17.839641950637386$ |
|
|
✓ |
$A_4$ (as 4T4) |
$[2]$ |
$2$ |
$1$ |
$5.93153383032$ |
| 4.4.26569.1 |
$x^{4} - x^{3} - 7 x^{2} + 2 x + 9$ |
$4$ |
[4,0] |
$163^{2}$ |
$1$ |
$12.7671453348$ |
$29.839513369337443$ |
|
|
✓ |
$A_4$ (as 4T4) |
trivial |
$2$ |
$3$ |
$15.7092112624$ |
| 4.0.29241.1 |
$x^{4} - x^{3} + 3 x^{2} + x + 20$ |
$4$ |
[0,2] |
$3^{4}\cdot 19^{2}$ |
$2$ |
$13.0766968306$ |
$18.859860385004858$ |
|
|
|
$A_4$ (as 4T4) |
$[4]$ |
$2$ |
$1$ |
$3.40952909212$ |
| 4.0.29584.1 |
$x^{4} - 2 x^{3} + 2 x^{2} + 10 x + 9$ |
$4$ |
[0,2] |
$2^{4}\cdot 43^{2}$ |
$2$ |
$13.1148770486$ |
$24.54759593904292$ |
|
|
|
$A_4$ (as 4T4) |
$[2]$ |
$2$ |
$1$ |
$3.69556149659$ |
| 4.4.33489.1 |
$x^{4} - 7 x^{2} - 3 x + 1$ |
$4$ |
[4,0] |
$3^{2}\cdot 61^{2}$ |
$2$ |
$13.5277492585$ |
$26.839876760292654$ |
|
|
✓ |
$A_4$ (as 4T4) |
trivial |
$2$ |
$3$ |
$15.9211987195$ |
| 4.0.40401.1 |
$x^{4} - x^{3} + 4 x^{2} - 12 x + 24$ |
$4$ |
[0,2] |
$3^{2}\cdot 67^{2}$ |
$2$ |
$14.1774468788$ |
$28.57220971835363$ |
|
|
|
$A_4$ (as 4T4) |
$[4]$ |
$2$ |
$1$ |
$3.58601958256$ |
| 4.0.41209.1 |
$x^{4} - x^{3} + 5 x^{2} - 6 x + 7$ |
$4$ |
[0,2] |
$7^{2}\cdot 29^{2}$ |
$2$ |
$14.2478068488$ |
$19.705964328162043$ |
|
|
✓ |
$A_4$ (as 4T4) |
$[2]$ |
$2$ |
$1$ |
$6.43827437234$ |
| 4.0.43681.1 |
$x^{4} - x^{3} - 9 x^{2} + 6 x + 25$ |
$4$ |
[0,2] |
$11^{2}\cdot 19^{2}$ |
$2$ |
$14.4568322948$ |
$23.615586898971756$ |
|
|
✓ |
$A_4$ (as 4T4) |
$[4]$ |
$2$ |
$1$ |
$3.0088394055$ |
| 4.0.47961.1 |
$x^{4} - x^{3} - 2 x^{2} + 24$ |
$4$ |
[0,2] |
$3^{2}\cdot 73^{2}$ |
$2$ |
$14.7986485869$ |
$30.253516886595015$ |
|
|
|
$A_4$ (as 4T4) |
$[4]$ |
$2$ |
$1$ |
$4.0636795625$ |
| 4.0.61504.1 |
$x^{4} - 6 x^{2} - 8 x + 28$ |
$4$ |
[0,2] |
$2^{6}\cdot 31^{2}$ |
$2$ |
$15.748015748$ |
$27.911689339648817$ |
|
|
|
$A_4$ (as 4T4) |
$[2]$ |
$2$ |
$1$ |
$4.45423636647$ |
| 4.4.61504.1 |
$x^{4} - 2 x^{3} - 7 x^{2} + 6 x + 11$ |
$4$ |
[4,0] |
$2^{6}\cdot 31^{2}$ |
$2$ |
$15.748015748$ |
$27.911689339648817$ |
|
|
✓ |
$A_4$ (as 4T4) |
trivial |
$2$ |
$3$ |
$19.2289949229$ |
| 4.0.63504.1 |
$x^{4} - 2 x^{3} + 6 x^{2} - 4 x + 20$ |
$4$ |
[0,2] |
$2^{4}\cdot 3^{4}\cdot 7^{2}$ |
$3$ |
$15.8745078664$ |
$31.66579252742446$ |
|
|
|
$A_4$ (as 4T4) |
$[2]$ |
$2$ |
$1$ |
$7.23230290986$ |
| 4.0.74529.1 |
$x^{4} - x^{3} + 7 x^{2} + 9 x + 24$ |
$4$ |
[0,2] |
$3^{2}\cdot 7^{2}\cdot 13^{2}$ |
$3$ |
$16.5227116419$ |
$35.04194650073235$ |
|
|
|
$A_4$ (as 4T4) |
$[4]$ |
$2$ |
$1$ |
$6.10125795499$ |
| 4.4.76729.1 |
$x^{4} - x^{3} - 11 x^{2} + 4 x + 12$ |
$4$ |
[4,0] |
$277^{2}$ |
$1$ |
$16.6433169771$ |
$42.49323998594522$ |
|
|
|
$A_4$ (as 4T4) |
$[2]$ |
$2$ |
$3$ |
$12.7131864943$ |
| 4.0.82369.1 |
$x^{4} - x^{3} + 4 x^{2} - 7 x + 8$ |
$4$ |
[0,2] |
$7^{2}\cdot 41^{2}$ |
$2$ |
$16.9410743461$ |
$23.430989084024507$ |
|
|
✓ |
$A_4$ (as 4T4) |
$[2]$ |
$2$ |
$1$ |
$9.489766948$ |
| 4.0.87616.1 |
$x^{4} - 8 x^{2} - 8 x + 44$ |
$4$ |
[0,2] |
$2^{6}\cdot 37^{2}$ |
$2$ |
$17.2046505341$ |
$31.406013247262095$ |
|
|
|
$A_4$ (as 4T4) |
trivial |
$2$ |
$1$ |
$19.61785529$ |
| 4.0.90601.1 |
$x^{4} - x^{3} - 7 x^{2} + 9 x + 38$ |
$4$ |
[0,2] |
$7^{2}\cdot 43^{2}$ |
$2$ |
$17.3493515729$ |
$23.99567223510292$ |
|
|
|
$A_4$ (as 4T4) |
$[4]$ |
$2$ |
$1$ |
$4.84179776389$ |
| 4.0.95481.1 |
$x^{4} + 13 x^{2} - 3 x + 46$ |
$4$ |
[0,2] |
$3^{2}\cdot 103^{2}$ |
$2$ |
$17.5783958312$ |
$38.0585388267201$ |
|
|
|
$A_4$ (as 4T4) |
$[4]$ |
$2$ |
$1$ |
$6.47837346034$ |
| 4.0.99225.1 |
$x^{4} - x^{3} + 7 x + 14$ |
$4$ |
[0,2] |
$3^{4}\cdot 5^{2}\cdot 7^{2}$ |
$3$ |
$17.7482393493$ |
$35.40343232636298$ |
|
|
|
$A_4$ (as 4T4) |
$[2]$ |
$2$ |
$1$ |
$11.8933108956$ |
| 4.0.110889.1 |
$x^{4} - x^{3} + 6 x^{2} + 11 x + 10$ |
$4$ |
[0,2] |
$3^{4}\cdot 37^{2}$ |
$2$ |
$18.2482875909$ |
$26.318584936813835$ |
|
|
|
$A_4$ (as 4T4) |
$[2]$ |
$2$ |
$1$ |
$14.5871081372$ |
| 4.0.112225.1 |
$x^{4} + 11 x^{2} - 5 x + 29$ |
$4$ |
[0,2] |
$5^{2}\cdot 67^{2}$ |
$2$ |
$18.3030052177$ |
$36.886564134509776$ |
|
|
|
$A_4$ (as 4T4) |
$[2]$ |
$2$ |
$1$ |
$7.05792068684$ |
| 4.0.118336.1 |
$x^{4} - 2 x^{3} + 9 x^{2} - 6 x + 7$ |
$4$ |
[0,2] |
$2^{6}\cdot 43^{2}$ |
$2$ |
$18.547236991$ |
$34.715543100649214$ |
|
|
✓ |
$A_4$ (as 4T4) |
$[2]$ |
$2$ |
$1$ |
$5.76275101161$ |
| 4.0.118336.2 |
$x^{4} - 6 x^{2} - 8 x + 40$ |
$4$ |
[0,2] |
$2^{6}\cdot 43^{2}$ |
$2$ |
$18.547236991$ |
$34.715543100649214$ |
|
|
|
$A_4$ (as 4T4) |
$[4]$ |
$2$ |
$1$ |
$8.60226112239$ |
| 4.4.121801.1 |
$x^{4} - x^{3} - 10 x^{2} + 3 x + 20$ |
$4$ |
[4,0] |
$349^{2}$ |
$1$ |
$18.6815416923$ |
$49.56977542044145$ |
|
|
✓ |
$A_4$ (as 4T4) |
trivial |
$2$ |
$3$ |
$41.6921959227$ |
| 4.0.132496.1 |
$x^{4} - 2 x^{3} + 14 x^{2} - 12 x + 20$ |
$4$ |
[0,2] |
$2^{4}\cdot 7^{2}\cdot 13^{2}$ |
$3$ |
$19.0787840283$ |
$40.46295449025258$ |
|
|
|
$A_4$ (as 4T4) |
$[2]$ |
$2$ |
$1$ |
$7.48102306505$ |
| 4.4.157609.1 |
$x^{4} - 13 x^{2} - 2 x + 19$ |
$4$ |
[4,0] |
$397^{2}$ |
$1$ |
$19.9248588452$ |
$54.016570132056195$ |
|
|
|
$A_4$ (as 4T4) |
trivial |
$2$ |
$3$ |
$38.8326454303$ |
| 4.0.159201.1 |
$x^{4} - 2 x^{3} + 7 x^{2} + 21 x + 63$ |
$4$ |
[0,2] |
$3^{2}\cdot 7^{2}\cdot 19^{2}$ |
$3$ |
$19.9749843554$ |
$45.129624639238735$ |
|
|
|
$A_4$ (as 4T4) |
$[4]$ |
$2$ |
$1$ |
$9.36730810327$ |
| 4.0.162409.1 |
$x^{4} - x^{3} - 6 x^{2} + 7 x + 18$ |
$4$ |
[0,2] |
$13^{2}\cdot 31^{2}$ |
$2$ |
$20.0748598999$ |
$30.78291537771342$ |
|
|
✓ |
$A_4$ (as 4T4) |
$[4]$ |
$2$ |
$1$ |
$5.71818568496$ |
| 4.4.165649.1 |
$x^{4} - 2 x^{3} - 9 x^{2} - x + 3$ |
$4$ |
[4,0] |
$11^{2}\cdot 37^{2}$ |
$2$ |
$20.1742410018$ |
$36.82681487204538$ |
|
|
✓ |
$A_4$ (as 4T4) |
trivial |
$2$ |
$3$ |
$49.5879834514$ |
| 4.0.190096.1 |
$x^{4} - 2 x^{3} + 5 x^{2} + 4 x + 5$ |
$4$ |
[0,2] |
$2^{4}\cdot 109^{2}$ |
$2$ |
$20.8806130178$ |
$45.636709948584894$ |
|
|
✓ |
$A_4$ (as 4T4) |
$[2]$ |
$2$ |
$1$ |
$7.17096769187$ |
| 4.0.205209.1 |
$x^{4} - x^{3} + 4 x^{2} - 3 x + 12$ |
$4$ |
[0,2] |
$3^{2}\cdot 151^{2}$ |
$2$ |
$21.2837966538$ |
$49.114748617819366$ |
|
|
✓ |
$A_4$ (as 4T4) |
$[8]$ |
$2$ |
$1$ |
$4.8948196374$ |
| 4.0.219024.1 |
$x^{4} - 2 x^{3} + 3 x^{2} + 6 x + 6$ |
$4$ |
[0,2] |
$2^{4}\cdot 3^{4}\cdot 13^{2}$ |
$3$ |
$21.6333076528$ |
$47.84323859612865$ |
|
|
✓ |
$A_4$ (as 4T4) |
$[4]$ |
$2$ |
$1$ |
$16.9094353527$ |
| 4.4.223729.1 |
$x^{4} - x^{3} - 16 x^{2} - 7 x + 27$ |
$4$ |
[4,0] |
$11^{2}\cdot 43^{2}$ |
$2$ |
$21.7485631709$ |
$40.70758261752865$ |
|
|
|
$A_4$ (as 4T4) |
trivial |
$2$ |
$3$ |
$46.2265209627$ |
| 4.0.227529.1 |
$x^{4} - x^{3} + 3 x^{2} - 8 x + 11$ |
$4$ |
[0,2] |
$3^{4}\cdot 53^{2}$ |
$2$ |
$21.8403296678$ |
$31.499206078816627$ |
|
|
✓ |
$A_4$ (as 4T4) |
$[2]$ |
$2$ |
$1$ |
$21.8968929894$ |
| 4.0.238144.1 |
$x^{4} - 2 x^{3} + 14 x^{2} - 4 x + 6$ |
$4$ |
[0,2] |
$2^{6}\cdot 61^{2}$ |
$2$ |
$22.0907220344$ |
$43.82933521460097$ |
|
|
|
$A_4$ (as 4T4) |
trivial |
$2$ |
$1$ |
$70.8952291769$ |
| 4.0.246016.1 |
$x^{4} + 2 x^{2} - 4 x + 10$ |
$4$ |
[0,2] |
$2^{8}\cdot 31^{2}$ |
$2$ |
$22.2710574513$ |
$39.473089612875896$ |
|
|
✓ |
$A_4$ (as 4T4) |
$[2, 2]$ |
$2$ |
$1$ |
$6.72733869619$ |
| 4.0.246016.2 |
$x^{4} + 10 x^{2} - 4 x + 2$ |
$4$ |
[0,2] |
$2^{8}\cdot 31^{2}$ |
$2$ |
$22.2710574513$ |
$39.473089612875896$ |
|
|
✓ |
$A_4$ (as 4T4) |
$[2, 2]$ |
$2$ |
$1$ |
$7.81085798599$ |
| 4.0.247009.1 |
$x^{4} - x^{3} + 9 x + 10$ |
$4$ |
[0,2] |
$7^{2}\cdot 71^{2}$ |
$2$ |
$22.2934968096$ |
$30.833857978493015$ |
|
|
✓ |
$A_4$ (as 4T4) |
$[4]$ |
$2$ |
$1$ |
$9.72655721929$ |
| 4.0.254016.1 |
$x^{4} - 12 x^{2} - 8 x + 72$ |
$4$ |
[0,2] |
$2^{6}\cdot 3^{4}\cdot 7^{2}$ |
$3$ |
$22.4499443206$ |
$44.78219325557628$ |
|
|
|
$A_4$ (as 4T4) |
trivial |
$2$ |
$1$ |
$38.5230267277$ |
| 4.0.254016.2 |
$x^{4} - 6 x^{2} - 8 x + 60$ |
$4$ |
[0,2] |
$2^{6}\cdot 3^{4}\cdot 7^{2}$ |
$3$ |
$22.4499443206$ |
$44.78219325557628$ |
|
|
|
$A_4$ (as 4T4) |
$[2]$ |
$2$ |
$1$ |
$15.0605288679$ |
| 4.0.254016.3 |
$x^{4} + 18 x^{2} - 8 x + 120$ |
$4$ |
[0,2] |
$2^{6}\cdot 3^{4}\cdot 7^{2}$ |
$3$ |
$22.4499443206$ |
$44.78219325557628$ |
|
|
|
$A_4$ (as 4T4) |
$[4]$ |
$2$ |
$1$ |
$20.2503128909$ |
| 4.0.258064.1 |
$x^{4} - 2 x^{3} + 10 x^{2} - 4 x + 36$ |
$4$ |
[0,2] |
$2^{4}\cdot 127^{2}$ |
$2$ |
$22.5388553392$ |
$50.53192113129331$ |
|
|
|
$A_4$ (as 4T4) |
$[2]$ |
$2$ |
$1$ |
$7.87901635395$ |
