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 |
4.0.125.1 |
$x^{4} - x^{3} + x^{2} - x + 1$ |
$4$ |
[0,2] |
$5^{3}$ |
$1$ |
$3.34370152488$ |
$3.34370152488211$ |
✓ |
✓ |
✓ |
$C_4$ (as 4T1) |
trivial |
$10$ |
$1$ |
$0.962423650119$ |
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 |
$2$ |
$3$ |
$1.16545519432$ |
4.4.2000.1 |
$x^{4} - 5 x^{2} + 5$ |
$4$ |
[4,0] |
$2^{4}\cdot 5^{3}$ |
$2$ |
$6.68740304976$ |
$6.68740304976422$ |
|
✓ |
✓ |
$C_4$ (as 4T1) |
trivial |
$2$ |
$3$ |
$1.85281056397$ |
4.4.2048.1 |
$x^{4} - 4 x^{2} + 2$ |
$4$ |
[4,0] |
$2^{11}$ |
$1$ |
$6.72717132203$ |
$6.727171322029716$ |
|
✓ |
✓ |
$C_4$ (as 4T1) |
trivial |
$2$ |
$3$ |
$2.44179500662$ |
4.0.2048.2 |
$x^{4} + 4 x^{2} + 2$ |
$4$ |
[0,2] |
$2^{11}$ |
$1$ |
$6.72717132203$ |
$6.727171322029716$ |
✓ |
✓ |
✓ |
$C_4$ (as 4T1) |
trivial |
$2$ |
$1$ |
$1.76274717404$ |
4.0.2197.1 |
$x^{4} - x^{3} + 2 x^{2} + 4 x + 3$ |
$4$ |
[0,2] |
$13^{3}$ |
$1$ |
$6.84632504202$ |
$6.846325042023046$ |
✓ |
✓ |
|
$C_4$ (as 4T1) |
trivial |
$2$ |
$1$ |
$2.38952643457$ |
4.4.4913.1 |
$x^{4} - x^{3} - 6 x^{2} + x + 1$ |
$4$ |
[4,0] |
$17^{3}$ |
$1$ |
$8.37214402859$ |
$8.37214402859269$ |
|
✓ |
|
$C_4$ (as 4T1) |
trivial |
$2$ |
$3$ |
$3.46198873228$ |
4.4.6125.1 |
$x^{4} - x^{3} - 9 x^{2} + 9 x + 11$ |
$4$ |
[4,0] |
$5^{3}\cdot 7^{2}$ |
$2$ |
$8.84660269327$ |
$8.846602693265513$ |
|
✓ |
✓ |
$C_4$ (as 4T1) |
trivial |
$2$ |
$3$ |
$3.36611485007$ |
4.4.8000.1 |
$x^{4} - 10 x^{2} + 20$ |
$4$ |
[4,0] |
$2^{6}\cdot 5^{3}$ |
$2$ |
$9.45741609003$ |
$9.457416090031758$ |
|
✓ |
|
$C_4$ (as 4T1) |
trivial |
$2$ |
$3$ |
$4.50325854125$ |
4.0.8000.2 |
$x^{4} + 10 x^{2} + 20$ |
$4$ |
[0,2] |
$2^{6}\cdot 5^{3}$ |
$2$ |
$9.45741609003$ |
$9.457416090031758$ |
✓ |
✓ |
|
$C_4$ (as 4T1) |
$[2]$ |
$2$ |
$1$ |
$0.962423650119$ |
4.4.15125.1 |
$x^{4} - x^{3} - 14 x^{2} + 14 x + 31$ |
$4$ |
[4,0] |
$5^{3}\cdot 11^{2}$ |
$2$ |
$11.089803369$ |
$11.08980336897316$ |
|
✓ |
✓ |
$C_4$ (as 4T1) |
trivial |
$2$ |
$3$ |
$5.29445586371$ |
4.0.18000.1 |
$x^{4} + 15 x^{2} + 45$ |
$4$ |
[0,2] |
$2^{4}\cdot 3^{2}\cdot 5^{3}$ |
$3$ |
$11.5829218529$ |
$11.582921852882691$ |
✓ |
✓ |
|
$C_4$ (as 4T1) |
$[2, 2]$ |
$2$ |
$1$ |
$0.962423650119$ |
4.4.18432.1 |
$x^{4} - 12 x^{2} + 18$ |
$4$ |
[4,0] |
$2^{11}\cdot 3^{2}$ |
$2$ |
$11.651802521$ |
$11.651802520975762$ |
|
✓ |
|
$C_4$ (as 4T1) |
trivial |
$2$ |
$3$ |
$11.1753272808$ |
4.0.18432.2 |
$x^{4} + 12 x^{2} + 18$ |
$4$ |
[0,2] |
$2^{11}\cdot 3^{2}$ |
$2$ |
$11.651802521$ |
$11.651802520975762$ |
✓ |
✓ |
|
$C_4$ (as 4T1) |
$[2]$ |
$2$ |
$1$ |
$1.76274717404$ |
4.4.19773.1 |
$x^{4} - x^{3} - 11 x^{2} - 9 x + 3$ |
$4$ |
[4,0] |
$3^{2}\cdot 13^{3}$ |
$2$ |
$11.8581828179$ |
$11.858182817915045$ |
|
✓ |
✓ |
$C_4$ (as 4T1) |
trivial |
$2$ |
$3$ |
$9.44732277257$ |
4.0.21125.1 |
$x^{4} - x^{3} + 16 x^{2} - 16 x + 61$ |
$4$ |
[0,2] |
$5^{3}\cdot 13^{2}$ |
$2$ |
$12.0558872978$ |
$12.055887297809578$ |
✓ |
✓ |
|
$C_4$ (as 4T1) |
$[2]$ |
$2$ |
$1$ |
$0.962423650119$ |
4.0.24389.1 |
$x^{4} - x^{3} + 4 x^{2} - 20 x + 23$ |
$4$ |
[0,2] |
$29^{3}$ |
$1$ |
$12.4967907643$ |
$12.496790764308276$ |
✓ |
✓ |
|
$C_4$ (as 4T1) |
trivial |
$2$ |
$1$ |
$3.29446229274$ |
4.4.35152.1 |
$x^{4} - 13 x^{2} + 13$ |
$4$ |
[4,0] |
$2^{4}\cdot 13^{3}$ |
$2$ |
$13.692650084$ |
$13.692650084046091$ |
|
✓ |
|
$C_4$ (as 4T1) |
trivial |
$2$ |
$3$ |
$8.93062001005$ |
4.0.36125.1 |
$x^{4} - x^{3} + 21 x^{2} - 21 x + 101$ |
$4$ |
[0,2] |
$5^{3}\cdot 17^{2}$ |
$2$ |
$13.7864345676$ |
$13.786434567627778$ |
✓ |
✓ |
|
$C_4$ (as 4T1) |
$[2]$ |
$2$ |
$1$ |
$0.962423650119$ |
4.0.44217.1 |
$x^{4} - x^{3} + 11 x^{2} + x + 52$ |
$4$ |
[0,2] |
$3^{2}\cdot 17^{3}$ |
$2$ |
$14.5009788258$ |
$14.500978825806921$ |
✓ |
✓ |
|
$C_4$ (as 4T1) |
$[10]$ |
$2$ |
$1$ |
$4.18942509452$ |
4.4.45125.1 |
$x^{4} - x^{3} - 24 x^{2} + 24 x + 101$ |
$4$ |
[4,0] |
$5^{3}\cdot 19^{2}$ |
$2$ |
$14.5748570443$ |
$14.574857044323968$ |
|
✓ |
|
$C_4$ (as 4T1) |
trivial |
$2$ |
$3$ |
$9.85038342716$ |
4.0.50653.1 |
$x^{4} - x^{3} + 5 x^{2} - 7 x + 49$ |
$4$ |
[0,2] |
$37^{3}$ |
$1$ |
$15.002073644$ |
$15.002073644034486$ |
✓ |
✓ |
|
$C_4$ (as 4T1) |
trivial |
$2$ |
$1$ |
$4.98355970529$ |
4.4.51200.1 |
$x^{4} - 20 x^{2} + 50$ |
$4$ |
[4,0] |
$2^{11}\cdot 5^{2}$ |
$2$ |
$15.0424123723$ |
$15.042412372345574$ |
|
✓ |
|
$C_4$ (as 4T1) |
$[2]$ |
$2$ |
$3$ |
$9.82803187415$ |
4.0.51200.2 |
$x^{4} + 20 x^{2} + 50$ |
$4$ |
[0,2] |
$2^{11}\cdot 5^{2}$ |
$2$ |
$15.0424123723$ |
$15.042412372345574$ |
✓ |
✓ |
|
$C_4$ (as 4T1) |
$[2]$ |
$2$ |
$1$ |
$1.76274717404$ |
4.0.54925.1 |
$x^{4} - x^{3} + 15 x^{2} + 17 x + 29$ |
$4$ |
[0,2] |
$5^{2}\cdot 13^{3}$ |
$2$ |
$15.30884819$ |
$15.308848190022635$ |
✓ |
✓ |
|
$C_4$ (as 4T1) |
$[2]$ |
$2$ |
$1$ |
$2.38952643457$ |
4.0.55125.1 |
$x^{4} - x^{3} + 26 x^{2} - 26 x + 151$ |
$4$ |
[0,2] |
$3^{2}\cdot 5^{3}\cdot 7^{2}$ |
$3$ |
$15.3227653391$ |
$15.322765339111537$ |
✓ |
✓ |
|
$C_4$ (as 4T1) |
$[2, 2]$ |
$2$ |
$1$ |
$0.962423650119$ |
4.4.66125.1 |
$x^{4} - x^{3} - 29 x^{2} + 29 x + 151$ |
$4$ |
[4,0] |
$5^{3}\cdot 23^{2}$ |
$2$ |
$16.0358291776$ |
$16.03582917757843$ |
|
✓ |
|
$C_4$ (as 4T1) |
trivial |
$2$ |
$3$ |
$9.82555546678$ |
4.4.68921.1 |
$x^{4} - x^{3} - 15 x^{2} - 18 x - 4$ |
$4$ |
[4,0] |
$41^{3}$ |
$1$ |
$16.2027187143$ |
$16.202718714300598$ |
|
✓ |
|
$C_4$ (as 4T1) |
trivial |
$2$ |
$3$ |
$13.5247244386$ |
4.4.72000.1 |
$x^{4} - 30 x^{2} + 180$ |
$4$ |
[4,0] |
$2^{6}\cdot 3^{2}\cdot 5^{3}$ |
$3$ |
$16.3807251763$ |
$16.3807251762544$ |
|
✓ |
|
$C_4$ (as 4T1) |
$[2]$ |
$2$ |
$3$ |
$8.40003000533$ |
4.0.72000.2 |
$x^{4} + 30 x^{2} + 180$ |
$4$ |
[0,2] |
$2^{6}\cdot 3^{2}\cdot 5^{3}$ |
$3$ |
$16.3807251763$ |
$16.3807251762544$ |
✓ |
✓ |
|
$C_4$ (as 4T1) |
$[2, 2]$ |
$2$ |
$1$ |
$0.962423650119$ |
4.0.78608.1 |
$x^{4} + 17 x^{2} + 68$ |
$4$ |
[0,2] |
$2^{4}\cdot 17^{3}$ |
$2$ |
$16.7442880572$ |
$16.74428805718538$ |
✓ |
✓ |
|
$C_4$ (as 4T1) |
$[2, 2]$ |
$2$ |
$1$ |
$4.18942509452$ |
4.0.98000.1 |
$x^{4} + 35 x^{2} + 245$ |
$4$ |
[0,2] |
$2^{4}\cdot 5^{3}\cdot 7^{2}$ |
$3$ |
$17.6932053865$ |
$17.693205386531027$ |
✓ |
✓ |
|
$C_4$ (as 4T1) |
$[2, 2]$ |
$2$ |
$1$ |
$0.962423650119$ |
4.4.100352.1 |
$x^{4} - 28 x^{2} + 98$ |
$4$ |
[4,0] |
$2^{11}\cdot 7^{2}$ |
$2$ |
$17.798422345$ |
$17.798422345016238$ |
|
✓ |
✓ |
$C_4$ (as 4T1) |
trivial |
$2$ |
$3$ |
$23.4339005965$ |
4.0.100352.5 |
$x^{4} + 28 x^{2} + 98$ |
$4$ |
[0,2] |
$2^{11}\cdot 7^{2}$ |
$2$ |
$17.798422345$ |
$17.798422345016238$ |
✓ |
✓ |
|
$C_4$ (as 4T1) |
$[2, 2]$ |
$2$ |
$1$ |
$1.76274717404$ |
4.0.105125.2 |
$x^{4} - x^{3} + 36 x^{2} - 36 x + 281$ |
$4$ |
[0,2] |
$5^{3}\cdot 29^{2}$ |
$2$ |
$18.0063837774$ |
$18.006383777357115$ |
✓ |
✓ |
|
$C_4$ (as 4T1) |
$[2, 2]$ |
$2$ |
$1$ |
$0.962423650119$ |
4.4.107653.1 |
$x^{4} - x^{3} - 24 x^{2} - 22 x + 29$ |
$4$ |
[4,0] |
$7^{2}\cdot 13^{3}$ |
$2$ |
$18.1136734559$ |
$18.113673455906813$ |
|
✓ |
|
$C_4$ (as 4T1) |
trivial |
$2$ |
$3$ |
$13.2792379456$ |
4.4.120125.1 |
$x^{4} - x^{3} - 39 x^{2} + 39 x + 281$ |
$4$ |
[4,0] |
$5^{3}\cdot 31^{2}$ |
$2$ |
$18.6169421902$ |
$18.616942190179014$ |
|
✓ |
|
$C_4$ (as 4T1) |
trivial |
$2$ |
$3$ |
$11.6880189501$ |
4.4.122825.1 |
$x^{4} - x^{3} - 23 x^{2} + x + 86$ |
$4$ |
[4,0] |
$5^{2}\cdot 17^{3}$ |
$2$ |
$18.7206831654$ |
$18.720683165352195$ |
|
✓ |
|
$C_4$ (as 4T1) |
$[2]$ |
$2$ |
$3$ |
$61.2253005252$ |
4.0.136125.2 |
$x^{4} - x^{3} + 41 x^{2} - 41 x + 361$ |
$4$ |
[0,2] |
$3^{2}\cdot 5^{3}\cdot 11^{2}$ |
$3$ |
$19.208102881$ |
$19.208102881010017$ |
✓ |
✓ |
|
$C_4$ (as 4T1) |
$[2, 2, 2]$ |
$2$ |
$1$ |
$0.962423650119$ |
4.4.140608.1 |
$x^{4} - 26 x^{2} + 52$ |
$4$ |
[4,0] |
$2^{6}\cdot 13^{3}$ |
$2$ |
$19.3643314537$ |
$19.364331453687083$ |
|
✓ |
|
$C_4$ (as 4T1) |
trivial |
$2$ |
$3$ |
$56.3106022511$ |
4.0.140608.2 |
$x^{4} + 26 x^{2} + 52$ |
$4$ |
[0,2] |
$2^{6}\cdot 13^{3}$ |
$2$ |
$19.3643314537$ |
$19.364331453687083$ |
✓ |
✓ |
|
$C_4$ (as 4T1) |
$[2]$ |
$2$ |
$1$ |
$2.38952643457$ |
4.0.148877.1 |
$x^{4} - x^{3} + 7 x^{2} + 43 x + 47$ |
$4$ |
[0,2] |
$53^{3}$ |
$1$ |
$19.64295864$ |
$19.64295863997752$ |
✓ |
✓ |
|
$C_4$ (as 4T1) |
trivial |
$2$ |
$1$ |
$3.9314409433$ |
4.0.171125.1 |
$x^{4} - x^{3} + 46 x^{2} - 46 x + 451$ |
$4$ |
[0,2] |
$5^{3}\cdot 37^{2}$ |
$2$ |
$20.3389423481$ |
$20.33894234805392$ |
✓ |
✓ |
|
$C_4$ (as 4T1) |
$[10]$ |
$2$ |
$1$ |
$0.962423650119$ |
4.4.190125.1 |
$x^{4} - x^{3} - 49 x^{2} + 49 x + 451$ |
$4$ |
[4,0] |
$3^{2}\cdot 5^{3}\cdot 13^{2}$ |
$3$ |
$20.8814093301$ |
$20.88140933013045$ |
|
✓ |
|
$C_4$ (as 4T1) |
$[2]$ |
$2$ |
$3$ |
$12.0903797544$ |
4.0.210125.1 |
$x^{4} - x^{3} + 51 x^{2} - 51 x + 551$ |
$4$ |
[0,2] |
$5^{3}\cdot 41^{2}$ |
$2$ |
$21.4101362767$ |
$21.410136276713814$ |
✓ |
✓ |
|
$C_4$ (as 4T1) |
$[2, 4]$ |
$2$ |
$1$ |
$0.962423650119$ |
4.4.219501.1 |
$x^{4} - x^{3} - 25 x^{2} + 67 x - 35$ |
$4$ |
[4,0] |
$3^{2}\cdot 29^{3}$ |
$2$ |
$21.6450765353$ |
$21.645076535339435$ |
|
✓ |
|
$C_4$ (as 4T1) |
trivial |
$2$ |
$3$ |
$44.1658756648$ |
4.0.226981.1 |
$x^{4} - x^{3} + 8 x^{2} - 42 x + 117$ |
$4$ |
[0,2] |
$61^{3}$ |
$1$ |
$21.8271672516$ |
$21.827167251622598$ |
✓ |
✓ |
|
$C_4$ (as 4T1) |
trivial |
$2$ |
$1$ |
$7.32843692177$ |
4.4.231125.1 |
$x^{4} - x^{3} - 54 x^{2} + 54 x + 551$ |
$4$ |
[4,0] |
$5^{3}\cdot 43^{2}$ |
$2$ |
$21.926117193$ |
$21.92611719302929$ |
|
✓ |
|
$C_4$ (as 4T1) |
trivial |
$2$ |
$3$ |
$25.6771237386$ |
4.0.240737.1 |
$x^{4} - x^{3} + 28 x^{2} + x + 239$ |
$4$ |
[0,2] |
$7^{2}\cdot 17^{3}$ |
$2$ |
$22.1506110401$ |
$22.150611040070693$ |
✓ |
✓ |
|
$C_4$ (as 4T1) |
$[2]$ |
$2$ |
$1$ |
$4.18942509452$ |
4.0.242000.2 |
$x^{4} + 55 x^{2} + 605$ |
$4$ |
[0,2] |
$2^{4}\cdot 5^{3}\cdot 11^{2}$ |
$3$ |
$22.1796067379$ |
$22.17960673794632$ |
✓ |
✓ |
|
$C_4$ (as 4T1) |
$[2, 2, 2]$ |
$2$ |
$1$ |
$0.962423650119$ |