| 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 |
| 4.2.28227.1 |
$x^{4} + 7 x^{2} - 12$ |
$4$ |
[2,1] |
$-\,3\cdot 97^{2}$ |
$2$ |
$12.9618258102$ |
$17.05872210923198$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$22.6396260317$ |
| 4.2.75272.1 |
$x^{4} + 5 x^{2} - 18$ |
$4$ |
[2,1] |
$-\,2^{3}\cdot 97^{2}$ |
$2$ |
$16.5637384397$ |
$27.85677655436824$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$47.8446860963$ |
| 4.0.75272.1 |
$x^{4} + 13 x^{2} + 18$ |
$4$ |
[0,2] |
$2^{3}\cdot 97^{2}$ |
$2$ |
$16.5637384397$ |
$27.85677655436824$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[3]$ |
$2$ |
$1$ |
$18.648766192$ |
| 4.2.103499.1 |
$x^{4} - 2 x^{3} + 10 x^{2} - 9 x - 4$ |
$4$ |
[2,1] |
$-\,11\cdot 97^{2}$ |
$2$ |
$17.9363486993$ |
$32.66496594212215$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$36.1162295403$ |
| 4.4.112908.1 |
$x^{4} - x^{3} - 16 x^{2} - 4 x + 16$ |
$4$ |
[4,0] |
$2^{2}\cdot 3\cdot 97^{2}$ |
$3$ |
$18.3307898539$ |
$34.11744421846396$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$92.4845210605$ |
| 4.0.112908.2 |
$x^{4} + 17 x^{2} + 48$ |
$4$ |
[0,2] |
$2^{2}\cdot 3\cdot 97^{2}$ |
$3$ |
$18.3307898539$ |
$34.11744421846396$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$1$ |
$18.648766192$ |
| 4.4.235225.1 |
$x^{4} - 51 x^{2} + 529$ |
$4$ |
[4,0] |
$5^{2}\cdot 97^{2}$ |
$2$ |
$22.0227155455$ |
$22.02271554554524$ |
|
✓ |
|
$C_2^2$ (as 4T2) |
trivial |
$2$ |
$3$ |
$33.9639753083$ |
| 4.2.291679.1 |
$x^{4} - 2 x^{3} + 21 x^{2} - 20 x + 3$ |
$4$ |
[2,1] |
$-\,31\cdot 97^{2}$ |
$2$ |
$23.2394738149$ |
$54.83611948342078$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$42.868691205$ |
| 4.2.301088.1 |
$x^{4} - 5 x^{2} - 18$ |
$4$ |
[2,1] |
$-\,2^{5}\cdot 97^{2}$ |
$2$ |
$23.4246635451$ |
$39.395431207184416$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$56.598830378$ |
| 4.4.301088.1 |
$x^{4} - 13 x^{2} + 18$ |
$4$ |
[4,0] |
$2^{5}\cdot 97^{2}$ |
$2$ |
$23.4246635451$ |
$39.395431207184416$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$131.958341177$ |
| 4.0.413996.1 |
$x^{4} - x^{3} + x^{2} - 61 x + 132$ |
$4$ |
[0,2] |
$2^{2}\cdot 11\cdot 97^{2}$ |
$3$ |
$25.3658275901$ |
$65.3299318842443$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[8]$ |
$2$ |
$1$ |
$18.648766192$ |
| 4.4.413996.1 |
$x^{4} - x^{3} - 22 x^{2} - x + 1$ |
$4$ |
[4,0] |
$2^{2}\cdot 11\cdot 97^{2}$ |
$3$ |
$25.3658275901$ |
$65.3299318842443$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$106.040987495$ |
| 4.2.451632.1 |
$x^{4} - 7 x^{2} - 12$ |
$4$ |
[2,1] |
$-\,2^{4}\cdot 3\cdot 97^{2}$ |
$3$ |
$25.9236516204$ |
$34.11744421846396$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$2$ |
$76.5184981458$ |
| 4.0.461041.1 |
$x^{4} - x^{3} - 2 x^{2} - 11 x + 24$ |
$4$ |
[0,2] |
$7^{2}\cdot 97^{2}$ |
$2$ |
$26.0576284416$ |
$36.039981591316774$ |
|
|
✓ |
$A_4$ (as 4T4) |
$[2]$ |
$2$ |
$1$ |
$22.7304574253$ |
| 4.0.461041.2 |
$x^{4} - 45 x^{2} + 676$ |
$4$ |
[0,2] |
$7^{2}\cdot 97^{2}$ |
$2$ |
$26.0576284416$ |
$26.057628441590765$ |
✓ |
✓ |
|
$C_2^2$ (as 4T2) |
$[9]$ |
$2$ |
$1$ |
$18.648766192$ |
| 4.0.498677.1 |
$x^{4} - 2 x^{3} + 12 x^{2} - 11 x + 6$ |
$4$ |
[0,2] |
$53\cdot 97^{2}$ |
$2$ |
$26.5738717401$ |
$71.7007670809734$ |
✓ |
|
✓ |
$D_{4}$ (as 4T3) |
$[5]$ |
$2$ |
$1$ |
$18.648766192$ |
| 4.2.677448.1 |
$x^{4} - 15 x^{2} - 162$ |
$4$ |
[2,1] |
$-\,2^{3}\cdot 3^{2}\cdot 97^{2}$ |
$3$ |
$28.6892365409$ |
$48.249352327259274$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$2$ |
$133.742892857$ |
| 4.4.677448.1 |
$x^{4} - x^{3} - 23 x^{2} + 48 x - 24$ |
$4$ |
[4,0] |
$2^{3}\cdot 3^{2}\cdot 97^{2}$ |
$3$ |
$28.6892365409$ |
$48.249352327259274$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$134.509901928$ |
| 4.2.743311.1 |
$x^{4} - 2 x^{3} - 13 x^{2} + 14 x - 48$ |
$4$ |
[2,1] |
$-\,79\cdot 97^{2}$ |
$2$ |
$29.3624736437$ |
$87.53856293085921$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$453.659695687$ |
| 4.0.837401.1 |
$x^{4} - x^{3} - 2 x^{2} - 11 x + 121$ |
$4$ |
[0,2] |
$89\cdot 97^{2}$ |
$2$ |
$30.2505565207$ |
$92.91393867445294$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[3]$ |
$2$ |
$1$ |
$18.648766192$ |
| 4.2.931491.1 |
$x^{4} - 2 x^{3} - 24 x^{2} + 25 x - 62$ |
$4$ |
[2,1] |
$-\,3^{2}\cdot 11\cdot 97^{2}$ |
$3$ |
$31.0666672495$ |
$56.57738063926254$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$2$ |
$106.807999515$ |
| 4.2.940900.1 |
$x^{4} - x^{3} - 23 x^{2} - 49 x - 24$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 5^{2}\cdot 97^{2}$ |
$3$ |
$31.1448230048$ |
$44.04543109109048$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$2$ |
$158.072997132$ |
| 4.0.1025581.1 |
$x^{4} - 2 x^{3} + 20 x^{2} - 19 x + 66$ |
$4$ |
[0,2] |
$97^{2}\cdot 109$ |
$2$ |
$31.8231005932$ |
$102.82509421342633$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[15]$ |
$2$ |
$1$ |
$18.648766192$ |
| 4.0.1166716.1 |
$x^{4} - x^{3} + 9 x^{2} - 65 x + 248$ |
$4$ |
[0,2] |
$2^{2}\cdot 31\cdot 97^{2}$ |
$3$ |
$32.8655790515$ |
$109.67223896684156$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[22]$ |
$2$ |
$1$ |
$18.648766192$ |
| 4.4.1166716.1 |
$x^{4} - x^{3} - 21 x^{2} + 47 x - 22$ |
$4$ |
[4,0] |
$2^{2}\cdot 31\cdot 97^{2}$ |
$3$ |
$32.8655790515$ |
$109.67223896684156$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$312.908803568$ |
| 4.0.1213761.1 |
$x^{4} - x^{3} + 5 x^{2} - 63 x + 186$ |
$4$ |
[0,2] |
$3\cdot 43\cdot 97^{2}$ |
$3$ |
$33.1919902851$ |
$111.86152153444007$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[18]$ |
$2$ |
$1$ |
$18.648766192$ |
| 4.4.1213761.1 |
$x^{4} - 2 x^{3} - 19 x^{2} + 20 x + 3$ |
$4$ |
[4,0] |
$3\cdot 43\cdot 97^{2}$ |
$3$ |
$33.1919902851$ |
$111.86152153444007$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$175.294620168$ |
| 4.0.1326669.1 |
$x^{4} - 2 x^{3} + 36 x^{2} - 35 x + 88$ |
$4$ |
[0,2] |
$3\cdot 47\cdot 97^{2}$ |
$3$ |
$33.9383438377$ |
$116.94870670511924$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[14]$ |
$2$ |
$1$ |
$18.648766192$ |
| 4.4.1326669.1 |
$x^{4} - 2 x^{3} - 10 x^{2} + 11 x + 6$ |
$4$ |
[4,0] |
$3\cdot 47\cdot 97^{2}$ |
$3$ |
$33.9383438377$ |
$116.94870670511924$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$438.917537326$ |
| 4.2.1533667.1 |
$x^{4} - 2 x^{3} - 6 x^{2} + 7 x - 12$ |
$4$ |
[2,1] |
$-\,97^{2}\cdot 163$ |
$2$ |
$35.1910940079$ |
$125.7417989373462$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$276.804265158$ |
| 4.2.1571303.1 |
$x^{4} - 2 x^{3} + 5 x^{2} - 4 x - 93$ |
$4$ |
[2,1] |
$-\,97^{2}\cdot 167$ |
$2$ |
$35.405031484$ |
$127.27529218194708$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$209.912175429$ |
| 4.4.1590121.1 |
$x^{4} - 55 x^{2} + 441$ |
$4$ |
[4,0] |
$13^{2}\cdot 97^{2}$ |
$2$ |
$35.5105618091$ |
$35.510561809129406$ |
|
✓ |
|
$C_2^2$ (as 4T2) |
trivial |
$2$ |
$3$ |
$251.268885153$ |
| 4.2.1655984.1 |
$x^{4} + 13 x^{2} - 176$ |
$4$ |
[2,1] |
$-\,2^{4}\cdot 11\cdot 97^{2}$ |
$3$ |
$35.8726973987$ |
$65.3299318842443$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$2$ |
$219.396623873$ |
| 4.2.1721847.1 |
$x^{4} - x^{3} - 13 x^{2} + 140 x - 188$ |
$4$ |
[2,1] |
$-\,3\cdot 61\cdot 97^{2}$ |
$3$ |
$36.2241863687$ |
$133.23287882501077$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$53.6858018534$ |
| 4.2.1721847.2 |
$x^{4} - 2 x^{3} - 17 x^{2} + 18 x - 16$ |
$4$ |
[2,1] |
$-\,3\cdot 61\cdot 97^{2}$ |
$3$ |
$36.2241863687$ |
$133.23287882501077$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$622.18864161$ |
| 4.2.1797119.1 |
$x^{4} - 2 x^{3} + 35 x^{2} - 34 x - 99$ |
$4$ |
[2,1] |
$-\,97^{2}\cdot 191$ |
$2$ |
$36.6137497564$ |
$136.11392287345186$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$206.541198287$ |
| 4.2.1806528.1 |
$x^{4} - 14 x^{2} - 48$ |
$4$ |
[2,1] |
$-\,2^{6}\cdot 3\cdot 97^{2}$ |
$3$ |
$36.6615797078$ |
$48.249352327259274$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$2$ |
$81.0990227362$ |
| 4.2.1806528.2 |
$x^{4} + 14 x^{2} - 48$ |
$4$ |
[2,1] |
$-\,2^{6}\cdot 3\cdot 97^{2}$ |
$3$ |
$36.6615797078$ |
$48.249352327259274$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$2$ |
$154.937038763$ |
| 4.0.1806528.1 |
$x^{4} + 34 x^{2} + 192$ |
$4$ |
[0,2] |
$2^{6}\cdot 3\cdot 97^{2}$ |
$3$ |
$36.6615797078$ |
$68.23488843692792$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[2, 2]$ |
$2$ |
$1$ |
$18.648766192$ |
| 4.4.1806528.1 |
$x^{4} - 34 x^{2} + 192$ |
$4$ |
[4,0] |
$2^{6}\cdot 3\cdot 97^{2}$ |
$3$ |
$36.6615797078$ |
$68.23488843692792$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$492.374083977$ |
| 4.2.1844164.1 |
$x^{4} - x^{3} + 4 x^{2} + 83 x + 99$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 7^{2}\cdot 97^{2}$ |
$3$ |
$36.8510515454$ |
$52.11525688318153$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$164.260162547$ |
| 4.4.1853573.1 |
$x^{4} - x^{3} - 26 x^{2} + x + 1$ |
$4$ |
[4,0] |
$97^{2}\cdot 197$ |
$2$ |
$36.8979657735$ |
$138.23530663329106$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$439.24350521$ |
| 4.2.1881800.3 |
$x^{4} - x^{3} + 2 x^{2} - 13 x - 25$ |
$4$ |
[2,1] |
$-\,2^{3}\cdot 5^{2}\cdot 97^{2}$ |
$3$ |
$37.0376451128$ |
$81.45370877440502$ |
|
|
|
$S_4$ (as 4T5) |
$[6]$ |
$2$ |
$2$ |
$32.0601071159$ |
| 4.2.1994708.1 |
$x^{4} + 5 x^{2} - 212$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 53\cdot 97^{2}$ |
$3$ |
$37.5811298196$ |
$143.4015341619468$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$83.4561749237$ |
| 4.2.1994708.2 |
$x^{4} - x^{3} - 13 x^{2} + 43 x + 6$ |
$4$ |
[2,1] |
$-\,2^{2}\cdot 53\cdot 97^{2}$ |
$3$ |
$37.5811298196$ |
$143.4015341619468$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$813.429194242$ |
| 4.2.2060571.1 |
$x^{4} - 2 x^{3} - 18 x^{2} + 19 x - 128$ |
$4$ |
[2,1] |
$-\,3\cdot 73\cdot 97^{2}$ |
$3$ |
$37.8875825691$ |
$145.74978559160903$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$389.300141459$ |
| 4.2.2060571.2 |
$x^{4} - 2 x^{3} + 8 x^{2} - 7 x - 12$ |
$4$ |
[2,1] |
$-\,3\cdot 73\cdot 97^{2}$ |
$3$ |
$37.8875825691$ |
$145.74978559160903$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$468.741097985$ |
| 4.0.2117025.1 |
$x^{4} - 41 x^{2} + 784$ |
$4$ |
[0,2] |
$3^{2}\cdot 5^{2}\cdot 97^{2}$ |
$3$ |
$38.1444622455$ |
$38.144462245521304$ |
✓ |
✓ |
|
$C_2^2$ (as 4T2) |
$[2, 14]$ |
$2$ |
$1$ |
$18.648766192$ |
| 4.0.2117025.2 |
$x^{4} - x^{3} - 22 x^{2} + 193 x + 2329$ |
$4$ |
[0,2] |
$3^{2}\cdot 5^{2}\cdot 97^{2}$ |
$3$ |
$38.1444622455$ |
$38.144462245521304$ |
✓ |
✓ |
|
$C_2^2$ (as 4T2) |
$[8]$ |
$2$ |
$1$ |
$7.5694115262$ |
| 4.0.2117025.3 |
$x^{4} + 143 x^{2} + 5476$ |
$4$ |
[0,2] |
$3^{2}\cdot 5^{2}\cdot 97^{2}$ |
$3$ |
$38.1444622455$ |
$38.144462245521304$ |
✓ |
✓ |
|
$C_2^2$ (as 4T2) |
$[56]$ |
$2$ |
$1$ |
$0.962423650119$ |
