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| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 4.2.3275.1 | $x^{4} - x^{3} + 2 x^{2} + 6 x - 9$ | $-\,5^{2}\cdot 131$ | $D_{4}$ (as 4T3) | trivial |
| 4.2.4192.1 | $x^{4} + x^{2} - 2 x - 2$ | $-\,2^{5}\cdot 131$ | $S_4$ (as 4T5) | trivial |
| 4.2.5371.1 | $x^{4} - 2 x^{3} - 2 x^{2} + x + 3$ | $-\,41\cdot 131$ | $S_4$ (as 4T5) | trivial |
| 4.0.6681.1 | $x^{4} - 2 x^{3} + x^{2} - 3 x + 5$ | $3\cdot 17\cdot 131$ | $S_4$ (as 4T5) | trivial |
| 4.2.13100.1 | $x^{4} - x^{3} + 2 x^{2} - 4 x - 4$ | $-\,2^{2}\cdot 5^{2}\cdot 131$ | $S_4$ (as 4T5) | $[2]$ |
| 4.2.13231.1 | $x^{4} + x^{2} - 5 x + 1$ | $-\,101\cdot 131$ | $S_4$ (as 4T5) | trivial |
| 4.2.14279.1 | $x^{4} - 2 x^{3} - 3 x^{2} + 3 x - 2$ | $-\,109\cdot 131$ | $S_4$ (as 4T5) | trivial |
| 4.2.16375.1 | $x^{4} - x^{3} + x^{2} + 14 x - 44$ | $-\,5^{3}\cdot 131$ | $D_{4}$ (as 4T3) | trivial |
| 4.0.21877.1 | $x^{4} - 2 x^{3} - 5 x + 17$ | $131\cdot 167$ | $S_4$ (as 4T5) | trivial |
| 4.2.22139.1 | $x^{4} - x^{3} - 7 x^{2} - 11 x - 9$ | $-\,13^{2}\cdot 131$ | $D_{4}$ (as 4T3) | trivial |
| 4.2.25152.1 | $x^{4} - 2 x^{3} - 5 x^{2} - 6 x - 1$ | $-\,2^{6}\cdot 3\cdot 131$ | $S_4$ (as 4T5) | trivial |
| 4.0.25152.1 | $x^{4} - 2 x^{3} + 11 x^{2} - 10 x + 27$ | $2^{6}\cdot 3\cdot 131$ | $D_{4}$ (as 4T3) | trivial |
| 4.2.27903.1 | $x^{4} + 3 x^{2} - 11 x + 3$ | $-\,3\cdot 71\cdot 131$ | $S_4$ (as 4T5) | trivial |
| 4.0.28165.1 | $x^{4} + 6 x^{2} - x + 4$ | $5\cdot 43\cdot 131$ | $S_4$ (as 4T5) | trivial |
| 4.2.28296.1 | $x^{4} - x^{3} + 6 x^{2} + x - 1$ | $-\,2^{3}\cdot 3^{3}\cdot 131$ | $S_4$ (as 4T5) | trivial |
| 4.0.28296.1 | $x^{4} - x^{3} + 6 x^{2} + 8 x + 16$ | $2^{3}\cdot 3^{3}\cdot 131$ | $S_4$ (as 4T5) | $[2]$ |
| 4.2.32095.1 | $x^{4} - x^{3} - 5 x^{2} + 7$ | $-\,5\cdot 7^{2}\cdot 131$ | $S_4$ (as 4T5) | trivial |
| 4.4.36025.1 | $x^{4} - x^{3} - 21 x^{2} + 20 x + 80$ | $5^{2}\cdot 11\cdot 131$ | $D_{4}$ (as 4T3) | trivial |
| 4.2.39300.1 | $x^{4} - 2 x^{3} - 7 x^{2} - 12$ | $-\,2^{2}\cdot 3\cdot 5^{2}\cdot 131$ | $S_4$ (as 4T5) | trivial |
| 4.0.42444.1 | $x^{4} - x^{3} + 3 x^{2} - 12 x + 12$ | $2^{2}\cdot 3^{4}\cdot 131$ | $S_4$ (as 4T5) | $[3]$ |
| 4.0.45064.1 | $x^{4} - x^{3} - 7 x^{2} + 2 x + 18$ | $2^{3}\cdot 43\cdot 131$ | $S_4$ (as 4T5) | trivial |
| 4.0.49780.1 | $x^{4} - x^{3} + 6 x^{2} - 8 x + 12$ | $2^{2}\cdot 5\cdot 19\cdot 131$ | $S_4$ (as 4T5) | trivial |
| 4.2.52400.1 | $x^{4} - 4 x^{2} - 10 x - 6$ | $-\,2^{4}\cdot 5^{2}\cdot 131$ | $S_4$ (as 4T5) | $[2]$ |
| 4.4.52400.1 | $x^{4} - 23 x^{2} + 131$ | $2^{4}\cdot 5^{2}\cdot 131$ | $D_{4}$ (as 4T3) | trivial |
| 4.0.53972.1 | $x^{4} - 2 x^{3} - 4 x + 13$ | $2^{2}\cdot 103\cdot 131$ | $S_4$ (as 4T5) | trivial |
| 4.2.56592.1 | $x^{4} + 3 x^{2} - 6 x - 15$ | $-\,2^{4}\cdot 3^{3}\cdot 131$ | $S_4$ (as 4T5) | trivial |
| 4.4.56592.1 | $x^{4} - 2 x^{3} - 9 x^{2} + 10 x + 22$ | $2^{4}\cdot 3^{3}\cdot 131$ | $D_{4}$ (as 4T3) | trivial |
| 4.2.56723.1 | $x^{4} - x^{3} - 3 x^{2} - 7 x - 1$ | $-\,131\cdot 433$ | $S_4$ (as 4T5) | trivial |
| 4.2.57247.1 | $x^{4} - 2 x^{3} + x^{2} - 7 x + 8$ | $-\,19\cdot 23\cdot 131$ | $S_4$ (as 4T5) | trivial |
| 4.2.57771.1 | $x^{4} - x^{3} - 2 x^{2} - 12 x - 3$ | $-\,3^{2}\cdot 7^{2}\cdot 131$ | $D_{4}$ (as 4T3) | trivial |
| 4.0.58164.1 | $x^{4} - 10 x^{2} - 2 x + 32$ | $2^{2}\cdot 3\cdot 37\cdot 131$ | $S_4$ (as 4T5) | trivial |
| 4.2.61439.1 | $x^{4} - x^{3} - 9 x^{2} - 10 x - 1$ | $-\,7\cdot 67\cdot 131$ | $S_4$ (as 4T5) | trivial |
| 4.0.62225.1 | $x^{4} - x^{3} + 25 x^{2} - 8 x + 164$ | $5^{2}\cdot 19\cdot 131$ | $D_{4}$ (as 4T3) | $[4]$ |
| 4.4.62225.1 | $x^{4} - 2 x^{3} - 25 x^{2} + 26 x + 149$ | $5^{2}\cdot 19\cdot 131$ | $D_{4}$ (as 4T3) | trivial |
| 4.4.66417.1 | $x^{4} - x^{3} - 13 x^{2} + 18 x + 12$ | $3\cdot 13^{2}\cdot 131$ | $D_{4}$ (as 4T3) | trivial |
| 4.2.70871.1 | $x^{4} - x^{3} - 2 x^{2} + 9 x - 16$ | $-\,131\cdot 541$ | $S_4$ (as 4T5) | trivial |
| 4.2.72312.1 | $x^{4} - x^{3} - x^{2} - 6 x + 6$ | $-\,2^{3}\cdot 3\cdot 23\cdot 131$ | $S_4$ (as 4T5) | trivial |
| 4.0.74932.1 | $x^{4} - x^{3} + 5 x^{2} - 7 x + 8$ | $2^{2}\cdot 11\cdot 13\cdot 131$ | $S_4$ (as 4T5) | $[3]$ |
| 4.2.75456.2 | $x^{4} - 2 x^{3} + 4 x^{2} + 18 x - 39$ | $-\,2^{6}\cdot 3^{2}\cdot 131$ | $D_{4}$ (as 4T3) | trivial |
| 4.2.75980.1 | $x^{4} - 2 x^{2} - 20 x + 5$ | $-\,2^{2}\cdot 5\cdot 29\cdot 131$ | $S_4$ (as 4T5) | trivial |
| 4.4.76897.1 | $x^{4} - 13 x^{2} - 10 x + 3$ | $131\cdot 587$ | $S_4$ (as 4T5) | trivial |
| 4.2.80303.1 | $x^{4} - 3 x^{2} - 7 x + 1$ | $-\,131\cdot 613$ | $S_4$ (as 4T5) | trivial |
| 4.0.81744.1 | $x^{4} + 2 x^{2} - 10 x + 14$ | $2^{4}\cdot 3\cdot 13\cdot 131$ | $S_4$ (as 4T5) | trivial |
| 4.4.82661.1 | $x^{4} - 8 x^{2} - x + 10$ | $131\cdot 631$ | $S_4$ (as 4T5) | trivial |
| 4.0.82661.2 | $x^{4} - x^{3} - 2 x^{2} - 8 x + 17$ | $131\cdot 631$ | $S_4$ (as 4T5) | $[2]$ |
| 4.4.88949.1 | $x^{4} - 14 x^{2} - 11 x - 2$ | $7\cdot 97\cdot 131$ | $S_4$ (as 4T5) | trivial |
| 4.0.92224.1 | $x^{4} - 2 x^{3} + 21 x^{2} - 14 x + 83$ | $2^{6}\cdot 11\cdot 131$ | $D_{4}$ (as 4T3) | trivial |
| 4.2.94451.1 | $x^{4} - x^{3} + 8 x^{2} + 2 x - 1$ | $-\,7\cdot 103\cdot 131$ | $S_4$ (as 4T5) | trivial |
| 4.2.94975.2 | $x^{4} - x^{3} - 12 x^{2} + 43 x - 251$ | $-\,5^{2}\cdot 29\cdot 131$ | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.100608.2 | $x^{4} + 2 x^{2} - 28 x + 98$ | $2^{8}\cdot 3\cdot 131$ | $D_{4}$ (as 4T3) | $[2]$ |