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| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 4.2.848.1 | $x^{4} - x^{2} - 2 x + 1$ | $-\,2^{4}\cdot 53$ | $S_4$ (as 4T5) | trivial |
| 4.0.2597.1 | $x^{4} + 4 x^{2} - x + 1$ | $7^{2}\cdot 53$ | $S_4$ (as 4T5) | trivial |
| 4.0.3392.1 | $x^{4} - 2 x^{3} - 6 x + 17$ | $2^{6}\cdot 53$ | $D_{4}$ (as 4T3) | trivial |
| 4.0.4240.1 | $x^{4} - 5 x^{2} - 6 x + 18$ | $2^{4}\cdot 5\cdot 53$ | $D_{4}$ (as 4T3) | trivial |
| 4.0.5300.1 | $x^{4} - x^{3} + 4 x + 4$ | $2^{2}\cdot 5^{2}\cdot 53$ | $S_4$ (as 4T5) | trivial |
| 4.0.5724.1 | $x^{4} - x^{3} - 3 x^{2} + 6$ | $2^{2}\cdot 3^{3}\cdot 53$ | $S_4$ (as 4T5) | trivial |
| 4.2.7155.1 | $x^{4} - x^{3} - 3$ | $-\,3^{3}\cdot 5\cdot 53$ | $S_4$ (as 4T5) | trivial |
| 4.0.7473.1 | $x^{4} + x^{2} - 3 x + 3$ | $3\cdot 47\cdot 53$ | $S_4$ (as 4T5) | trivial |
| 4.0.10865.1 | $x^{4} - x^{3} + 4 x^{2} - 5 x + 4$ | $5\cdot 41\cdot 53$ | $S_4$ (as 4T5) | trivial |
| 4.0.11024.1 | $x^{4} - 2 x^{3} - 11 x^{2} + 12 x + 40$ | $2^{4}\cdot 13\cdot 53$ | $D_{4}$ (as 4T3) | trivial |
| 4.0.11024.2 | $x^{4} - 2 x^{3} - 7 x^{2} + 8 x + 41$ | $2^{4}\cdot 13\cdot 53$ | $D_{4}$ (as 4T3) | trivial |
| 4.2.11448.1 | $x^{4} - x^{3} - 3 x^{2} + 8 x - 8$ | $-\,2^{3}\cdot 3^{3}\cdot 53$ | $S_4$ (as 4T5) | trivial |
| 4.2.13356.1 | $x^{4} - x^{3} - 7 x^{2} + 7 x - 2$ | $-\,2^{2}\cdot 3^{2}\cdot 7\cdot 53$ | $S_4$ (as 4T5) | trivial |
| 4.0.14416.1 | $x^{4} - 2 x^{2} - 2 x + 5$ | $2^{4}\cdot 17\cdot 53$ | $S_4$ (as 4T5) | trivial |
| 4.4.15317.1 | $x^{4} - 2 x^{3} - 4 x^{2} + 5 x + 2$ | $17^{2}\cdot 53$ | $D_{4}$ (as 4T3) | trivial |
| 4.4.15529.1 | $x^{4} - x^{3} - 6 x^{2} - x + 2$ | $53\cdot 293$ | $S_4$ (as 4T5) | trivial |
| 4.0.15529.2 | $x^{4} - x^{3} + 3 x^{2} - 4 x + 5$ | $53\cdot 293$ | $S_4$ (as 4T5) | $[2]$ |
| 4.2.16271.1 | $x^{4} - x^{3} - 2 x^{2} + 7 x - 6$ | $-\,53\cdot 307$ | $S_4$ (as 4T5) | trivial |
| 4.0.17172.1 | $x^{4} - x^{3} - 3 x^{2} + 3 x + 6$ | $2^{2}\cdot 3^{4}\cdot 53$ | $S_4$ (as 4T5) | trivial |
| 4.0.20776.1 | $x^{4} - x^{3} + 11 x^{2} - x + 22$ | $2^{3}\cdot 7^{2}\cdot 53$ | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.21200.1 | $x^{4} + 6 x^{2} - 6 x + 2$ | $2^{4}\cdot 5^{2}\cdot 53$ | $S_4$ (as 4T5) | $[2]$ |
| 4.2.21412.1 | $x^{4} - x^{3} - 3 x^{2} + 7 x + 4$ | $-\,2^{2}\cdot 53\cdot 101$ | $S_4$ (as 4T5) | trivial |
| 4.4.22896.1 | $x^{4} - 9 x^{2} - 4 x + 3$ | $2^{4}\cdot 3^{3}\cdot 53$ | $S_4$ (as 4T5) | trivial |
| 4.0.23373.1 | $x^{4} - 2 x^{3} - 6 x^{2} + 7 x + 28$ | $3^{2}\cdot 7^{2}\cdot 53$ | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.24645.1 | $x^{4} + 2 x^{2} - 7 x + 5$ | $3\cdot 5\cdot 31\cdot 53$ | $S_4$ (as 4T5) | $[3]$ |
| 4.0.25228.1 | $x^{4} - x^{3} + 6 x^{2} - 9 x + 7$ | $2^{2}\cdot 7\cdot 17\cdot 53$ | $S_4$ (as 4T5) | trivial |
| 4.2.26871.1 | $x^{4} - 2 x^{3} + 5 x^{2} - 4 x - 9$ | $-\,3\cdot 13^{2}\cdot 53$ | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.27136.1 | $x^{4} - 18 x^{2} + 106$ | $2^{9}\cdot 53$ | $D_{4}$ (as 4T3) | $[3]$ |
| 4.2.27560.1 | $x^{4} - 5 x^{2} - 8 x + 8$ | $-\,2^{3}\cdot 5\cdot 13\cdot 53$ | $S_4$ (as 4T5) | trivial |
| 4.2.30263.1 | $x^{4} - x^{3} - 4 x^{2} + 5 x - 4$ | $-\,53\cdot 571$ | $S_4$ (as 4T5) | trivial |
| 4.0.32065.1 | $x^{4} - x^{3} - 6 x^{2} - x + 23$ | $5\cdot 11^{2}\cdot 53$ | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.32701.1 | $x^{4} - x^{3} + 5 x^{2} - 7 x + 5$ | $53\cdot 617$ | $S_4$ (as 4T5) | trivial |
| 4.2.33072.1 | $x^{4} - 2 x^{3} - 4 x^{2} + 2 x + 6$ | $-\,2^{4}\cdot 3\cdot 13\cdot 53$ | $S_4$ (as 4T5) | trivial |
| 4.2.33867.1 | $x^{4} - 2 x^{3} - 2 x^{2} - 9 x - 6$ | $-\,3^{2}\cdot 53\cdot 71$ | $S_4$ (as 4T5) | trivial |
| 4.2.34291.1 | $x^{4} - 8 x^{2} - 7 x + 25$ | $-\,53\cdot 647$ | $S_4$ (as 4T5) | trivial |
| 4.2.35563.1 | $x^{4} - 2 x^{3} - 2 x^{2} - 5 x - 3$ | $-\,11\cdot 53\cdot 61$ | $S_4$ (as 4T5) | trivial |
| 4.0.38160.2 | $x^{4} - 2 x^{3} - 3 x^{2} + 4 x + 148$ | $2^{4}\cdot 3^{2}\cdot 5\cdot 53$ | $D_{4}$ (as 4T3) | $[2]$ |
| 4.2.38531.1 | $x^{4} - 2 x^{3} + 2 x^{2} + x - 6$ | $-\,53\cdot 727$ | $S_4$ (as 4T5) | trivial |
| 4.2.38796.1 | $x^{4} - x^{3} + x^{2} + 9 x + 2$ | $-\,2^{2}\cdot 3\cdot 53\cdot 61$ | $S_4$ (as 4T5) | trivial |
| 4.2.40492.1 | $x^{4} - 8 x^{2} - 6 x + 8$ | $-\,2^{2}\cdot 53\cdot 191$ | $S_4$ (as 4T5) | trivial |
| 4.2.41287.1 | $x^{4} - x^{3} + 4 x^{2} - 9 x - 4$ | $-\,19\cdot 41\cdot 53$ | $S_4$ (as 4T5) | trivial |
| 4.2.42188.1 | $x^{4} - x^{3} - 6 x - 2$ | $-\,2^{2}\cdot 53\cdot 199$ | $S_4$ (as 4T5) | trivial |
| 4.0.43248.1 | $x^{4} + 7 x^{2} - 6 x + 13$ | $2^{4}\cdot 3\cdot 17\cdot 53$ | $S_4$ (as 4T5) | trivial |
| 4.0.44573.1 | $x^{4} - 2 x^{3} + 8 x^{2} - 7 x + 5$ | $29^{2}\cdot 53$ | $D_{4}$ (as 4T3) | trivial |
| 4.2.45315.1 | $x^{4} - 2 x^{3} - 2 x^{2} - 9 x + 15$ | $-\,3^{2}\cdot 5\cdot 19\cdot 53$ | $S_4$ (as 4T5) | trivial |
| 4.2.45527.1 | $x^{4} - x^{3} - 2 x^{2} - 7 x + 5$ | $-\,53\cdot 859$ | $S_4$ (as 4T5) | trivial |
| 4.2.45580.1 | $x^{4} - x^{3} - 6 x^{2} + 4 x - 2$ | $-\,2^{2}\cdot 5\cdot 43\cdot 53$ | $S_4$ (as 4T5) | trivial |
| 4.0.46004.1 | $x^{4} - x^{3} + 3 x^{2} + 7 x + 4$ | $2^{2}\cdot 7\cdot 31\cdot 53$ | $S_4$ (as 4T5) | trivial |
| 4.0.48336.1 | $x^{4} + 7 x^{2} - 6 x + 6$ | $2^{4}\cdot 3\cdot 19\cdot 53$ | $S_4$ (as 4T5) | $[6]$ |
| 4.0.48389.1 | $x^{4} - x^{3} - 5 x^{2} - x + 15$ | $11\cdot 53\cdot 83$ | $S_4$ (as 4T5) | $[4]$ |