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| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 4.0.3973.1 | $x^{4} - x^{3} + 3 x^{2} - 5 x + 3$ | $29\cdot 137$ | $S_4$ (as 4T5) | trivial |
| 4.2.4384.1 | $x^{4} - 2 x^{3} + 3 x^{2} - 4$ | $-\,2^{5}\cdot 137$ | $S_4$ (as 4T5) | trivial |
| 4.0.6713.1 | $x^{4} - 2 x^{3} - x^{2} + 2 x + 8$ | $7^{2}\cdot 137$ | $D_{4}$ (as 4T3) | trivial |
| 4.0.8768.1 | $x^{4} - 2 x^{3} + 3 x^{2} - 2 x + 9$ | $2^{6}\cdot 137$ | $D_{4}$ (as 4T3) | trivial |
| 4.4.8768.1 | $x^{4} - 2 x^{3} - 5 x^{2} + 6 x + 7$ | $2^{6}\cdot 137$ | $D_{4}$ (as 4T3) | trivial |
| 4.2.10960.1 | $x^{4} - 2 x^{3} + 2 x^{2} + 8 x - 4$ | $-\,2^{4}\cdot 5\cdot 137$ | $S_4$ (as 4T5) | trivial |
| 4.0.11097.1 | $x^{4} - x^{3} + 3 x^{2} - 2 x + 5$ | $3^{4}\cdot 137$ | $S_4$ (as 4T5) | trivial |
| 4.0.16577.1 | $x^{4} - x^{3} + x^{2} - 10 x + 12$ | $11^{2}\cdot 137$ | $D_{4}$ (as 4T3) | trivial |
| 4.0.19728.1 | $x^{4} - 2 x^{3} - 15 x^{2} + 16 x + 73$ | $2^{4}\cdot 3^{2}\cdot 137$ | $D_{4}$ (as 4T3) | $[2]$ |
| 4.2.24523.1 | $x^{4} - 4 x^{2} - 3 x + 5$ | $-\,137\cdot 179$ | $S_4$ (as 4T5) | trivial |
| 4.4.25893.1 | $x^{4} - 6 x^{2} - x + 3$ | $3^{3}\cdot 7\cdot 137$ | $S_4$ (as 4T5) | trivial |
| 4.2.26304.1 | $x^{4} - 2 x^{3} - 4 x^{2} - 6 x - 3$ | $-\,2^{6}\cdot 3\cdot 137$ | $S_4$ (as 4T5) | trivial |
| 4.2.27263.1 | $x^{4} - 2 x^{3} + 5 x^{2} + 4 x - 9$ | $-\,137\cdot 199$ | $S_4$ (as 4T5) | trivial |
| 4.2.28907.1 | $x^{4} - x^{3} - 5 x^{2} + 5 x - 16$ | $-\,137\cdot 211$ | $S_4$ (as 4T5) | trivial |
| 4.2.29592.1 | $x^{4} - x^{3} - 3 x^{2} + 10 x + 2$ | $-\,2^{3}\cdot 3^{3}\cdot 137$ | $S_4$ (as 4T5) | trivial |
| 4.2.32195.1 | $x^{4} - x^{3} + 2 x^{2} - 4 x - 3$ | $-\,5\cdot 47\cdot 137$ | $S_4$ (as 4T5) | trivial |
| 4.0.32880.1 | $x^{4} + 5 x^{2} - 6 x + 3$ | $2^{4}\cdot 3\cdot 5\cdot 137$ | $S_4$ (as 4T5) | trivial |
| 4.4.33428.1 | $x^{4} - x^{3} - 8 x^{2} + 8 x + 4$ | $2^{2}\cdot 61\cdot 137$ | $S_4$ (as 4T5) | trivial |
| 4.0.33428.2 | $x^{4} - x^{3} - 2 x^{2} - 4 x + 12$ | $2^{2}\cdot 61\cdot 137$ | $S_4$ (as 4T5) | $[2]$ |
| 4.0.35072.1 | $x^{4} + 12 x^{2} - 8 x + 41$ | $2^{8}\cdot 137$ | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.35072.2 | $x^{4} + 4 x^{2} - 16 x + 33$ | $2^{8}\cdot 137$ | $D_{4}$ (as 4T3) | $[2]$ |
| 4.2.36031.1 | $x^{4} + x^{2} - x - 5$ | $-\,137\cdot 263$ | $S_4$ (as 4T5) | trivial |
| 4.2.36579.1 | $x^{4} - x^{3} - x^{2} - 5 x + 3$ | $-\,3\cdot 89\cdot 137$ | $S_4$ (as 4T5) | trivial |
| 4.0.37264.1 | $x^{4} - 13 x^{2} - 20 x + 149$ | $2^{4}\cdot 17\cdot 137$ | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.37264.2 | $x^{4} - 2 x^{3} - x^{2} + 2 x + 145$ | $2^{4}\cdot 17\cdot 137$ | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.39593.1 | $x^{4} - x^{3} + 10 x^{2} - 7 x + 49$ | $17^{2}\cdot 137$ | $D_{4}$ (as 4T3) | trivial |
| 4.0.41237.1 | $x^{4} - x^{3} + 4 x^{2} + 7$ | $7\cdot 43\cdot 137$ | $S_4$ (as 4T5) | trivial |
| 4.0.42196.1 | $x^{4} - 2 x^{3} + 8 x^{2} - 2 x + 8$ | $2^{2}\cdot 7\cdot 11\cdot 137$ | $S_4$ (as 4T5) | $[5]$ |
| 4.0.43840.1 | $x^{4} - 2 x^{3} - 24 x^{2} + 22 x + 173$ | $2^{6}\cdot 5\cdot 137$ | $D_{4}$ (as 4T3) | $[4]$ |
| 4.2.47128.1 | $x^{4} - x^{3} - 6 x^{2} + 13 x - 5$ | $-\,2^{3}\cdot 43\cdot 137$ | $S_4$ (as 4T5) | trivial |
| 4.0.48909.1 | $x^{4} - x^{3} - 5 x^{2} + 9 x + 17$ | $3\cdot 7\cdot 17\cdot 137$ | $S_4$ (as 4T5) | trivial |
| 4.2.49183.1 | $x^{4} - 2 x^{3} + x^{2} - 5 x - 3$ | $-\,137\cdot 359$ | $S_4$ (as 4T5) | trivial |
| 4.0.49457.1 | $x^{4} - x^{3} - 3 x^{2} + 4 x + 16$ | $19^{2}\cdot 137$ | $D_{4}$ (as 4T3) | trivial |
| 4.2.49731.1 | $x^{4} - x^{3} - 8 x^{2} + 11$ | $-\,3\cdot 11^{2}\cdot 137$ | $S_4$ (as 4T5) | trivial |
| 4.0.50964.1 | $x^{4} - 2 x^{3} + 2 x^{2} + 4 x + 7$ | $2^{2}\cdot 3\cdot 31\cdot 137$ | $S_4$ (as 4T5) | trivial |
| 4.2.51512.1 | $x^{4} - x^{3} - 5 x^{2} + 8 x + 8$ | $-\,2^{3}\cdot 47\cdot 137$ | $S_4$ (as 4T5) | trivial |
| 4.0.52197.1 | $x^{4} - x^{3} + x^{2} + 6 x + 8$ | $3\cdot 127\cdot 137$ | $S_4$ (as 4T5) | trivial |
| 4.0.53704.1 | $x^{4} - x^{3} + 4 x^{2} - 2 x + 12$ | $2^{3}\cdot 7^{2}\cdot 137$ | $S_4$ (as 4T5) | trivial |
| 4.0.53704.2 | $x^{4} - x^{3} - 12 x^{2} - 7 x + 77$ | $2^{3}\cdot 7^{2}\cdot 137$ | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.53704.3 | $x^{4} - x^{3} + 2 x^{2} + 21 x + 63$ | $2^{3}\cdot 7^{2}\cdot 137$ | $D_{4}$ (as 4T3) | $[2]$ |
| 4.2.54115.1 | $x^{4} - x^{3} - 2 x^{2} - 5$ | $-\,5\cdot 79\cdot 137$ | $S_4$ (as 4T5) | trivial |
| 4.2.54252.1 | $x^{4} - x^{3} - 4 x^{2} - 2 x + 10$ | $-\,2^{2}\cdot 3^{2}\cdot 11\cdot 137$ | $S_4$ (as 4T5) | trivial |
| 4.0.54800.1 | $x^{4} - 27 x^{2} - 10 x + 221$ | $2^{4}\cdot 5^{2}\cdot 137$ | $D_{4}$ (as 4T3) | $[2]$ |
| 4.2.59184.1 | $x^{4} + 3 x^{2} - 6 x - 6$ | $-\,2^{4}\cdot 3^{3}\cdot 137$ | $S_4$ (as 4T5) | $[2]$ |
| 4.0.59869.1 | $x^{4} - x^{3} - 8 x^{2} + 2 x + 23$ | $19\cdot 23\cdot 137$ | $S_4$ (as 4T5) | trivial |
| 4.2.61376.2 | $x^{4} - 2 x^{3} - x^{2} - 20 x - 50$ | $-\,2^{6}\cdot 7\cdot 137$ | $D_{4}$ (as 4T3) | $[4]$ |
| 4.2.61376.3 | $x^{4} - 2 x^{3} + 15 x^{2} + 16 x - 64$ | $-\,2^{6}\cdot 7\cdot 137$ | $D_{4}$ (as 4T3) | $[2]$ |
| 4.2.61924.1 | $x^{4} - x^{3} + 6 x^{2} + 7 x + 1$ | $-\,2^{2}\cdot 113\cdot 137$ | $S_4$ (as 4T5) | trivial |
| 4.2.65075.1 | $x^{4} - x^{3} - 3 x^{2} - 3 x - 5$ | $-\,5^{2}\cdot 19\cdot 137$ | $S_4$ (as 4T5) | trivial |
| 4.2.68500.1 | $x^{4} - x^{3} + 6 x^{2} - 6 x - 4$ | $-\,2^{2}\cdot 5^{3}\cdot 137$ | $S_4$ (as 4T5) | $[2]$ |