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| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 4.0.697.1 | $x^{4} - x^{3} + 2 x^{2} - x + 2$ | $17\cdot 41$ | $S_4$ (as 4T5) | trivial |
| 4.2.731.1 | $x^{4} - x^{3} + 2 x^{2} - 1$ | $-\,17\cdot 43$ | $S_4$ (as 4T5) | trivial |
| 4.0.1088.1 | $x^{4} - 2 x^{3} + x^{2} - 2 x + 3$ | $2^{6}\cdot 17$ | $D_{4}$ (as 4T3) | trivial |
| 4.0.1088.2 | $x^{4} - 2 x^{3} + 5 x^{2} - 4 x + 2$ | $2^{6}\cdot 17$ | $D_{4}$ (as 4T3) | trivial |
| 4.0.2057.1 | $x^{4} - x^{3} + 3 x + 2$ | $11^{2}\cdot 17$ | $S_4$ (as 4T5) | trivial |
| 4.0.2448.1 | $x^{4} - x^{2} - 6 x + 10$ | $2^{4}\cdot 3^{2}\cdot 17$ | $D_{4}$ (as 4T3) | $[2]$ |
| 4.2.4063.1 | $x^{4} - x^{3} - 3 x^{2} - 2 x + 1$ | $-\,17\cdot 239$ | $S_4$ (as 4T5) | trivial |
| 4.0.4352.1 | $x^{4} - 2 x^{2} - 4 x + 6$ | $2^{8}\cdot 17$ | $D_{4}$ (as 4T3) | $[2]$ |
| 4.4.4352.1 | $x^{4} - 6 x^{2} - 4 x + 2$ | $2^{8}\cdot 17$ | $D_{4}$ (as 4T3) | trivial |
| 4.2.4675.1 | $x^{4} - 2 x^{3} - 3 x - 1$ | $-\,5^{2}\cdot 11\cdot 17$ | $S_4$ (as 4T5) | trivial |
| 4.0.5440.1 | $x^{4} - 2 x^{3} - 4 x^{2} - 2 x + 25$ | $2^{6}\cdot 5\cdot 17$ | $D_{4}$ (as 4T3) | $[2]$ |
| 4.2.5644.1 | $x^{4} - x^{3} - 2 x^{2} - 4 x - 2$ | $-\,2^{2}\cdot 17\cdot 83$ | $S_4$ (as 4T5) | trivial |
| 4.0.6137.1 | $x^{4} - x^{3} + x^{2} + 2 x + 4$ | $17\cdot 19^{2}$ | $D_{4}$ (as 4T3) | trivial |
| 4.2.6664.1 | $x^{4} - x^{3} - 3 x^{2} - 2 x - 2$ | $-\,2^{3}\cdot 7^{2}\cdot 17$ | $S_4$ (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 |
| 4.2.6800.1 | $x^{4} - x^{2} - 2 x - 3$ | $-\,2^{4}\cdot 5^{2}\cdot 17$ | $S_4$ (as 4T5) | trivial |
| 4.0.6800.1 | $x^{4} - 2 x^{3} - x^{2} + 2 x + 26$ | $2^{4}\cdot 5^{2}\cdot 17$ | $D_{4}$ (as 4T3) | $[2]$ |
| 4.2.6987.1 | $x^{4} - x^{3} - 5 x^{2} + 3 x - 3$ | $-\,3\cdot 17\cdot 137$ | $S_4$ (as 4T5) | trivial |
| 4.2.7344.2 | $x^{4} - 3 x^{2} - 6 x + 9$ | $-\,2^{4}\cdot 3^{3}\cdot 17$ | $S_4$ (as 4T5) | trivial |
| 4.2.7463.1 | $x^{4} - 2 x^{3} + x^{2} - 8 x - 1$ | $-\,17\cdot 439$ | $S_4$ (as 4T5) | trivial |
| 4.2.7616.1 | $x^{4} - 2 x^{3} + 3 x^{2} - 2 x - 7$ | $-\,2^{6}\cdot 7\cdot 17$ | $D_{4}$ (as 4T3) | trivial |
| 4.2.8619.1 | $x^{4} - x^{3} - 4 x^{2} - 6 x - 3$ | $-\,3\cdot 13^{2}\cdot 17$ | $D_{4}$ (as 4T3) | trivial |
| 4.0.8704.1 | $x^{4} - 10 x^{2} + 34$ | $2^{9}\cdot 17$ | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.8704.2 | $x^{4} - 6 x^{2} + 34$ | $2^{9}\cdot 17$ | $D_{4}$ (as 4T3) | $[2]$ |
| 4.2.9163.1 | $x^{4} + x^{2} - 8 x - 3$ | $-\,7^{2}\cdot 11\cdot 17$ | $S_4$ (as 4T5) | trivial |
| 4.2.9384.1 | $x^{4} - x^{3} + x^{2} + 6 x - 6$ | $-\,2^{3}\cdot 3\cdot 17\cdot 23$ | $S_4$ (as 4T5) | trivial |
| 4.2.9452.1 | $x^{4} - x^{3} - 4 x^{2} - 6 x - 2$ | $-\,2^{2}\cdot 17\cdot 139$ | $S_4$ (as 4T5) | trivial |
| 4.2.10064.1 | $x^{4} - x^{2} - 2 x - 7$ | $-\,2^{4}\cdot 17\cdot 37$ | $S_4$ (as 4T5) | trivial |
| 4.0.11152.2 | $x^{4} - 5 x^{2} - 12 x + 45$ | $2^{4}\cdot 17\cdot 41$ | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.12325.1 | $x^{4} - 4 x^{2} - x + 7$ | $5^{2}\cdot 17\cdot 29$ | $S_4$ (as 4T5) | trivial |
| 4.2.13056.1 | $x^{4} + 2 x^{2} - 4 x - 1$ | $-\,2^{8}\cdot 3\cdot 17$ | $S_4$ (as 4T5) | trivial |
| 4.2.13175.1 | $x^{4} - 2 x^{3} + 5 x^{2} + x - 1$ | $-\,5^{2}\cdot 17\cdot 31$ | $S_4$ (as 4T5) | $[2]$ |
| 4.0.13328.1 | $x^{4} - 3 x^{2} - 14 x + 53$ | $2^{4}\cdot 7^{2}\cdot 17$ | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.13396.1 | $x^{4} + 8 x^{2} - 2 x + 1$ | $2^{2}\cdot 17\cdot 197$ | $S_4$ (as 4T5) | $[5]$ |
| 4.0.13549.1 | $x^{4} - x^{3} + 2 x^{2} - 6 x + 9$ | $17\cdot 797$ | $S_4$ (as 4T5) | trivial |
| 4.0.14144.1 | $x^{4} - 2 x^{3} - 12 x^{2} + 8 x + 58$ | $2^{6}\cdot 13\cdot 17$ | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.14144.2 | $x^{4} - 2 x^{3} - 8 x^{2} - 2 x + 61$ | $2^{6}\cdot 13\cdot 17$ | $D_{4}$ (as 4T3) | $[2]$ |
| 4.2.14688.1 | $x^{4} - 2 x^{3} + 3 x^{2} + 8 x - 16$ | $-\,2^{5}\cdot 3^{3}\cdot 17$ | $S_4$ (as 4T5) | trivial |
| 4.2.15147.1 | $x^{4} - x^{3} - 3 x^{2} + 3 x - 3$ | $-\,3^{4}\cdot 11\cdot 17$ | $S_4$ (as 4T5) | trivial |
| 4.2.15283.1 | $x^{4} - x^{3} + 5 x^{2} + x - 1$ | $-\,17\cdot 29\cdot 31$ | $S_4$ (as 4T5) | trivial |
| 4.0.15436.1 | $x^{4} + 2 x^{2} - 4 x + 16$ | $2^{2}\cdot 17\cdot 227$ | $S_4$ (as 4T5) | trivial |
| 4.2.15759.1 | $x^{4} - x^{3} - x^{2} + 4 x - 5$ | $-\,3^{2}\cdot 17\cdot 103$ | $S_4$ (as 4T5) | trivial |
| 4.2.16048.1 | $x^{4} - 4 x^{2} - 12 x - 4$ | $-\,2^{4}\cdot 17\cdot 59$ | $S_4$ (as 4T5) | trivial |
| 4.2.16320.1 | $x^{4} - 2 x^{3} + 2 x^{2} + 4 x - 2$ | $-\,2^{6}\cdot 3\cdot 5\cdot 17$ | $S_4$ (as 4T5) | trivial |
| 4.0.16524.1 | $x^{4} - 2 x^{3} + 9 x^{2} - 6 x + 12$ | $2^{2}\cdot 3^{5}\cdot 17$ | $S_4$ (as 4T5) | trivial |
| 4.4.16609.1 | $x^{4} - 7 x^{2} - x + 9$ | $17\cdot 977$ | $S_4$ (as 4T5) | trivial |
| 4.2.16847.1 | $x^{4} + x^{2} - 8 x - 7$ | $-\,17\cdot 991$ | $S_4$ (as 4T5) | trivial |
| 4.0.17680.2 | $x^{4} - 15 x^{2} - 6 x + 73$ | $2^{4}\cdot 5\cdot 13\cdot 17$ | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.17680.3 | $x^{4} - 11 x^{2} - 12 x + 72$ | $2^{4}\cdot 5\cdot 13\cdot 17$ | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.17884.1 | $x^{4} - x^{3} + 3 x^{2} - 4 x + 8$ | $2^{2}\cdot 17\cdot 263$ | $S_4$ (as 4T5) | trivial |