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| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 4.0.189.1 | $ x^{4} - x^{3} + 2 x + 1 $ | $3^{3}\cdot 7$ | $D_{4}$ (as 4T3) | trivial |
| 4.2.448.1 | $ x^{4} - 2 x^{3} + x^{2} - 2 x + 1 $ | $-\,2^{6}\cdot 7$ | $D_{4}$ (as 4T3) | trivial |
| 4.0.1008.1 | $ x^{4} - 5 x^{2} + 7 $ | $2^{4}\cdot 3^{2}\cdot 7$ | $D_{4}$ (as 4T3) | trivial |
| 4.2.1456.1 | $ x^{4} - 2 x^{2} - 2 x + 1 $ | $-\,2^{4}\cdot 7\cdot 13$ | $S_4$ (as 4T5) | trivial |
| 4.0.1953.1 | $ x^{4} - 2 x^{3} - 5 x^{2} + 6 x + 12 $ | $3^{2}\cdot 7\cdot 31$ | $D_{4}$ (as 4T3) | trivial |
| 4.0.1953.2 | $ x^{4} - x^{3} + 8 x^{2} - 5 x + 13 $ | $3^{2}\cdot 7\cdot 31$ | $D_{4}$ (as 4T3) | trivial |
| 4.2.2051.1 | $ x^{4} - x^{3} - x^{2} + 3 x + 1 $ | $-\,7\cdot 293$ | $S_4$ (as 4T5) | trivial |
| 4.2.2191.1 | $ x^{4} - x^{3} + 3 x^{2} - 1 $ | $-\,7\cdot 313$ | $S_4$ (as 4T5) | trivial |
| 4.2.2219.1 | $ x^{4} - x^{3} + 3 x^{2} - x - 1 $ | $-\,7\cdot 317$ | $S_4$ (as 4T5) | trivial |
| 4.0.2296.1 | $ x^{4} - x^{3} - 2 x^{2} + x + 3 $ | $2^{3}\cdot 7\cdot 41$ | $S_4$ (as 4T5) | trivial |
| 4.0.2429.1 | $ x^{4} - x^{3} - 2 x^{2} + 2 x + 3 $ | $7\cdot 347$ | $S_4$ (as 4T5) | trivial |
| 4.2.2443.1 | $ x^{4} - 3 x - 1 $ | $-\,7\cdot 349$ | $S_4$ (as 4T5) | trivial |
| 4.0.2457.2 | $ x^{4} - x^{3} - 6 x^{2} - x + 19 $ | $3^{3}\cdot 7\cdot 13$ | $D_{4}$ (as 4T3) | $[2]$ |
| 4.0.2709.1 | $ x^{4} - x^{3} - 7 x^{2} + 7 x + 19 $ | $3^{2}\cdot 7\cdot 43$ | $D_{4}$ (as 4T3) | trivial |
| 4.0.3024.1 | $ x^{4} - 2 x^{3} + 3 $ | $2^{4}\cdot 3^{3}\cdot 7$ | $S_4$ (as 4T5) | trivial |
| 4.2.3052.1 | $ x^{4} - x^{3} + x^{2} - x - 2 $ | $-\,2^{2}\cdot 7\cdot 109$ | $S_4$ (as 4T5) | trivial |
| 4.2.4032.1 | $ x^{4} - 2 x^{3} - x^{2} - 4 x - 2 $ | $-\,2^{6}\cdot 3^{2}\cdot 7$ | $D_{4}$ (as 4T3) | trivial |
| 4.0.4032.2 | $ x^{4} - 10 x^{2} + 28 $ | $2^{6}\cdot 3^{2}\cdot 7$ | $D_{4}$ (as 4T3) | trivial |
| 4.0.4221.2 | $ x^{4} - 2 x^{3} - 8 x^{2} + 9 x + 27 $ | $3^{2}\cdot 7\cdot 67$ | $D_{4}$ (as 4T3) | trivial |
| 4.2.4319.1 | $ x^{4} - x^{3} - 4 x^{2} - x + 2 $ | $-\,7\cdot 617$ | $S_4$ (as 4T5) | trivial |
| 4.2.4564.1 | $ x^{4} - x^{3} - 5 x + 1 $ | $-\,2^{2}\cdot 7\cdot 163$ | $S_4$ (as 4T5) | trivial |
| 4.2.4648.1 | $ x^{4} + x^{2} - 6 x - 4 $ | $-\,2^{3}\cdot 7\cdot 83$ | $S_4$ (as 4T5) | trivial |
| 4.2.4907.1 | $ x^{4} - x^{3} - 2 x^{2} - 4 x - 1 $ | $-\,7\cdot 701$ | $S_4$ (as 4T5) | trivial |
| 4.0.4977.2 | $ x^{4} - x^{3} - 11 x^{2} + 6 x + 36 $ | $3^{2}\cdot 7\cdot 79$ | $D_{4}$ (as 4T3) | trivial |
| 4.2.5348.1 | $ x^{4} - x^{3} + 4 x^{2} - x - 1 $ | $-\,2^{2}\cdot 7\cdot 191$ | $S_4$ (as 4T5) | trivial |
| 4.2.5432.1 | $ x^{4} - x^{3} + x - 3 $ | $-\,2^{3}\cdot 7\cdot 97$ | $S_4$ (as 4T5) | trivial |
| 4.2.5887.1 | $ x^{4} - x^{3} - 3 x^{2} - 2 x + 4 $ | $-\,7\cdot 29^{2}$ | $D_{4}$ (as 4T3) | trivial |
| 4.0.6209.1 | $ x^{4} + x^{2} - x + 3 $ | $7\cdot 887$ | $S_4$ (as 4T5) | trivial |
| 4.0.6489.1 | $ x^{4} - x^{3} + 14 x^{2} - 5 x + 43 $ | $3^{2}\cdot 7\cdot 103$ | $D_{4}$ (as 4T3) | trivial |
| 4.0.6489.2 | $ x^{4} - x^{3} - 11 x^{2} + 48 $ | $3^{2}\cdot 7\cdot 103$ | $D_{4}$ (as 4T3) | trivial |
| 4.0.6685.1 | $ x^{4} - 2 x^{3} + 4 x^{2} - x + 3 $ | $5\cdot 7\cdot 191$ | $S_4$ (as 4T5) | trivial |
| 4.0.6832.1 | $ x^{4} - x^{2} - 2 x + 9 $ | $2^{4}\cdot 7\cdot 61$ | $S_4$ (as 4T5) | trivial |
| 4.4.7168.1 | $ x^{4} - 6 x^{2} + 7 $ | $2^{10}\cdot 7$ | $D_{4}$ (as 4T3) | trivial |
| 4.2.7259.1 | $ x^{4} + 4 x^{2} - x - 1 $ | $-\,7\cdot 17\cdot 61$ | $S_4$ (as 4T5) | trivial |
| 4.0.7504.1 | $ x^{4} + 5 x^{2} - 2 x + 1 $ | $2^{4}\cdot 7\cdot 67$ | $S_4$ (as 4T5) | $[2]$ |
| 4.2.7532.1 | $ x^{4} - 4 x^{2} - 2 x - 3 $ | $-\,2^{2}\cdot 7\cdot 269$ | $S_4$ (as 4T5) | trivial |
| 4.2.7616.2 | $ x^{4} - 2 x^{3} + 5 x^{2} + 6 x - 9 $ | $-\,2^{6}\cdot 7\cdot 17$ | $D_{4}$ (as 4T3) | trivial |
| 4.0.8001.2 | $ x^{4} - x^{3} - 14 x^{2} + 9 x + 57 $ | $3^{2}\cdot 7\cdot 127$ | $D_{4}$ (as 4T3) | $[3]$ |
| 4.0.8057.1 | $ x^{4} - 2 x^{3} + 5 x^{2} - x + 2 $ | $7\cdot 1151$ | $S_4$ (as 4T5) | trivial |
| 4.0.8092.1 | $ x^{4} - x^{3} + 5 x^{2} - 4 x + 6 $ | $2^{2}\cdot 7\cdot 17^{2}$ | $S_4$ (as 4T5) | trivial |
| 4.2.8127.1 | $ x^{4} - x^{3} - 7 x - 2 $ | $-\,3^{3}\cdot 7\cdot 43$ | $S_4$ (as 4T5) | trivial |
| 4.0.8757.1 | $ x^{4} - 2 x^{3} - 14 x^{2} + 15 x + 57 $ | $3^{2}\cdot 7\cdot 139$ | $D_{4}$ (as 4T3) | trivial |
| 4.0.8757.2 | $ x^{4} - x^{3} - 13 x^{2} + 13 x + 61 $ | $3^{2}\cdot 7\cdot 139$ | $D_{4}$ (as 4T3) | trivial |
| 4.2.8960.1 | $ x^{4} - 4 x - 2 $ | $-\,2^{8}\cdot 5\cdot 7$ | $S_4$ (as 4T5) | trivial |
| 4.2.9247.1 | $ x^{4} - x^{3} - 3 x^{2} + 6 x - 1 $ | $-\,7\cdot 1321$ | $S_4$ (as 4T5) | trivial |
| 4.0.9513.1 | $ x^{4} - x^{3} + 17 x^{2} - 8 x + 64 $ | $3^{2}\cdot 7\cdot 151$ | $D_{4}$ (as 4T3) | trivial |
| 4.2.9583.1 | $ x^{4} - 3 x^{2} - 7 $ | $-\,7\cdot 37^{2}$ | $D_{4}$ (as 4T3) | trivial |
| 4.2.9667.1 | $ x^{4} - 2 x^{3} - 2 x^{2} - x + 2 $ | $-\,7\cdot 1381$ | $S_4$ (as 4T5) | trivial |
| 4.2.10059.1 | $ x^{4} - x^{3} - 2 x^{2} - 6 x + 3 $ | $-\,3\cdot 7\cdot 479$ | $S_4$ (as 4T5) | trivial |
| 4.0.10269.2 | $ x^{4} - x^{3} - 14 x^{2} + 75 $ | $3^{2}\cdot 7\cdot 163$ | $D_{4}$ (as 4T3) | trivial |