Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)
Refine search
| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 4.0.54025.1 | $x^{4} - x^{3} + 23 x^{2} - 12 x + 144$ | $5^{2}\cdot 2161$ | $D_{4}$ (as 4T3) | $[11]$ |
| 4.0.57025.1 | $x^{4} - 2 x^{3} + 27 x^{2} - 26 x + 149$ | $5^{2}\cdot 2281$ | $D_{4}$ (as 4T3) | $[11]$ |
| 4.0.61504.3 | $x^{4} - 2 x^{3} + 13 x^{2} - 12 x + 98$ | $2^{6}\cdot 31^{2}$ | $C_2^2$ (as 4T2) | $[12]$ |
| 4.0.63025.1 | $x^{4} - 2 x^{3} + 27 x^{2} - 26 x + 164$ | $5^{2}\cdot 2521$ | $D_{4}$ (as 4T3) | $[11]$ |
| 4.0.64576.2 | $x^{4} - 2 x^{3} + 21 x^{2} - 20 x + 68$ | $2^{6}\cdot 1009$ | $D_{4}$ (as 4T3) | $[13]$ |
| 4.0.65025.2 | $x^{4} - x^{2} + 64$ | $3^{2}\cdot 5^{2}\cdot 17^{2}$ | $C_2^2$ (as 4T2) | $[12]$ |
| 4.0.65025.3 | $x^{4} + 23 x^{2} + 196$ | $3^{2}\cdot 5^{2}\cdot 17^{2}$ | $C_2^2$ (as 4T2) | $[12]$ |
| 4.0.65025.4 | $x^{4} - x^{3} + 22 x^{2} + 21 x + 441$ | $3^{2}\cdot 5^{2}\cdot 17^{2}$ | $C_2^2$ (as 4T2) | $[12]$ |
| 4.0.67581.1 | $x^{4} - x^{3} + 9 x^{2} - 2 x + 8$ | $3^{3}\cdot 2503$ | $S_4$ (as 4T5) | $[11]$ |
| 4.0.67648.1 | $x^{4} - 2 x^{3} + 25 x^{2} - 24 x + 72$ | $2^{6}\cdot 7\cdot 151$ | $D_{4}$ (as 4T3) | $[12]$ |
| 4.0.69025.1 | $x^{4} - 2 x^{3} + 31 x^{2} - 30 x + 180$ | $5^{2}\cdot 11\cdot 251$ | $D_{4}$ (as 4T3) | $[12]$ |
| 4.0.69264.4 | $x^{4} + 19 x^{2} - 30 x + 46$ | $2^{4}\cdot 3^{2}\cdot 13\cdot 37$ | $D_{4}$ (as 4T3) | $[12]$ |
| 4.0.76025.1 | $x^{4} - x^{3} + 28 x^{2} - 7 x + 199$ | $5^{2}\cdot 3041$ | $D_{4}$ (as 4T3) | $[11]$ |
| 4.0.76176.2 | $x^{4} - 2 x^{3} + 7 x^{2} - 6 x + 78$ | $2^{4}\cdot 3^{2}\cdot 23^{2}$ | $C_2^2$ (as 4T2) | $[2, 6]$ |
| 4.0.78912.1 | $x^{4} - 2 x^{3} + 21 x^{2} - 20 x + 82$ | $2^{6}\cdot 3^{2}\cdot 137$ | $D_{4}$ (as 4T3) | $[14]$ |
| 4.0.79025.2 | $x^{4} - x^{3} + 28 x^{2} - 17 x + 209$ | $5^{2}\cdot 29\cdot 109$ | $D_{4}$ (as 4T3) | $[12]$ |
| 4.0.82953.2 | $x^{4} - x^{3} + 46 x^{2} - 9 x + 567$ | $3^{2}\cdot 13\cdot 709$ | $D_{4}$ (as 4T3) | $[12]$ |
| 4.0.83008.2 | $x^{4} - 2 x^{3} + 19 x^{2} - 12 x + 92$ | $2^{6}\cdot 1297$ | $D_{4}$ (as 4T3) | $[15]$ |
| 4.0.84025.1 | $x^{4} - x^{3} + 29 x^{2} - 10 x + 220$ | $5^{2}\cdot 3361$ | $D_{4}$ (as 4T3) | $[13]$ |
| 4.0.86132.1 | $x^{4} - x^{3} + 7 x^{2} - 7 x + 6$ | $2^{2}\cdot 61\cdot 353$ | $S_4$ (as 4T5) | $[11]$ |
| 4.0.87025.1 | $x^{4} + 27 x^{2} + 256$ | $5^{2}\cdot 59^{2}$ | $C_2^2$ (as 4T2) | $[12]$ |
| 4.0.87104.2 | $x^{4} - 2 x^{3} + 19 x^{2} - 16 x + 98$ | $2^{6}\cdot 1361$ | $D_{4}$ (as 4T3) | $[11]$ |
| 4.0.89152.1 | $x^{4} - 2 x^{3} + 21 x^{2} - 20 x + 92$ | $2^{6}\cdot 7\cdot 199$ | $D_{4}$ (as 4T3) | $[12]$ |
| 4.0.89401.1 | $x^{4} + 5 x^{2} + 81$ | $13^{2}\cdot 23^{2}$ | $C_2^2$ (as 4T2) | $[12]$ |
| 4.0.93248.1 | $x^{4} - 2 x^{3} + 29 x^{2} - 28 x + 98$ | $2^{6}\cdot 31\cdot 47$ | $D_{4}$ (as 4T3) | $[14]$ |
| 4.0.93456.1 | $x^{4} + 13 x^{2} - 12 x + 52$ | $2^{4}\cdot 3^{2}\cdot 11\cdot 59$ | $D_{4}$ (as 4T3) | $[14]$ |
| 4.0.94013.1 | $x^{4} - x^{3} - 8 x^{2} + 13 x + 35$ | $41\cdot 2293$ | $S_4$ (as 4T5) | $[11]$ |
| 4.0.94025.1 | $x^{4} - x^{3} + 33 x^{2} - 2 x + 244$ | $5^{2}\cdot 3761$ | $D_{4}$ (as 4T3) | $[11]$ |
| 4.0.94156.1 | $x^{4} - x^{3} + 2 x^{2} - 5 x + 39$ | $2^{2}\cdot 23539$ | $S_4$ (as 4T5) | $[11]$ |
| 4.0.94740.1 | $x^{4} - 4 x^{2} - 14 x + 29$ | $2^{2}\cdot 3\cdot 5\cdot 1579$ | $S_4$ (as 4T5) | $[11]$ |
| 4.0.95296.1 | $x^{4} - 2 x^{3} + 21 x^{2} - 20 x + 98$ | $2^{6}\cdot 1489$ | $D_{4}$ (as 4T3) | $[13]$ |
| 4.0.97344.2 | $x^{4} + 10 x^{2} + 64$ | $2^{6}\cdot 3^{2}\cdot 13^{2}$ | $C_2^2$ (as 4T2) | $[12]$ |
| 4.0.97344.6 | $x^{4} - 26 x^{2} + 676$ | $2^{6}\cdot 3^{2}\cdot 13^{2}$ | $C_2^2$ (as 4T2) | $[2, 6]$ |
| 4.0.99856.1 | $x^{4} - 39 x^{2} + 400$ | $2^{4}\cdot 79^{2}$ | $C_2^2$ (as 4T2) | $[15]$ |
| 4.0.101569.1 | $x^{4} - x^{3} + 17 x^{2} + 16 x + 48$ | $13^{2}\cdot 601$ | $D_{4}$ (as 4T3) | $[13]$ |
| 4.0.102976.1 | $x^{4} - 2 x^{3} - 13 x^{2} - 4 x + 114$ | $2^{6}\cdot 1609$ | $D_{4}$ (as 4T3) | $[11]$ |
| 4.0.103832.1 | $x^{4} - x^{3} + 6 x^{2} + 6 x + 8$ | $2^{3}\cdot 12979$ | $S_4$ (as 4T5) | $[11]$ |
| 4.0.104000.2 | $x^{4} - 2 x^{3} + 9 x^{2} - 8 x + 6$ | $2^{6}\cdot 5^{3}\cdot 13$ | $D_{4}$ (as 4T3) | $[12]$ |
| 4.0.104512.1 | $x^{4} - 2 x^{3} + 23 x^{2} - 8 x + 112$ | $2^{6}\cdot 23\cdot 71$ | $D_{4}$ (as 4T3) | $[16]$ |
| 4.0.104980.1 | $x^{4} - 2 x^{3} + 10 x^{2} - 4 x + 15$ | $2^{2}\cdot 5\cdot 29\cdot 181$ | $S_4$ (as 4T5) | $[11]$ |
| 4.0.105633.2 | $x^{4} - x^{3} + 7 x^{2} + 9 x + 48$ | $3^{2}\cdot 11^{2}\cdot 97$ | $D_{4}$ (as 4T3) | $[14]$ |
| 4.0.105641.1 | $x^{4} + 11 x^{2} - 24 x + 20$ | $149\cdot 709$ | $S_4$ (as 4T5) | $[11]$ |
| 4.0.106025.1 | $x^{4} - x^{3} + 34 x^{2} - 5 x + 275$ | $5^{2}\cdot 4241$ | $D_{4}$ (as 4T3) | $[13]$ |
| 4.0.106932.1 | $x^{4} - x^{3} + 5 x^{2} + 3 x + 6$ | $2^{2}\cdot 3\cdot 7\cdot 19\cdot 67$ | $S_4$ (as 4T5) | $[11]$ |
| 4.0.106956.2 | $x^{4} - x^{3} + 10 x^{2} - 6 x + 12$ | $2^{2}\cdot 3^{2}\cdot 2971$ | $S_4$ (as 4T5) | $[12]$ |
| 4.0.108025.1 | $x^{4} - x^{3} + 33 x^{2} - 22 x + 284$ | $5^{2}\cdot 29\cdot 149$ | $D_{4}$ (as 4T3) | $[16]$ |
| 4.0.108025.2 | $x^{4} - 2 x^{3} + 37 x^{2} - 36 x + 279$ | $5^{2}\cdot 29\cdot 149$ | $D_{4}$ (as 4T3) | $[12]$ |
| 4.0.108225.1 | $x^{4} - x^{3} - 53 x^{2} + 36 x + 756$ | $3^{2}\cdot 5^{2}\cdot 13\cdot 37$ | $D_{4}$ (as 4T3) | $[2, 6]$ |
| 4.0.108400.1 | $x^{4} + 33 x^{2} + 271$ | $2^{4}\cdot 5^{2}\cdot 271$ | $D_{4}$ (as 4T3) | $[12]$ |
| 4.0.108608.1 | $x^{4} - 2 x^{3} + 25 x^{2} - 24 x + 112$ | $2^{6}\cdot 1697$ | $D_{4}$ (as 4T3) | $[11]$ |