Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)
Refine search
Label | Polynomial | Discriminant | Galois group | Class group |
---|---|---|---|---|
4.4.725.1 | $x^{4} - x^{3} - 3 x^{2} + x + 1$ | $5^{2}\cdot 29$ | $D_{4}$ (as 4T3) | trivial |
4.4.1125.1 | $x^{4} - x^{3} - 4 x^{2} + 4 x + 1$ | $3^{2}\cdot 5^{3}$ | $C_4$ (as 4T1) | trivial |
4.4.1600.1 | $x^{4} - 6 x^{2} + 4$ | $2^{6}\cdot 5^{2}$ | $C_2^2$ (as 4T2) | trivial |
4.4.1957.1 | $x^{4} - 4 x^{2} - x + 1$ | $19\cdot 103$ | $S_4$ (as 4T5) | trivial |
4.4.2000.1 | $x^{4} - 5 x^{2} + 5$ | $2^{4}\cdot 5^{3}$ | $C_4$ (as 4T1) | trivial |
4.4.2048.1 | $x^{4} - 4 x^{2} + 2$ | $2^{11}$ | $C_4$ (as 4T1) | trivial |
4.4.2225.1 | $x^{4} - x^{3} - 5 x^{2} + 2 x + 4$ | $5^{2}\cdot 89$ | $D_{4}$ (as 4T3) | trivial |
4.4.2304.1 | $x^{4} - 4 x^{2} + 1$ | $2^{8}\cdot 3^{2}$ | $C_2^2$ (as 4T2) | trivial |
4.4.2525.1 | $x^{4} - 2 x^{3} - 4 x^{2} + 5 x + 5$ | $5^{2}\cdot 101$ | $D_{4}$ (as 4T3) | trivial |
4.4.2624.1 | $x^{4} - 2 x^{3} - 3 x^{2} + 2 x + 1$ | $2^{6}\cdot 41$ | $D_{4}$ (as 4T3) | trivial |
4.4.2777.1 | $x^{4} - x^{3} - 4 x^{2} + x + 2$ | $2777$ | $S_4$ (as 4T5) | trivial |
4.4.3600.1 | $x^{4} - 2 x^{3} - 7 x^{2} + 8 x + 1$ | $2^{4}\cdot 3^{2}\cdot 5^{2}$ | $C_2^2$ (as 4T2) | trivial |
4.4.3981.1 | $x^{4} - x^{3} - 4 x^{2} + 2 x + 1$ | $3\cdot 1327$ | $S_4$ (as 4T5) | trivial |
4.4.4205.1 | $x^{4} - x^{3} - 5 x^{2} - x + 1$ | $5\cdot 29^{2}$ | $D_{4}$ (as 4T3) | trivial |
4.4.4225.1 | $x^{4} - 9 x^{2} + 4$ | $5^{2}\cdot 13^{2}$ | $C_2^2$ (as 4T2) | trivial |
4.4.4352.1 | $x^{4} - 6 x^{2} - 4 x + 2$ | $2^{8}\cdot 17$ | $D_{4}$ (as 4T3) | trivial |
4.4.4400.1 | $x^{4} - 7 x^{2} + 11$ | $2^{4}\cdot 5^{2}\cdot 11$ | $D_{4}$ (as 4T3) | trivial |
4.4.4525.1 | $x^{4} - x^{3} - 7 x^{2} + 3 x + 9$ | $5^{2}\cdot 181$ | $D_{4}$ (as 4T3) | trivial |
4.4.4752.1 | $x^{4} - 2 x^{3} - 3 x^{2} + 4 x + 1$ | $2^{4}\cdot 3^{3}\cdot 11$ | $D_{4}$ (as 4T3) | trivial |
4.4.4913.1 | $x^{4} - x^{3} - 6 x^{2} + x + 1$ | $17^{3}$ | $C_4$ (as 4T1) | trivial |
4.4.5125.1 | $x^{4} - 2 x^{3} - 6 x^{2} + 7 x + 11$ | $5^{3}\cdot 41$ | $D_{4}$ (as 4T3) | trivial |
4.4.5225.1 | $x^{4} - x^{3} - 8 x^{2} + x + 11$ | $5^{2}\cdot 11\cdot 19$ | $D_{4}$ (as 4T3) | trivial |
4.4.5725.1 | $x^{4} - x^{3} - 8 x^{2} + 6 x + 11$ | $5^{2}\cdot 229$ | $D_{4}$ (as 4T3) | trivial |
4.4.5744.1 | $x^{4} - 5 x^{2} - 2 x + 1$ | $2^{4}\cdot 359$ | $S_4$ (as 4T5) | trivial |
4.4.6125.1 | $x^{4} - x^{3} - 9 x^{2} + 9 x + 11$ | $5^{3}\cdot 7^{2}$ | $C_4$ (as 4T1) | trivial |
4.4.6224.1 | $x^{4} - 6 x^{2} - 2 x + 5$ | $2^{4}\cdot 389$ | $S_4$ (as 4T5) | trivial |
4.4.6809.1 | $x^{4} - 5 x^{2} - x + 1$ | $11\cdot 619$ | $S_4$ (as 4T5) | trivial |
4.4.7053.1 | $x^{4} - 2 x^{3} - 4 x^{2} + 3 x + 3$ | $3\cdot 2351$ | $S_4$ (as 4T5) | trivial |
4.4.7056.1 | $x^{4} - 5 x^{2} + 1$ | $2^{4}\cdot 3^{2}\cdot 7^{2}$ | $C_2^2$ (as 4T2) | trivial |
4.4.7168.1 | $x^{4} - 6 x^{2} + 7$ | $2^{10}\cdot 7$ | $D_{4}$ (as 4T3) | trivial |
4.4.7225.1 | $x^{4} - 11 x^{2} + 9$ | $5^{2}\cdot 17^{2}$ | $C_2^2$ (as 4T2) | trivial |
4.4.7232.1 | $x^{4} - 2 x^{3} - 5 x^{2} + 4 x + 4$ | $2^{6}\cdot 113$ | $D_{4}$ (as 4T3) | trivial |
4.4.7488.1 | $x^{4} - 2 x^{3} - 4 x^{2} + 2 x + 1$ | $2^{6}\cdot 3^{2}\cdot 13$ | $D_{4}$ (as 4T3) | trivial |
4.4.7537.1 | $x^{4} - x^{3} - 5 x^{2} + 4 x + 3$ | $7537$ | $S_4$ (as 4T5) | trivial |
4.4.7600.1 | $x^{4} - 9 x^{2} + 19$ | $2^{4}\cdot 5^{2}\cdot 19$ | $D_{4}$ (as 4T3) | trivial |
4.4.7625.1 | $x^{4} - x^{3} - 9 x^{2} + 4 x + 16$ | $5^{3}\cdot 61$ | $D_{4}$ (as 4T3) | trivial |
4.4.8000.1 | $x^{4} - 10 x^{2} + 20$ | $2^{6}\cdot 5^{3}$ | $C_4$ (as 4T1) | trivial |
4.4.8069.1 | $x^{4} - x^{3} - 5 x^{2} + 5 x + 1$ | $8069$ | $S_4$ (as 4T5) | trivial |
4.4.8112.1 | $x^{4} - 5 x^{2} + 3$ | $2^{4}\cdot 3\cdot 13^{2}$ | $D_{4}$ (as 4T3) | trivial |
4.4.8468.1 | $x^{4} - x^{3} - 5 x^{2} + 3 x + 4$ | $2^{2}\cdot 29\cdot 73$ | $S_4$ (as 4T5) | trivial |
4.4.8525.1 | $x^{4} - 2 x^{3} - 8 x^{2} + 9 x + 19$ | $5^{2}\cdot 11\cdot 31$ | $D_{4}$ (as 4T3) | trivial |
4.4.8725.1 | $x^{4} - x^{3} - 10 x^{2} + 2 x + 19$ | $5^{2}\cdot 349$ | $D_{4}$ (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 |
4.4.8789.1 | $x^{4} - x^{3} - 6 x^{2} - 2 x + 1$ | $11\cdot 17\cdot 47$ | $S_4$ (as 4T5) | trivial |
4.4.8957.1 | $x^{4} - x^{3} - 5 x^{2} + x + 1$ | $13^{2}\cdot 53$ | $D_{4}$ (as 4T3) | trivial |
4.4.9225.1 | $x^{4} - x^{3} - 10 x^{2} + 7 x + 19$ | $3^{2}\cdot 5^{2}\cdot 41$ | $D_{4}$ (as 4T3) | trivial |
4.4.9248.1 | $x^{4} - 5 x^{2} + 2$ | $2^{5}\cdot 17^{2}$ | $D_{4}$ (as 4T3) | trivial |
4.4.9301.1 | $x^{4} - x^{3} - 5 x^{2} + x + 3$ | $71\cdot 131$ | $S_4$ (as 4T5) | trivial |
4.4.9792.1 | $x^{4} - 2 x^{3} - 7 x^{2} + 2 x + 7$ | $2^{6}\cdot 3^{2}\cdot 17$ | $D_{4}$ (as 4T3) | trivial |
4.4.9909.1 | $x^{4} - 6 x^{2} - 3 x + 3$ | $3^{3}\cdot 367$ | $S_4$ (as 4T5) | trivial |