Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)
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Results (7 matches)
Download displayed columns for resultsLabel | Polynomial | Discriminant | Galois group | Class group |
---|---|---|---|---|
7.1.2892422420992.1 | $x^{7} - 3 x^{6} + 22 x^{5} - 130 x^{4} + 380 x^{3} - 372 x^{2} - 472 x + 904$ | $-\,2^{9}\cdot 13^{3}\cdot 137^{3}$ | $D_{7}$ (as 7T2) | $[167]$ |
7.1.32666728508063.1 | $x^{7} - 3 x^{6} - 3 x^{5} + 15 x^{4} - 214 x^{3} + 580 x^{2} + 968 x - 7744$ | $-\,13^{3}\cdot 2459^{3}$ | $D_{7}$ (as 7T2) | $[127]$ |
7.1.62110699441984375.2 | $x^{7} - 845$ | $-\,5^{6}\cdot 7^{7}\cdot 13^{6}$ | $F_7$ (as 7T4) | $[7, 28]$ |
7.1.357109822457554887.2 | $x^{7} - 87$ | $-\,3^{6}\cdot 7^{7}\cdot 29^{6}$ | $F_7$ (as 7T4) | $[14, 14]$ |
7.1.489...000.1 | $x^{7} - 16820$ | $-\,2^{6}\cdot 5^{6}\cdot 7^{7}\cdot 29^{6}$ | $F_7$ (as 7T4) | $[14, 14]$ |
7.7.177...121.6 | $x^{7} - 1491 x^{5} - 29323 x^{4} - 118783 x^{3} + 662004 x^{2} + 1844864 x + 899641$ | $7^{12}\cdot 71^{6}$ | $C_7$ (as 7T1) | $[2, 2, 2, 2, 2, 14]$ |
7.1.391...352.7 | $x^{7} - 602$ | $-\,2^{6}\cdot 7^{13}\cdot 43^{6}$ | $F_7$ (as 7T4) | $[7, 21]$ |