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Download displayed columns for results| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 21.7.297...000.1 | $x^{21} - 3 x^{20} - 9 x^{19} + 124 x^{18} - 631 x^{17} + 802 x^{16} + 1826 x^{15} - 27193 x^{14} + 110548 x^{13} - 224650 x^{12} + 303049 x^{11} + 450353 x^{10} - 265331 x^{9} + 796296 x^{8} + 5445541 x^{7} - 12181122 x^{6} - 15402246 x^{5} + 20340053 x^{4} + 8297097 x^{3} - 25045665 x^{2} + 26864880 x + 1121605$ | $-\,2^{18}\cdot 5^{14}\cdot 7^{7}\cdot 41^{12}$ | $C_7^2:S_3$ (as 21T18) | trivial |
| 21.7.191...384.1 | $x^{21} - 42 x^{19} - 252 x^{18} - 126 x^{17} + 1078 x^{16} + 8876 x^{15} + 112790 x^{14} - 464520 x^{13} - 1249444 x^{12} + 7005208 x^{11} + 85428 x^{10} - 61941628 x^{9} + 217917392 x^{8} - 47675940 x^{7} - 3034648008 x^{6} + 9194214624 x^{5} + 622814024 x^{4} - 56041091848 x^{3} + 94469690336 x^{2} + 18876673312 x - 82335377944$ | $-\,2^{18}\cdot 7^{36}\cdot 31^{7}$ | $C_7^2:S_3$ (as 21T18) | trivial |