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Results (4 matches)
Download displayed columns for resultsLabel | Polynomial | Discriminant | Galois group | Class group |
---|---|---|---|---|
18.0.189...247.1 | $x^{18} - 2 x^{17} - 2 x^{16} + 31 x^{15} - 24 x^{14} - 91 x^{13} + 259 x^{12} + 6 x^{11} - 586 x^{10} + 373 x^{9} + 529 x^{8} + 213 x^{7} - 2352 x^{6} + 1533 x^{5} + 3474 x^{4} - 7270 x^{3} + 5988 x^{2} - 2458 x + 421$ | $-\,7^{17}\cdot 13^{8}$ | $C_9:C_6$ (as 18T14) | trivial |
18.0.657...567.1 | $x^{18} + 42 x^{16} + 693 x^{14} + 5761 x^{12} + 26040 x^{10} + 65772 x^{8} + 90587 x^{6} + 61257 x^{4} + 15435 x^{2} + 1183$ | $-\,3^{24}\cdot 7^{17}$ | $C_9:C_6$ (as 18T14) | $[2, 2]$ |
18.18.177...309.1 | $x^{18} - 42 x^{16} - 14 x^{15} + 567 x^{14} + 378 x^{13} - 3339 x^{12} - 3402 x^{11} + 8505 x^{10} + 12726 x^{9} - 5481 x^{8} - 18417 x^{7} - 8008 x^{6} + 5796 x^{5} + 7770 x^{4} + 3731 x^{3} + 945 x^{2} + 126 x + 7$ | $3^{27}\cdot 7^{17}$ | $C_9:C_6$ (as 18T14) | trivial |
18.18.373...701.1 | $x^{18} - 2 x^{17} - 37 x^{16} + 87 x^{15} + 529 x^{14} - 1470 x^{13} - 3542 x^{12} + 12270 x^{11} + 10019 x^{10} - 52953 x^{9} - 1627 x^{8} + 114292 x^{7} - 37793 x^{6} - 119105 x^{5} + 54518 x^{4} + 52230 x^{3} - 20493 x^{2} - 5034 x - 167$ | $3^{9}\cdot 7^{17}\cdot 13^{8}$ | $C_9:C_6$ (as 18T14) | trivial |