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Download displayed columns for resultsLabel | Polynomial | Discriminant | Galois group | Class group |
---|---|---|---|---|
19.1.714...419.1 | $x^{19} + 19 x^{15} - 19 x^{14} - 19 x^{13} + 171 x^{12} + 19 x^{11} - 266 x^{10} + 19 x^{9} + 475 x^{8} + 741 x^{7} + 437 x^{6} + 38 x^{5} - 38 x^{4} - 19 x^{3} + 1$ | $-\,19^{21}$ | $C_{19}:C_{6}$ (as 19T4) | trivial |
19.1.158...459.1 | $x^{19} - 171 x^{16} - 950 x^{15} + 570 x^{14} + 8683 x^{13} + 45277 x^{12} + 196973 x^{11} + 941507 x^{10} + 5016304 x^{9} + 7072465 x^{8} - 53817785 x^{7} - 342335673 x^{6} - 1023131209 x^{5} - 1426640821 x^{4} + 157805450 x^{3} + 1883060322 x^{2} - 656755330 x - 2423978601$ | $-\,19^{33}$ | $C_{19}:C_{6}$ (as 19T4) | trivial |