Note: Search results may be incomplete. Given $p$-adic completions contain an unramified field and completions are only searched for ramified primes.
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Results (5 matches)
Download displayed columns for results| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 18.18.204...625.1 | $x^{18} - 252 x^{16} - 54 x^{15} + 23193 x^{14} + 10422 x^{13} - 948111 x^{12} - 706428 x^{11} + 17011926 x^{10} + 20460382 x^{9} - 130011723 x^{8} - 218884986 x^{7} + 325746051 x^{6} + 751622598 x^{5} + 1793520 x^{4} - 495568872 x^{3} + 129781728 x - 28840384$ | $3^{26}\cdot 5^{9}\cdot 7^{6}\cdot 29^{9}\cdot 41^{2}\cdot 379^{2}$ | $C_3^6.D_6:D_6$ (as 18T798) | trivial |
| 19.3.596...440.1 | $x^{19} - 6 x - 4$ | $2^{34}\cdot 5\cdot 41\cdot 2819\cdot 847901\cdot 708003258176033$ | $S_{19}$ (as 19T8) | trivial |
| 19.1.315...179.1 | $x^{19} + 6 x - 5$ | $-\,41\cdot 79\cdot 1096349\cdot 83926868840161\cdot 105771667957849$ | $S_{19}$ (as 19T8) | trivial |
| 19.1.322...579.1 | $x^{19} + 3 x - 7$ | $-\,11\cdot 41\cdot 211\cdot 509\cdot 12098189\cdot 36681902501\cdot 149876708897039$ | $S_{19}$ (as 19T8) | trivial |
| 20.10.241...419.1 | $x^{20} - 10 x^{19} + 34 x^{18} - 21 x^{17} - 135 x^{16} + 264 x^{15} + 122 x^{14} - 680 x^{13} + 158 x^{12} + 898 x^{11} - 439 x^{10} - 737 x^{9} + 429 x^{8} + 396 x^{7} - 229 x^{6} - 136 x^{5} + 74 x^{4} + 28 x^{3} - 15 x^{2} - 2 x + 1$ | $-\,11^{2}\cdot 41\cdot 3691\cdot 3628255063^{2}$ | $C_2^{10}.S_{10}$ (as 20T1110) | trivial |