Further refine search
Results (displaying all 4 matches)
| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 18.0.94412655580832901097225443.1 | x18 - 3x17 + 24x16 - 57x15 + 339x14 - 750x13 + 2691x12 - 4620x11 + 12813x10 - 19451x9 + 38334x8 - 40263x7 + 55569x6 - 41604x5 + 50556x4 - 25632x3 + 19056x2 + 1056x + 64 | \( -\,3^{33}\cdot 19^{8} \) | $C_2\times He_3$ (as 18T15) | $[3]$ |
| 18.0.6149740048489888978791661947.1 | x18 - 3x17 + 27x16 - 26x15 + 321x14 - 123x13 + 2645x12 + 1020x11 + 13374x10 + 10200x9 + 51657x8 + 49845x7 + 115629x6 + 89958x5 + 147603x4 + 114065x3 + 107682x2 + 43053x + 16129 | \( -\,3^{27}\cdot 73^{8} \) | $C_2\times He_3$ (as 18T15) | $[21]$ (GRH) |
| 18.18.24749711184581860025231066529792.1 | x18 - 54x16 + 1089x14 - 10116x12 + 43200x10 - 74196x8 + 58644x6 - 21627x4 + 3078x2 - 27 | \( 2^{18}\cdot 3^{33}\cdot 19^{8} \) | $C_2\times He_3$ (as 18T15) | Trivial (GRH) |
| 18.18.61466572643771419985172814453125.1 | x18 - 3x17 - 45x16 + 108x15 + 792x14 - 1416x13 - 7026x12 + 8616x11 + 33624x10 - 25698x9 - 85104x8 + 37308x7 + 103944x6 - 26562x5 - 48483x4 + 12969x3 + 6732x2 - 2397x + 181 | \( 3^{32}\cdot 5^{9}\cdot 19^{8} \) | $C_2\times He_3$ (as 18T15) | Trivial (GRH) |