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Results (displaying all 6 matches)
| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 18.0.13950087665617805207.1 | x18 - x17 + 4x15 - 5x14 + x13 + 6x12 - 9x11 + 7x10 + x9 - 12x8 + 11x7 - 2x6 - 5x5 + 6x4 - x3 - x2 - x + 1 | \( -\,11^{4}\cdot 23^{11} \) | 18T217 | Trivial |
| 18.0.2439192980259653120000.1 | x18 - x17 - 5x16 - 2x15 + 21x14 + 6x13 - 30x12 - 20x11 + 22x10 + 44x9 + 2x8 - 48x7 - 52x6 + 32x5 + 39x4 - 7x3 + 9x2 - 4x + 1 | \( -\,2^{12}\cdot 5^{4}\cdot 23^{11} \) | 18T217 | Trivial |
| 18.10.7287505788086698516480000.1 | x18 - x17 - 3x16 + 10x15 - 26x14 - 16x13 + 66x12 + 14x11 + 3x10 - 201x9 + 269x8 - 58x7 - 216x6 + 262x5 - 142x4 + 32x3 + 13x2 - 9x + 1 | \( 2^{16}\cdot 5^{4}\cdot 37^{11} \) | 18T217 | Trivial |
| 18.10.7287505788086698516480000.2 | x18 - x17 + x16 - 4x15 - 46x14 + 70x13 + 80x12 - 70x11 - 19x10 - 181x9 + 199x8 - 86x7 + 46x6 + 64x5 - 98x4 + 62x3 - 19x2 - x + 1 | \( 2^{16}\cdot 5^{4}\cdot 37^{11} \) | 18T217 | Trivial |
| 18.18.1312344314786811555857947230208.1 | x18 - 3x17 - 39x16 + 94x15 + 516x14 - 964x13 - 2986x12 + 3986x11 + 8125x10 - 6047x9 - 10989x8 + 2338x7 + 6508x6 + 816x5 - 1194x4 - 324x3 + 37x2 + 17x + 1 | \( 2^{16}\cdot 37^{11}\cdot 103^{4} \) | 18T217 | Trivial (GRH) |
| 18.18.8579614079673266727444373410729984.1 | x18 - 60x16 - 14x15 + 1404x14 + 594x13 - 16313x12 - 8910x11 + 100266x10 + 57000x9 - 332226x8 - 153702x7 + 603459x6 + 148230x5 - 574938x4 + 23814x3 + 223074x2 - 78732x + 6561 | \( 2^{12}\cdot 3^{25}\cdot 47^{11} \) | 18T217 | Trivial (GRH) |