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Results (displaying all 3 matches)
| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 17.1.124890250818288107857441.1 | x17 - 4x16 + 6x15 - 5x14 + 7x13 - 17x12 + 24x11 - 16x10 + 42x9 - 83x8 + 82x7 - 72x6 + 37x5 + 24x4 - 10x3 + 14x2 - 2x + 1 | \( 11^{8}\cdot 17^{12} \) | $C_{17}:C_{4}$ (as 17T3) | Trivial |
| 17.1.266353469466055312828111323136.1 | x17 + 17x15 + 85x13 - 68x12 + 595x11 - 1496x10 + 3638x9 - 4420x8 - 952x7 - 816x6 + 9248x5 - 7616x4 + 10880x3 - 4352x2 - 4096 | \( 2^{16}\cdot 17^{20} \) | $C_{17}:C_{4}$ (as 17T3) | Trivial (GRH) |
| 17.17.8972555039016074378226050552414591426720707963201.1 | x17 - 4x16 - 476x15 + 3026x14 + 82996x13 - 736812x12 - 6121180x11 + 80531352x10 + 108448584x9 - 4267795762x8 + 9723361580x7 + 95353221324x6 - 524744382701x5 - 7660737412x4 + 6800548404356x3 - 21491689501032x2 + 27480501953536x - 12878683864992 | \( 17^{12}\cdot 137^{16} \) | $C_{17}:C_{4}$ (as 17T3) | $[17]$ (GRH) |