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Results (displaying all 10 matches)
| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 17.1.239072435685151324847153.1 | x17 - 34x12 + 17x11 + 85x10 + 102x9 - 170x8 - 272x7 - 68x6 + 255x5 + 255x4 + 68x3 + 17x2 + 17x + 4 | \( 17^{19} \) | $F_{17}$ (as 17T5) | Trivial |
| 17.1.604462909807314587353088.1 | x17 - 2x16 + 8x13 + 16x12 - 16x11 + 64x9 - 32x8 - 80x7 + 32x6 + 40x5 + 80x4 + 16x3 - 128x2 - 2x + 68 | \( 2^{79} \) | $F_{17}$ (as 17T5) | Trivial |
| 17.1.54214017802982966177103872.1 | x17 - 2 | \( 2^{16}\cdot 17^{17} \) | $F_{17}$ (as 17T5) | Trivial |
| 17.1.323140727299350298506640625.1 | x17 + 17x15 + 119x13 + 442x11 + 935x9 + 1122x7 + 714x5 + 204x3 + 17x - 1 | \( 5^{8}\cdot 17^{17} \) | $F_{17}$ (as 17T5) | Trivial |
| 17.1.35609980753388072399570113617.1 | x17 - 3 | \( 3^{16}\cdot 17^{17} \) | $F_{17}$ (as 17T5) | Trivial (GRH) |
| 17.1.126226846601308710354156494140625.1 | x17 - 5 | \( 5^{16}\cdot 17^{17} \) | $F_{17}$ (as 17T5) | Trivial (GRH) |
| 17.1.2333735698654040712778226966003712.1 | x17 - 6 | \( 2^{16}\cdot 3^{16}\cdot 17^{17} \) | $F_{17}$ (as 17T5) | Trivial (GRH) |
| 17.1.27491618187647178051040055821983377.1 | x17 - 7 | \( 7^{16}\cdot 17^{17} \) | $F_{17}$ (as 17T5) | Trivial (GRH) |
| 17.17.597436338855434422471226103296950272.1 | x17 - 51x15 + 1071x13 - 11934x11 + 75735x9 - 272646x7 + 520506x5 - 446148x3 + 111537x - 22482 | \( 2^{24}\cdot 3^{16}\cdot 17^{17} \) | $F_{17}$ (as 17T5) | Trivial (GRH) |
| 17.17.8272402618863367641770000000000000000.1 | x17 - 85x15 + 2975x13 - 55250x11 + 584375x9 - 3506250x7 + 11156250x5 - 15937500x3 + 6640625x - 1737500 | \( 2^{16}\cdot 5^{16}\cdot 17^{17} \) | $F_{17}$ (as 17T5) | Trivial (GRH) |