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Results (displaying all 7 matches)
| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 17.5.3621113810274499901.1 | x17 - 5x15 - x14 + 5x13 + 6x12 + 9x11 - 16x10 - 21x9 + 19x8 + 13x7 - 5x6 - 4x5 - 5x4 + 3x3 - x + 1 | \( 55954279\cdot 64715583419 \) | $S_{17}$ (as 17T10) | Trivial |
| 17.5.4755937542258621701.1 | x17 - 6x15 - 2x14 + 17x13 + 13x12 - 27x11 - 34x10 + 20x9 + 47x8 - 38x6 - 13x5 + 17x4 + 12x3 - 2x2 - 3x - 1 | \( 97\cdot 2927\cdot 2315407\cdot 7234597 \) | $S_{17}$ (as 17T10) | Trivial |
| 17.5.14517428819890014793.1 | x17 - 2x16 + 4x15 - 2x14 + 6x12 - 5x11 + x10 + 3x9 - 6x8 - 7x7 - x6 - 5x5 - 9x4 - 3x3 - 2x2 - 3x - 1 | \( 10170343\cdot 1427427651151 \) | $S_{17}$ (as 17T10) | Trivial |
| 17.5.89056089711131593861.1 | x17 - 2x16 - 5x15 + 8x14 + 14x13 - 6x12 - 34x11 - 12x10 + 42x9 + 47x8 - 33x7 - 52x6 + 13x5 + 21x4 + 3x3 - 5x2 - 2x + 1 | \( 946391\cdot 3063653\cdot 30715207 \) | $S_{17}$ (as 17T10) | Trivial |
| 17.5.37475477362914554710500388.1 | x17 - x16 - 4x15 + 4x14 + 6x13 - 6x12 - 8x11 + 8x10 + 9x9 - 7x8 - 9x7 + 3x6 + 9x5 - 2x4 - 6x3 + 4x2 + 2x - 1 | \( 2^{2}\cdot 9368869340728638677625097 \) | $S_{17}$ (as 17T10) | Trivial (GRH) |
| 17.5.47814524918055414168841988.1 | x17 - 2x16 - 2x15 + 9x14 - 8x13 - 6x12 + 22x11 - 20x10 - 4x9 + 23x8 - 20x7 + 7x6 + x5 - 11x4 + 11x3 - x2 - 3x + 1 | \( 2^{2}\cdot 71\cdot 113\cdot 398023\cdot 3743302227733793 \) | $S_{17}$ (as 17T10) | Trivial (GRH) |
| 17.5.87883485894978177600000000000000.1 | x17 - 8x16 - 17x15 + 376x14 - 1517x13 + 2374x12 - 258x11 - 2424x10 - 507x9 - 2266x8 + 26723x7 - 46312x6 + 33731x5 - 13660x4 + 980x3 + 10560x2 - 10440x + 2880 | \( 2^{18}\cdot 3^{28}\cdot 5^{14}\cdot 7^{4} \) | $A_{17}$ (as 17T9) | Trivial (GRH) |