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Results (displaying both matches)
| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 19.13.801631882964189735135508990628664.1 | x19 - 2x18 - 18x17 + 32x16 + 132x15 - 202x14 - 502x13 + 645x12 + 1045x11 - 1122x10 - 1176x9 + 1078x8 + 700x7 - 557x6 - 220x5 + 151x4 + 34x3 - 20x2 - 2x + 1 | \( -\,2^{3}\cdot 13^{2}\cdot 17\cdot 3229\cdot 34365587\cdot 85132367\cdot 3692009831 \) | $S_{19}$ (as 19T8) | Trivial (GRH) |
| 19.13.6102326046691495371062145790782484.1 | x19 - 3x18 - 12x17 + 40x16 + 52x15 - 216x14 - 88x13 + 614x12 + 8x11 - 987x10 + 143x9 + 904x8 - 163x7 - 461x6 + 72x5 + 128x4 - 14x3 - 18x2 + x + 1 | \( -\,2^{2}\cdot 90313\cdot 16881409121807\cdot 1000636759045331 \) | $S_{19}$ (as 19T8) | Trivial (GRH) |