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Results (displaying all 6 matches)
| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 15.3.1483978183108890624.1 | x15 - 3x14 + 5x13 - 2x12 + 3x11 + 11x10 + x9 + 22x8 + 13x7 + 9x6 + 5x5 - 12x4 - 14x3 - 12x2 - 8x - 2 | \( 2^{12}\cdot 3^{6}\cdot 89^{6} \) | $S_5$ (as 15T10) | Trivial |
| 15.3.1850284719998930944.1 | x15 - 2x14 + 13x12 - 18x11 + 38x9 - 58x8 + 38x7 - 12x6 - 58x5 + 110x4 - 77x3 + 22x2 - 1 | \( 2^{12}\cdot 277^{6} \) | $S_5$ (as 15T10) | Trivial |
| 15.3.2229025112064000000.1 | x15 - 5x14 + 9x13 - 11x12 + 17x11 - 17x10 - 3x9 + 13x8 - x7 + 21x6 - 25x5 - 5x4 - 13x3 - 3x2 - x - 1 | \( 2^{28}\cdot 3^{12}\cdot 5^{6} \) | $S_5$ (as 15T10) | Trivial |
| 15.3.13760231424506302464.1 | x15 - x14 - 2x13 - 2x12 + 5x11 + 7x10 - 42x9 + 132x8 - 204x7 + 180x6 - 114x5 + 108x3 - 108x2 + 72x - 36 | \( 2^{12}\cdot 3^{12}\cdot 43^{6} \) | $S_5$ (as 15T10) | $[2]$ |
| 15.15.3429179358086139904000000.1 | x15 - 25x13 - 2x12 + 229x11 + 40x10 - 981x9 - 228x8 + 2103x7 + 546x6 - 2175x5 - 568x4 + 923x3 + 198x2 - 120x - 8 | \( 2^{18}\cdot 5^{6}\cdot 307^{6} \) | $S_5$ (as 15T10) | Trivial (GRH) |
| 15.15.3658983920858973184000000.1 | x15 - 3x14 - 27x13 + 85x12 + 201x11 - 751x10 - 255x9 + 2109x8 - 473x7 - 2181x6 + 883x5 + 715x4 - 261x3 - 69x2 + 19x - 1 | \( 2^{16}\cdot 5^{6}\cdot 17^{6}\cdot 23^{6} \) | $S_5$ (as 15T10) | Trivial (GRH) |