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Results (displaying all 6 matches)
| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 15.3.1788527348449625.1 | x15 - 2x14 + 4x13 - 9x12 + 13x11 - 15x10 + 18x9 - 23x8 + 33x7 - 44x6 + 48x5 - 44x4 + 30x3 - 16x2 + 6x - 1 | \( 5^{3}\cdot 7^{10}\cdot 37^{3} \) | $S_5 \times C_3$ (as 15T24) | Trivial |
| 15.3.4864965285308625.1 | x15 - 3x14 + 6x13 - 12x12 + 14x11 - 17x10 + 24x9 - 28x8 + 31x7 - 21x6 + 18x5 - 15x4 + 16x3 - 11x2 + 5x - 1 | \( 3^{9}\cdot 5^{3}\cdot 7^{11} \) | $S_5 \times C_3$ (as 15T24) | Trivial |
| 15.9.1373787160843911247.1 | x15 - 4x14 - 5x13 + 39x12 - 17x11 - 126x10 + 132x9 + 157x8 - 232x7 - 95x6 + 178x5 + 49x4 - 76x3 - 19x2 + 18x - 1 | \( -\,7^{12}\cdot 463^{3} \) | $S_5 \times C_3$ (as 15T24) | Trivial |
| 15.9.3132021267584993727.1 | x15 - 3x13 - 9x12 - 9x11 + 21x10 + 3x9 + 99x7 + 63x6 - 36x5 - 9x4 - 27x2 - 18x - 3 | \( -\,3^{24}\cdot 223^{3} \) | $S_5 \times C_3$ (as 15T24) | Trivial |
| 15.15.585891880179643237473.1 | x15 - x14 - 21x13 + 10x12 + 165x11 - 14x10 - 597x9 - 103x8 + 994x7 + 271x6 - 683x5 - 92x4 + 197x3 - 24x2 - 7x + 1 | \( 3^{6}\cdot 7^{10}\cdot 13^{3}\cdot 109^{3} \) | $S_5 \times C_3$ (as 15T24) | Trivial (GRH) |
| 15.15.1006329085257882652672.1 | x15 - 5x14 - 9x13 + 71x12 + 3x11 - 367x10 + 187x9 + 827x8 - 660x7 - 740x6 + 816x5 + 86x4 - 327x3 + 127x2 - 19x + 1 | \( 2^{12}\cdot 7^{11}\cdot 499^{3} \) | $S_5 \times C_3$ (as 15T24) | Trivial (GRH) |