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Results (displaying all 8 matches)

Label Polynomial Discriminant Galois group Class group
18.0.1999004627104432128.1 x18 - 6x17 + 24x16 - 68x15 + 159x14 - 300x13 + 479x12 - 630x11 + 702x10 - 636x9 + 480x8 - 270x7 + 114x6 - 12x5 - 12x4 + 14x3 - 3x2 + 1 \( -\,2^{18}\cdot 3^{27} \) $S_3 \times C_6$ (as 18T6) Trivial
18.0.9651146816936671875.1 x18 - 9x17 + 36x16 - 78x15 + 84x14 - 111x12 + 90x11 + 72x10 - 156x9 + 45x8 + 81x7 - 57x6 - 27x5 + 36x4 - 9x2 + 3 \( -\,3^{31}\cdot 5^{6} \) $S_3 \times C_6$ (as 18T6) Trivial
18.6.110730297608000000000.1 x18 - 5x17 + 5x16 + 10x15 - 19x14 + 7x13 - 18x12 + 34x11 + 21x10 - 70x9 + 22x8 + 14x7 + 11x6 - 7x5 - 20x4 + 13x3 - x2 + 4x - 1 \( 2^{12}\cdot 5^{9}\cdot 7^{12} \) $S_3 \times C_6$ (as 18T6) Trivial
18.6.209657417785715740672.1 x18 - 5x17 + 9x16 - 6x15 - 5x14 + 16x13 - 14x12 + 13x11 - 33x10 + 54x9 - 59x8 + 34x7 - 12x6 + 35x5 - 39x4 + 8x3 - 3x2 + 6x - 1 \( 2^{12}\cdot 13^{15} \) $S_3 \times C_6$ (as 18T6) Trivial
18.0.91437830330543390573883.1 x18 + 12x16 - 6x15 + 108x14 - 42x13 + 381x12 - 36x11 + 948x10 - 38x9 + 972x8 + 186x7 + 690x6 + 108x5 + 186x4 + 60x3 + 36x2 + 6x + 1 \( -\,3^{31}\cdot 23^{6} \) $S_3 \times C_6$ (as 18T6) Trivial
18.0.105226667788517176205647.1 x18 - 6x17 + 17x16 - 26x15 + 40x14 - 98x13 + 214x12 - 180x11 + 94x10 + 240x9 - 166x8 - 346x7 + 387x6 + 144x5 + 183x4 + 45x3 + 21x2 + 3x + 1 \( -\,7^{15}\cdot 53^{6} \) $S_3 \times C_6$ (as 18T6) $[2]$
18.18.13314770360250302126953125.1 x18 - 24x16 - 3x15 + 216x14 + 42x13 - 943x12 - 180x11 + 2190x10 + 272x9 - 2772x8 - 54x7 + 1819x6 - 180x5 - 522x4 + 110x3 + 36x2 - 6x - 1 \( 3^{24}\cdot 5^{9}\cdot 17^{6} \) $S_3 \times C_6$ (as 18T6) Trivial (GRH)
18.18.110730297608000000000000000.1 x18 - 3x17 - 25x16 + 86x15 + 210x14 - 928x13 - 506x12 + 4615x11 - 1713x10 - 10195x9 + 9755x8 + 7035x7 - 12770x6 + 2985x5 + 2555x4 - 1109x3 - 13x2 + 20x + 1 \( 2^{18}\cdot 5^{15}\cdot 7^{12} \) $S_3 \times C_6$ (as 18T6) Trivial (GRH)



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