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Results (10 matches)

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Label Polynomial Discriminant Galois group Class group
18.2.238...125.1 x18 - 4x17 + 5x16 - x15 - 4x13 + 6x12 + 15x11 - x10 + 60x7 + 25x6 + 64x3 + 64x2 + 20x + 1 \( 5^{15}\cdot 23^{8} \) $D_{18}$ (as 18T13) trivial
18.0.246...336.1 x18 + x16 - 2x14 - 7x12 + 10x10 + 33x8 + 13x6 + 20x4 + 16x2 + 4 \( -\,2^{24}\cdot 59^{8} \) $D_{18}$ (as 18T13) trivial
18.0.523...083.1 x18 - 3x17 + 6x16 - 23x15 + 36x14 - 69x13 + 124x12 - 87x11 + 237x10 - 80x9 + 306x8 - 24x7 + 173x6 + 75x5 + 51x4 + 33x3 + 27x2 + 3x + 1 \( -\,3^{21}\cdot 29^{8} \) $D_{18}$ (as 18T13) trivial
18.2.505...469.1 x18 - x15 + 4x12 + 4x9 + 11x6 - 13x3 - 1 \( 3^{20}\cdot 29^{9} \) $D_{18}$ (as 18T13) trivial
18.2.476...777.1 x18 - 2x17 + 17x15 - 17x14 + 51x13 + 119x12 - 476x11 + 493x10 + 1632x9 - 3638x8 - 3502x7 + 6936x6 + 1972x5 - 3451x4 + 3264x3 + 17x2 - 750x + 225 \( 7^{8}\cdot 17^{17} \) $D_{18}$ (as 18T13) trivial
18.0.333...439.1 x18 - 4x17 + 17x16 - 51x15 + 170x14 - 408x13 + 918x12 - 1445x11 + 1870x10 - 1887x9 + 3672x8 - 5797x7 + 8058x6 - 8143x5 + 9044x4 - 6851x3 + 5916x2 - 2826x + 1971 \( -\,7^{9}\cdot 17^{17} \) $D_{18}$ (as 18T13) $[10]$ (GRH)
18.0.519...963.1 x18 - 3x17 + 19x16 - 46x15 + 209x14 - 457x13 + 1289x12 - 2046x11 + 4263x10 - 5541x9 + 9392x8 - 9256x7 + 11934x6 - 8321x5 + 9457x4 - 4564x3 + 3678x2 + 60x + 1 \( -\,3^{9}\cdot 1129^{8} \) $D_{18}$ (as 18T13) $[2, 38]$ (GRH)
18.0.691...184.1 x18 + 29x16 + 338x14 + 2070x12 + 7345x10 + 15603x8 + 19532x6 + 13258x4 + 3756x2 + 1 \( -\,2^{18}\cdot 1129^{8} \) $D_{18}$ (as 18T13) $[178]$ (GRH)
18.18.354...208.1 x18 - 6x17 - 29x16 + 232x15 + 122x14 - 2972x13 + 2218x12 + 15816x11 - 21375x10 - 33384x9 + 61321x8 + 17204x7 - 59508x6 + 13790x5 + 7002x4 - 1052x3 - 340x2 - 8x + 1 \( 2^{27}\cdot 1129^{8} \) $D_{18}$ (as 18T13) trivial (GRH)
18.18.136...672.1 x18 - 6x17 - 38x16 + 280x15 + 350x14 - 4460x13 + 932x12 + 30696x11 - 23739x10 - 93216x9 + 86432x8 + 120652x7 - 101484x6 - 59266x5 + 34798x4 + 12148x3 - 3288x2 - 564x + 109 \( 2^{18}\cdot 3^{9}\cdot 1129^{8} \) $D_{18}$ (as 18T13) trivial (GRH)
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