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Results (12 matches)

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Label Polynomial Discriminant Galois group Class group
17.1.463...841.1 x17 - x16 - x15 - x14 + x12 + 13x11 + 7x10 + 11x9 + 4x8 + x7 + 7x6 + 23x5 + 31x4 + 42x3 + 24x2 + 6x - 1 \( 383^{8} \) $D_{17}$ (as 17T2) trivial
17.1.930...721.1 x17 - x16 + 4x15 - 18x14 + 11x13 + 14x12 + 21x11 - 62x10 + 14x9 + 50x8 + 54x7 - 121x6 - 7x5 + 36x4 + 64x3 - 23x2 + 43x + 1 \( 991^{8} \) $D_{17}$ (as 17T2) trivial
17.1.183...561.1 x17 - x16 + 5x15 - 19x14 + 26x13 - 30x12 + 44x11 - 48x10 + 39x9 - 62x8 + 30x7 + 112x6 - 4x5 + 16x4 - 62x3 + 180x2 + 35x + 49 \( 13^{8}\cdot 83^{8} \) $D_{17}$ (as 17T2) trivial
17.1.200...521.1 x17 - 2x16 + 4x15 - 18x14 + 10x13 - 16x12 + 44x11 + 10x10 + 72x9 + 18x8 + 134x7 + 88x6 + 275x5 + 200x4 + 220x3 + 240x2 + 80x + 64 \( 1091^{8} \) $D_{17}$ (as 17T2) trivial (GRH)
17.1.105...401.1 x17 - 3x16 - 2x15 + 24x14 - 20x13 - 80x12 + 115x11 + 27x10 + 132x9 - 302x8 - 219x7 - 172x6 + 41x5 - 25x4 + 44x3 + 39x2 - 2x - 23 \( 17^{8}\cdot 79^{8} \) $D_{17}$ (as 17T2) trivial
17.1.160...625.1 x17 - 4x16 + x15 + 16x14 - 30x13 - 2x12 + 88x11 + 143x10 + 133x9 - 515x8 - 803x7 - 68x6 + 1252x5 + 2972x4 + 2855x3 + 1505x2 + 550x + 125 \( 5^{8}\cdot 283^{8} \) $D_{17}$ (as 17T2) trivial (GRH)
17.1.348...321.1 x17 - 2x16 - 3x14 + 24x13 + 18x12 - 138x10 - 203x9 - 75x8 + 352x7 + 588x6 + 384x5 + 132x4 + 493x3 + 1015x2 + 874x + 337 \( 1559^{8} \) $D_{17}$ (as 17T2) trivial
17.1.371...761.1 x17 - x16 + 5x15 + 9x14 - 13x13 + 17x12 + 56x11 - 62x10 + 55x9 - 535x8 + 181x7 - 1027x6 + 661x5 - 1041x4 + 166x3 - 416x2 - 88x - 16 \( 1571^{8} \) $D_{17}$ (as 17T2) trivial (GRH)
17.1.584...121.1 x17 - 2x16 + 9x15 - 23x14 + 59x13 - 112x12 + 156x11 - 49x10 + 221x9 - 25x8 - 162x7 - 4x6 + 553x5 + 1435x4 + 1716x3 + 1462x2 + 615x + 225 \( 1663^{8} \) $D_{17}$ (as 17T2) trivial
17.1.102...241.1 x17 - 7x16 + 30x15 - 61x14 + 115x13 - 158x12 + 94x11 - 111x10 + 268x9 - 411x8 + 465x7 - 473x6 + 314x5 - 109x4 + 446x3 - 498x2 + 175x + 1 \( 1783^{8} \) $D_{17}$ (as 17T2) trivial
17.1.397...976.1 x17 + 221x15 - 850x14 + 19601x13 - 97036x12 + 2452233x11 - 5536254x10 + 159332007x9 - 1851117488x8 + 12939379031x7 - 45700927246x6 + 12487240571x5 + 217180838276x4 - 328446625597x3 + 138506493022x2 + 2281813189964x + 1767616042808 \( 2^{24}\cdot 17^{32} \) $D_{17}$ (as 17T2) $[17]$ (GRH)
17.17.544...441.1 x17 - 3502x15 - 21012x14 + 3586048x13 + 27140500x12 - 1455974010x11 - 13391942168x10 + 247158969538x9 + 2699830692822x8 - 15367054046543x7 - 210262575924428x6 + 207808365630713x5 + 5600534069106679x4 + 891648638079425x3 - 50160692092741008x2 - 11309428987726617x + 145001801906376687 \( 17^{24}\cdot 103^{16} \) $D_{17}$ (as 17T2) $[17]$ (GRH)
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