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Label Polynomial Discriminant Galois group Class group
18.2.242058175735216736305152.1 x18 - 2x17 + 5x16 + 8x15 - 18x14 + 44x13 - 2x12 - 40x11 + 79x10 - 38x9 + 35x8 - 48x7 + 64x6 - 32x4 + 10x2 - 4x + 2 \( 2^{65}\cdot 3^{8} \) $F_9$ (as 18T28) Trivial
18.2.808432815650446861638683444433.1 x18 - 9x17 + 36x16 - 84x15 + 117x14 - 63x13 - 126x12 + 405x11 - 549x10 + 248x9 + 441x8 - 981x7 + 834x6 - 171x5 - 783x4 + 1269x3 - 36x2 - 549x + 166 \( 3^{24}\cdot 17^{15} \) $F_9$ (as 18T28) Trivial (GRH)
18.18.25617491467048076163656841929756672.1 x18 - x17 - 74x16 + 44x15 + 1964x14 + 138x13 - 23886x12 - 19944x11 + 130119x10 + 205707x9 - 218908x8 - 630088x7 - 156488x6 + 556336x5 + 492272x4 + 58864x3 - 86784x2 - 36864x - 4096 \( 2^{12}\cdot 113^{15} \) $F_9$ (as 18T28) $[3]$ (GRH)
18.18.332589179640167807831750158103157960113.1 x18 - x17 - 106x16 + 170x15 + 3859x14 - 6715x13 - 66283x12 + 122893x11 + 574770x10 - 1267248x9 - 2378317x8 + 7294071x7 + 2266049x6 - 20833143x5 + 13676925x4 + 18284163x3 - 31589145x2 + 17289425x - 3371474 \( 17^{15}\cdot 47^{12} \) $F_9$ (as 18T28) Trivial (GRH)


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