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Label Polynomial Discriminant Galois group Class group
18.6.366...625.1 x18 - 12x15 + 36x14 - 33x12 + 117x11 - 171x10 - 2x9 + 135x8 - 81x7 - 30x6 + 36x5 + 81x4 - 393x3 + 531x2 - 270x + 44 \( 3^{36}\cdot 5^{12} \) $C_3^2:S_3.C_2$ (as 18T49) trivial (GRH)
18.6.366...625.2 x18 - 12x15 + 9x14 + 54x13 - 18x12 + 72x11 - 261x10 - 14x9 + 135x8 - 270x7 + 840x6 - 1116x5 + 1269x4 - 1026x3 + 576x2 - 252x + 49 \( 3^{36}\cdot 5^{12} \) $C_3^2:S_3.C_2$ (as 18T49) trivial (GRH)
18.18.160...625.1 x18 - 6x17 - 18x16 + 141x15 + 108x14 - 1227x13 - 438x12 + 5220x11 + 1956x10 - 11198x9 - 5475x8 + 11283x7 + 6315x6 - 5184x5 - 3051x4 + 930x3 + 552x2 - 24x - 16 \( 3^{26}\cdot 5^{12}\cdot 11^{10} \) $C_3^2:S_3.C_2$ (as 18T49) trivial (GRH)
18.18.130...625.1 x18 - 3x17 - 63x16 + 147x15 + 1245x14 - 1968x13 - 9306x12 + 9264x11 + 28194x10 - 15305x9 - 31773x8 + 6729x7 + 13914x6 - 786x5 - 2355x4 + 57x3 + 144x2 - 6x - 1 \( 3^{30}\cdot 5^{12}\cdot 11^{10} \) $C_3^2:S_3.C_2$ (as 18T49) trivial (GRH)
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