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Label Polynomial Discriminant Galois group Class group
18.2.194...928.1 x18 + 2x16 - 6x14 - 16x12 + 37x10 + 166x8 + 372x6 - 88x4 + 36x2 - 8 \( 2^{47}\cdot 7^{12} \) $C_3^2 : C_4$ (as 18T10) $[3]$
18.2.226...125.1 x18 - 3x17 - 9x15 + 30x14 + 12x13 - 87x11 - 39x10 + 133x9 + 177x8 - 48x7 - 261x6 - 156x5 + 129x4 + 240x3 + 135x2 + 30x + 20 \( 3^{32}\cdot 5^{13} \) $C_3^2 : C_4$ (as 18T10) trivial
18.18.454...613.1 x18 - 36x16 + 486x14 - 3345x12 + 13113x10 - 30537x8 + 42276x6 - 33462x4 + 13689x2 - 2197 \( 3^{36}\cdot 13^{13} \) $C_3^2 : C_4$ (as 18T10) trivial (GRH)
18.18.925...000.1 x18 - 2x17 - 63x16 + 99x15 + 1595x14 - 1797x13 - 20806x12 + 14111x11 + 148967x10 - 34860x9 - 572263x8 - 108479x7 + 1034639x6 + 563303x5 - 562290x4 - 383111x3 + 79922x2 + 66448x + 5186 \( 2^{12}\cdot 5^{12}\cdot 41^{13} \) $C_3^2 : C_4$ (as 18T10) $[3]$ (GRH)
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