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Label Polynomial Discriminant Galois group Class group
18.0.12906538539418320896.1 x18 - 9x17 + 41x16 - 124x15 + 276x14 - 476x13 + 646x12 - 678x11 + 517x10 - 231x9 - 15x8 + 98x7 - 48x6 - 18x5 + 36x4 - 22x3 + 9x2 - 3x + 1 \( -\,2^{16}\cdot 11^{9}\cdot 17^{4} \) $C_3\wr C_3:C_2$ (as 18T88) Trivial
18.0.16481672572799864375.1 x18 + 2x16 - x15 - 5x14 - 5x12 + 10x11 - 11x10 + 19x9 - 8x8 - 17x7 + 46x6 - 57x5 + 52x4 - 37x3 + 14x2 - 3x + 1 \( -\,5^{4}\cdot 11^{4}\cdot 23^{9} \) $C_3\wr C_3:C_2$ (as 18T88) Trivial
18.18.4031470892249635921400320000.1 x18 - 3x17 - 33x16 + 106x15 + 365x14 - 1333x13 - 1544x12 + 7717x11 + 893x10 - 21464x9 + 9947x8 + 25981x7 - 22611x6 - 8420x5 + 13270x4 - 1416x3 - 1968x2 + 512x - 4 \( 2^{12}\cdot 5^{4}\cdot 37^{9}\cdot 59^{4} \) $C_3\wr C_3:C_2$ (as 18T88) Trivial (GRH)
18.18.277876082417270428595200000000.1 x18 - 3x17 - 43x16 + 144x15 + 618x14 - 2454x13 - 3140x12 + 18208x11 + 757x10 - 60741x9 + 28339x8 + 101212x7 - 73600x6 - 86246x5 + 77066x4 + 34932x3 - 36045x2 - 5051x + 6047 \( 2^{16}\cdot 5^{8}\cdot 17^{4}\cdot 37^{9} \) $C_3\wr C_3:C_2$ (as 18T88) Trivial (GRH)



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