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Label Polynomial Discriminant Galois group Class group
18.0.239338060927275176307.1 x18 - 3x17 + 12x16 - 21x15 + 51x14 - 60x13 + 114x12 - 75x11 + 165x10 - 4x9 + 174x8 + 96x7 + 135x6 + 108x5 + 72x4 + 48x3 + 21x2 + 6x + 1 \( -\,3^{25}\cdot 7^{10} \) $He_3:C_2$ (as 18T22) Trivial
18.0.2954312706550833698643.4 x18 - 6x15 + 24x12 + 88x9 + 69x6 + 12x3 + 1 \( -\,3^{45} \) $He_3:C_2$ (as 18T22) Trivial
18.18.1766000400360784868524139223996521.1 x18 - 6x17 - 42x16 + 232x15 + 515x14 - 2716x13 - 2617x12 + 14323x11 + 5233x10 - 37698x9 - 418x8 + 49453x7 - 9734x6 - 30769x5 + 9810x4 + 7729x3 - 2996x2 - 460x + 200 \( 7^{10}\cdot 569^{9} \) $He_3:C_2$ (as 18T22) Trivial (GRH)
18.18.2096291596176378856933557232324608.1 x18 - 3x17 - 39x16 + 124x15 + 588x14 - 2016x13 - 4354x12 + 16662x11 + 16569x10 - 76017x9 - 29151x8 + 193350x7 + 7892x6 - 257946x5 + 38376x4 + 147342x3 - 33795x2 - 14013x + 1863 \( 2^{12}\cdot 3^{20}\cdot 7^{12}\cdot 13^{9} \) $He_3:C_2$ (as 18T22) $[3]$ (GRH)


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