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Label Polynomial Discriminant Galois group Class group
18.0.2954312706550833698643.3 x18 - 6x15 + 24x12 - 74x9 + 150x6 + 12x3 + 1 \( -\,3^{45} \) $He_3:C_2$ (as 18T21) Trivial
18.0.11727564985436483639043.1 x18 - 3x16 - 6x15 + 6x14 + 15x13 - 6x12 - 24x11 - 3x10 + 43x9 + 54x8 - 24x7 - 12x6 - 42x5 + 12x4 + 15x3 + 6x2 + 3x + 1 \( -\,3^{25}\cdot 7^{12} \) $He_3:C_2$ (as 18T21) $[3]$
18.18.70720374548224359605005470978048.1 x18 - 6x17 - 24x16 + 208x15 + 12x14 - 2394x13 + 3125x12 + 10464x11 - 24564x10 - 9916x9 + 63708x8 - 28836x7 - 53993x6 + 47538x5 + 8760x4 - 17236x3 + 1836x2 + 1794x - 377 \( 2^{12}\cdot 3^{24}\cdot 7^{8}\cdot 13^{9} \) $He_3:C_2$ (as 18T21) $[3]$ (GRH)
18.18.178698494132131643847952616411136.1 x18 - 9x17 - 9x16 + 264x15 - 288x14 - 2916x13 + 5598x12 + 14526x11 - 39159x10 - 27383x9 + 128403x8 - 17730x7 - 188268x6 + 110070x5 + 90900x4 - 76710x3 - 9855x2 + 13041x - 623 \( 2^{12}\cdot 3^{37}\cdot 7^{13} \) $He_3:C_2$ (as 18T21) Trivial (GRH)



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