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Results (displaying all 6 matches)

Label Polynomial Discriminant Galois group Class group
18.0.118039224225889612726272.1 x18 - 12x15 - 18x14 + 51x12 + 72x11 + 72x10 + 36x9 + 72x8 + 90x7 + 75x6 + 72x5 + 54x4 - 18x2 + 3 \( -\,2^{18}\cdot 3^{37} \) $C_3:S_4$ (as 18T40) $[2]$
18.0.669462604992000000000000.1 x18 - 11x12 + 27x6 + 27 \( -\,2^{18}\cdot 3^{21}\cdot 5^{12} \) $C_3:S_4$ (as 18T40) $[3]$
18.6.3321979107367014091730799501594624.1 x18 - 54x15 - 180x14 + 1206x13 + 459x12 - 7848x11 + 11664x10 - 556x9 - 72756x8 + 184356x7 + 44463x6 - 598968x5 + 542700x4 + 351114x3 - 1003104x2 + 458298x - 59087 \( 2^{12}\cdot 3^{37}\cdot 23^{9} \) $C_3:S_4$ (as 18T40) $[4]$ (GRH)
18.6.25335674079416182011223462348869632.1 x18 - 5x17 + 17x16 - 26x15 - 97x14 + 413x13 - 3516x12 + 4203x11 - 7019x10 - 56398x9 + 398451x8 - 800673x7 + 337971x6 + 7233538x5 - 17698768x4 - 6903624x3 + 52507872x2 - 23700060x - 30249612 \( 2^{12}\cdot 7^{12}\cdot 197^{9} \) $C_3:S_4$ (as 18T40) $[2, 6]$ (GRH)
18.18.6523520634696466078625264232972681216.1 x18 - 9x17 - 42x16 + 498x15 + 231x14 - 8343x13 + 2989x12 + 59949x11 - 20253x10 - 226761x9 + 8409x8 + 452259x7 + 153052x6 - 375174x5 - 264699x4 + 1605x3 + 26424x2 + 2088x + 12 \( 2^{20}\cdot 3^{33}\cdot 47^{9} \) $C_3:S_4$ (as 18T40) $[12]$ (GRH)
18.18.56290847976736302998762533947799425024.1 x18 - 9x17 - 75x16 + 768x15 + 1986x14 - 25806x13 - 19822x12 + 438816x11 - 14037x10 - 4078547x9 + 1648491x8 + 21086784x7 - 11912402x6 - 58701558x5 + 36211158x4 + 78699796x3 - 48626967x2 - 36169521x + 22115221 \( 2^{12}\cdot 3^{33}\cdot 47^{11} \) $C_3:S_4$ (as 18T40) $[3]$ (GRH)


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