Learn more about

Further refine search

Results (displaying all 8 matches)

Label Polynomial Discriminant Galois group Class group
18.0.597168052405647575476347.1 x18 + 18x16 - 13x15 + 135x14 - 195x13 + 620x12 - 1170x11 + 2175x10 - 3813x9 + 5778x8 - 7992x7 + 10122x6 - 11340x5 + 10998x4 - 9323x3 + 6777x2 - 3426x + 991 \( -\,3^{27}\cdot 23^{8} \) $S_3\times D_9$ (as 18T50) Trivial (GRH)
18.2.774455350146061749097070592.1 x18 - 9x12 - 4x9 + 63x6 - 36x3 + 1 \( 2^{18}\cdot 3^{45} \) $S_3\times D_9$ (as 18T50) Trivial (GRH)
18.2.7735818598867901659628961792.1 x18 - 12x15 - 27x14 - 72x13 - 186x12 - 108x11 + 45x10 + 336x9 + 972x8 + 2052x7 + 3231x6 + 2592x5 + 1782x4 - 252x3 - 810x2 - 216x + 144 \( 2^{34}\cdot 3^{37} \) $S_3\times D_9$ (as 18T50) Trivial (GRH)
18.0.378152026438506713426304000000000.1 x18 + 18x16 - 18x15 + 243x14 - 306x13 + 1764x12 - 2916x11 + 11979x10 - 15620x9 + 36450x8 - 41922x7 + 55053x6 - 52002x5 + 46152x4 - 28872x3 + 19764x2 - 7848x + 2656 \( -\,2^{16}\cdot 3^{45}\cdot 5^{9} \) $S_3\times D_9$ (as 18T50) $[2]$ (GRH)
18.0.332869583280588772090547978346399892639407421875.1 x18 + 342x16 + 26163x14 - 56772x13 - 538365x12 - 8094114x11 + 47606400x10 + 687285632x9 + 3278237751x8 + 738088326x7 - 29706477732x6 - 100211012352x5 - 48798420480x4 + 431541779712x3 + 1408298336064x2 + 1686750632064x + 699473507584 \( -\,3^{45}\cdot 5^{8}\cdot 19^{16} \) $S_3\times D_9$ (as 18T50) $[3, 9, 9]$ (GRH)
18.0.1664347916402943860452739891731999463197037109375.1 x18 - 342x15 + 430920x12 + 3789702x9 + 403028703x6 - 2173425048x3 + 6068404224 \( -\,3^{45}\cdot 5^{9}\cdot 19^{16} \) $S_3\times D_9$ (as 18T50) $[3, 9, 18]$ (GRH)
18.18.1015634954431839220260170077569414080777988222222336.1 x18 - 318x16 - 212x15 + 36729x14 + 34980x13 - 2034564x12 - 2583432x11 + 58781664x10 + 103129520x9 - 889486704x8 - 2128457952x7 + 6135260496x6 + 21082331520x5 - 6285328512x4 - 77451096320x3 - 82190351232x2 - 18643490304x + 6047664640 \( 2^{35}\cdot 3^{27}\cdot 53^{16} \) $S_3\times D_9$ (as 18T50) Trivial (GRH)
18.18.393477790691475867882573798675110334618493697489618079842304.1 x18 - 954x16 + 296217x14 - 286200x13 - 36510216x12 + 84108456x11 + 1885287168x10 - 6956743536x9 - 38883795984x8 + 211649296032x7 + 191094022800x6 - 2602305600192x5 + 2974331897280x4 + 9205791789312x3 - 26694357563520x2 + 24196212919296x - 7334325786624 \( 2^{35}\cdot 3^{45}\cdot 53^{16} \) $S_3\times D_9$ (as 18T50) $[3]$ (GRH)


Download all search results for