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Results (displaying all 31 matches)

Label Polynomial Discriminant Galois group Class group
19.3.146525077331272123613812972.1 x19 - 2x18 + 7x16 - 10x15 - x14 + 19x13 - 19x12 - 9x11 + 33x10 - 19x9 - 20x8 + 32x7 - 9x6 - 17x5 + 17x4 - 3x3 - 5x2 + 4x - 1 \( 2^{2}\cdot 139\cdot 126311\cdot 1021043\cdot 2043393285469 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.3.7878347336355332175700013824.1 x19 - 2x18 + 7x16 - 10x15 - x14 + 19x13 - 19x12 - 9x11 + 33x10 - 19x9 - 20x8 + 33x7 - 9x6 - 18x5 + 17x4 - 3x3 - 5x2 + 4x - 1 \( 2^{8}\cdot 317\cdot 25373\cdot 137363\cdot 27854432176313 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.3.45730811992355144562119332263029.1 x19 - 3x - 1 \( 15451\cdot 1192721\cdot 1892107519\cdot 1311498030721 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.3.7925989089291768608053967330433893.1 x19 - 6x - 1 \( 1811\cdot 26072749799\cdot 167860372602034140737 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.3.10814939666659798383617290336993280.1 x19 - 4x - 2 \( 2^{18}\cdot 5\cdot 61\cdot 121171\cdot 1116312139673805569479 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.3.10815458295523592145202484064220277.1 x19 - 4x - 1 \( 277\cdot 1033\cdot 13915748550233\cdot 2716178228054209 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.3.21630397964161810184480087990337536.1 x19 - 8x - 4 \( 2^{18}\cdot 11\cdot 53\cdot 421\cdot 2482463\cdot 135422601683162041 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.3.202755077273610356289315823556602793.1 x19 - 9x - 4 \( 629113\cdot 661588211623\cdot 487141714838860007 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.3.749706696174552474691408242974194269.1 x19 - 5x - 3 \( 3^{18}\cdot 7\cdot 1193402926633\cdot 231645392486891 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.3.750472657854153391582754492683649024.1 x19 - 5x - 2 \( 2^{19}\cdot 7\cdot 4397\cdot 86323\cdot 197123\cdot 2733044013891403 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.3.750473176483017185344339686410876021.1 x19 - 5x - 1 \( 7\cdot 229\cdot 468167920451040040763780216101607 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.3.5960040257902096102153160387660349440.1 x19 - 6x - 4 \( 2^{34}\cdot 5\cdot 41\cdot 2819\cdot 847901\cdot 708003258176033 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.3.23975350514799135328710319731125844573.1 x19 - 6x - 3 \( 3^{18}\cdot 5526979\cdot 11347703\cdot 986703355583761 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.3.23976116476478736245601665980835299328.1 x19 - 6x - 2 \( 2^{18}\cdot 13\cdot 653\cdot 10774134287092701706273089133 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.3.49833868343434912581533776899657847989.1 x19 - 7x - 3 \( 3^{16}\cdot 13\cdot 89051486359588962351884125193 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.3.112126395263148453537673834586657521664.1 x19 - 7x - 2 \( 2^{18}\cdot 427728253414720358038611734720831 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.3.440958509520518504061851311423526515757.1 x19 - 7x - 5 \( 11\cdot 21881\cdot 1229121979\cdot 1490537448908633894245613 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.3.448369625607723462313706313916436185088.1 x19 - 7x - 4 \( 2^{18}\cdot 13\cdot 23\cdot 31\cdot 942847\cdot 195714118629896492875189 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.3.448505581571222677944456923540357313653.1 x19 - 7x - 1 \( 13\cdot 34500429351632513688035147964642870281 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.3.5469486785379930811435276902303735742464.1 x19 - 8x - 6 \( 2^{18}\cdot 3^{18}\cdot 1626601603931\cdot 33108756840559 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.3.5662867927830028610748493183646133367853.1 x19 - 8x - 5 \( 10771\cdot 2100606749\cdot 14133445561\cdot 17708737489650787 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.3.5670414233400424319920445864319527483997.1 x19 - 8x - 3 \( 3^{18}\cdot 4967\cdot 151598782807\cdot 19437585947910517 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.3.5670414999362103920837337210569236938752.1 x19 - 8x - 2 \( 2^{18}\cdot 269879\cdot 934176914887\cdot 85797908177168821 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.3.5670414999880732784631098795762964165749.1 x19 - 8x - 1 \( 29\cdot 6080707\cdot 32156055491577750487822407968083 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.3.49929477463126251574267177951112792264165.1 x19 - 9x - 7 \( 5\cdot 9985895492625250314853435590222558452833 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.3.52950234718276010481541335966586775273472.1 x19 - 9x - 6 \( 2^{19}\cdot 3^{18}\cdot 107\cdot 122029\cdot 19964965175341736357 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.3.53143615860726108280854552247929172898861.1 x19 - 9x - 5 \( 6219297888079\cdot 8544954240347693873940241859 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.3.53151162166296503990026504928602567015005.1 x19 - 9x - 3 \( 3^{18}\cdot 5\cdot 71\cdot 1069\cdot 2542879\cdot 142166878031666904029 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.3.53151162932258183590943396274852276469760.1 x19 - 9x - 2 \( 2^{19}\cdot 5\cdot 17\cdot 1192679975896906765005300101669587 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.3.53151162932776812454737157860046003696757.1 x19 - 9x - 1 \( 101\cdot 9221\cdot 1141909\cdot 263051581967\cdot 189994470465354439 \) $S_{19}$ (as 19T8) Trivial (GRH)
19.3.361091414843791210627932720501119778395310144000000000000000000.1 x19 - 380x - 360 \( 2^{24}\cdot 3^{36}\cdot 5^{18}\cdot 19^{20} \) $A_{19}$ (as 19T7) Trivial (GRH)


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