Number field search results

Results (36 matches)

 

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
17.3.158...023.1	$x^{17} - x^{15} - x^{14} - 5 x^{13} + 4 x^{12} + x^{11} + 15 x^{9} - 13 x^{8} - 2 x^{7} + 7 x^{6} - 18 x^{5} + 20 x^{4} - 10 x^{3} + 6 x^{2} - 4 x + 1$	$17$	[3,7]	$-\,2131\cdot 546781\cdot 1361451193$	$3$	$11.7655356049$	$1259503766.9586349$			?	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$130.579387289$
17.3.191...491.1	$x^{17} - 3 x^{16} + 4 x^{15} - 3 x^{14} + x^{13} + 4 x^{12} - 8 x^{11} + 9 x^{10} - 2 x^{9} - 9 x^{8} + 12 x^{7} - x^{6} - 4 x^{5} + 2 x^{4} - 3 x^{3} + x^{2} - x - 1$	$17$	[3,7]	$-\,227\cdot 2411\cdot 3533\cdot 988994191$	$4$	$11.895587848$	$1382866394.632848$			?	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$144.902374432$
17.3.215...383.1	$x^{17} - 2 x^{15} - 4 x^{14} + 4 x^{13} + 7 x^{12} - 3 x^{11} - 3 x^{10} - 3 x^{9} + 5 x^{8} - 5 x^{7} - 4 x^{6} + 14 x^{5} - 2 x^{4} - 7 x^{3} + 2 x + 1$	$17$	[3,7]	$-\,37^{5}\cdot 433\cdot 5531\cdot 12953$	$4$	$11.978222741$	$3569979.5655382182$			?	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$154.682742806$
17.3.231...203.1	$x^{17} - x^{16} + x^{15} - 3 x^{14} + 4 x^{13} - 4 x^{12} - x^{11} + 4 x^{10} - 5 x^{9} + 17 x^{8} - 42 x^{7} + 59 x^{6} - 45 x^{5} + 9 x^{4} + 15 x^{3} - 15 x^{2} + 6 x - 1$	$17$	[3,7]	$-\,16843\cdot 137239279050521$	$2$	$12.0289934072$	$1520368763.5070398$			?	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$161.12597366$
17.3.275...423.1	$x^{17} - 3 x^{16} + 7 x^{15} - 10 x^{14} + 12 x^{13} - 11 x^{12} + 10 x^{11} - 7 x^{10} + 2 x^{9} + 5 x^{8} - 13 x^{7} + 11 x^{6} - 5 x^{5} - 6 x^{4} + 11 x^{3} - 9 x^{2} + 5 x - 1$	$17$	[3,7]	$-\,75653\cdot 3119681\cdot 11682611$	$3$	$12.1544104314$	$1660497129.8707912$			?	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$178.334436956$
17.3.377...359.1	$x^{17} - 4 x^{16} + 12 x^{15} - 26 x^{14} + 48 x^{13} - 75 x^{12} + 105 x^{11} - 126 x^{10} + 136 x^{9} - 129 x^{8} + 107 x^{7} - 80 x^{6} + 47 x^{5} - 23 x^{4} + 11 x^{3} - 2 x^{2} - 2 x + 1$	$17$	[3,7]	$-\,137\cdot 1926157\cdot 14323744651$	$3$	$12.3820423069$	$1944170774.5272431$			?	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$206.585713852$
17.3.207...144.1	$x^{17} - 2 x^{16} + x^{15} + 2 x^{14} - 3 x^{13} + 3 x^{11} - 3 x^{10} - x^{9} + 6 x^{8} - 5 x^{7} - 4 x^{6} + 8 x^{5} - 3 x^{4} - 4 x^{3} + 3 x^{2} - 1$	$17$	[3,7]	$-\,2^{3}\cdot 17\cdot 20759\cdot 9318913\cdot 78851137$	$5$	$17.9447075771$				✓	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$12720.6080668$
17.3.855...476.1	$x^{17} - 3 x^{16} + 4 x^{15} + x^{14} - 13 x^{13} + 26 x^{12} - 25 x^{11} + 2 x^{10} + 35 x^{9} - 62 x^{8} + 59 x^{7} - 25 x^{6} - 13 x^{5} + 33 x^{4} - 30 x^{3} + 17 x^{2} - 6 x + 1$	$17$	[3,7]	$-\,2^{2}\cdot 11\cdot 53\cdot 34759\cdot 105529138935877$	$5$	$19.5041730705$				?	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$30334.8896134$
17.3.725...168.1	$x^{17} - 3 x^{16} + 3 x^{15} - 17 x^{14} + 27 x^{13} + 27 x^{12} + 85 x^{11} - 303 x^{10} + 141 x^{9} - 35 x^{8} + 609 x^{7} - 1599 x^{6} + 985 x^{5} + 513 x^{4} + 1935 x^{3} - 3869 x^{2} + 1272 x - 48$	$17$	[3,7]	$-\,2^{29}\cdot 3^{38}$	$2$	$38.021398883521194$					$S_{17}$ (as 17T10)	trivial	$2$	$9$	$111003394.88977265$
17.3.238...231.1	$x^{17} - 3 x - 1$	$17$	[3,7]	$-\,17987\cdot 132440913396223585034213$	$2$	$40.7765652895$	$48807936949412.984$			✓	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$21794558.2023$
17.3.253...408.1	$x^{17} - 9 x - 4$	$17$	[3,7]	$-\,2^{16}\cdot 38738303271636409747303$	$2$	$40.9295058634$				?	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$35818073.0947$
17.3.316...472.1	$x^{17} - 4 x - 2$	$17$	[3,7]	$-\,2^{16}\cdot 13\cdot 371913541399740797081579$	$3$	$54.3682076786$	$4221968810703.8623$			✓	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$215387191.314$
17.3.316...167.1	$x^{17} - 4 x - 1$	$17$	[3,7]	$-\,19\cdot 67\cdot 2269\cdot 109717694805120239246291$	$4$	$54.3687548216$	$562949952686575.06$			✓	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$178439333.016$
17.3.633...816.1	$x^{17} - 8 x - 4$	$17$	[3,7]	$-\,2^{16}\cdot 3\cdot 11\cdot 37\cdot 3121561\cdot 13503587\cdot 187895273$	$7$	$56.6310805607$	$5971020943878.205$			?	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$661339381.987$
17.3.140...383.1	$x^{17} - 5 x - 3$	$17$	[3,7]	$-\,7\cdot 618079271321299\cdot 3244645955426531$	$3$	$67.9508163213$	$3746750439351333.5$			✓	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$1622430410.88$
17.3.140...128.1	$x^{17} - 5 x - 2$	$17$	[3,7]	$-\,2^{16}\cdot 3\cdot 3131923046309\cdot 22855769909249$	$4$	$67.9609281377$				✓	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$4012523401.31$
17.3.140...823.1	$x^{17} - 5 x - 1$	$17$	[3,7]	$-\,3\cdot 89\cdot 1699\cdot 507289\cdot 2211365603\cdot 27655986893$	$6$	$67.9609435372$	$3751499544809456.5$			✓	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$1608750696.67$
17.3.771...496.1	$x^{17} - 6 x - 4$	$17$	[3,7]	$-\,2^{30}\cdot 2329417133\cdot 30854159809163$	$3$	$75.116093138$				?	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$6307148764.84$
17.3.312...759.1	$x^{17} - 6 x - 3$	$17$	[3,7]	$-\,3^{16}\cdot 41\cdot 487\cdot 363235722813937432337$	$4$	$81.5525851083$	$7573663128492.457$			✓	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$7426769692.05$
17.3.312...504.1	$x^{17} - 6 x - 2$	$17$	[3,7]	$-\,2^{16}\cdot 2791\cdot 724723\cdot 2355478215670018723$	$4$	$81.553131412$	$132534161671603.08$			✓	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$7992848902.06$
17.3.312...199.1	$x^{17} - 6 x - 1$	$17$	[3,7]	$-\,7\cdot 41\cdot 40841\cdot 6864777739\cdot 3880487013052123$	$5$	$81.5531322449$	$1.767036374269235e+16$			✓	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$13334665698.3$
17.3.107...160.1	$x^{17} - 7 x - 2$	$17$	[3,7]	$-\,2^{14}\cdot 5\cdot 3251\cdot 9473\cdot 425237890924282842001$	$5$	$87.6944566406$	$488668744925295.3$				$S_{17}$ (as 17T10)	trivial	$2$	$9$	$35856250594.5$
17.3.416...887.1	$x^{17} - 7 x - 5$	$17$	[3,7]	$-\,59\cdot 912539\cdot 77360031636376385786613287$	$3$	$94.978369744$	$6.45371885710573e+16$			✓	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$23844697497.8$
17.3.428...120.1	$x^{17} - 7 x - 4$	$17$	[3,7]	$-\,2^{32}\cdot 5\cdot 19\cdot 223\cdot 29611\cdot 18565699\cdot 85718383$	$7$	$95.1406852782$				✓	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$63630849252.3$
17.3.429...895.1	$x^{17} - 7 x - 3$	$17$	[3,7]	$-\,5\cdot 47\cdot 421\cdot 43374336132579615850126292617$	$4$	$95.1452745088$	$6.550755639830236e+16$			✓	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$88268686130.1$
17.3.429...335.1	$x^{17} - 7 x - 1$	$17$	[3,7]	$-\,5\cdot 11\cdot 78\!\cdots\!97$	$3$	$95.1453209524$	$6.550782819829009e+16$			✓	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$27208880284.7$
17.3.461...544.1	$x^{17} - 8 x - 2$	$17$	[3,7]	$-\,2^{16}\cdot 977\cdot 143572109\cdot 502067855635349603$	$4$	$95.5536915842$	$509548912718758.8$			?	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$89188105078.5$
17.3.392...056.1	$x^{17} - 8 x - 6$	$17$	[3,7]	$-\,2^{16}\cdot 598215319360726628348781489071$	$2$	$108.368285791$	$1485084324753195.0$			✓	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$124798789274$
17.3.414...143.1	$x^{17} - 8 x - 5$	$17$	[3,7]	$-\,3\cdot 2186209\cdot 164061345157\cdot 38486512346763137$	$4$	$108.718044655$	$2.0349974943885635e+17$			✓	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$181187719030$
17.3.415...151.1	$x^{17} - 8 x - 3$	$17$	[3,7]	$-\,61\cdot 3533\cdot 163481\cdot 1178985247918158460303967$	$4$	$108.737504176$	$2.0380956615992752e+17$			✓	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$105283536418$
17.3.415...591.1	$x^{17} - 8 x - 1$	$17$	[3,7]	$-\,3\cdot 2555684029\cdot 99995675629\cdot 54180108271117$	$4$	$108.73750966$	$2.038096535208227e+17$			✓	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$77933078470.4$
17.3.280...127.1	$x^{17} - 9 x - 7$	$17$	[3,7]	$-\,67\cdot 542797\cdot 80951558783101\cdot 95159072441773$	$4$	$121.657937767$	$5.292901704139748e+17$			✓	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$439207673777$
17.3.305...792.1	$x^{17} - 9 x - 6$	$17$	[3,7]	$-\,2^{16}\cdot 3^{16}\cdot 268235867903\cdot 403458097169$	$4$	$122.274915154$				✓	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$565594685120$
17.3.307...879.1	$x^{17} - 9 x - 5$	$17$	[3,7]	$-\,536705537\cdot 572964977325919334221374767$	$2$	$122.326745281$	$5.54538975941187e+17$			✓	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$184025053070$
17.3.307...887.1	$x^{17} - 9 x - 3$	$17$	[3,7]	$-\,3^{16}\cdot 593\cdot 33641\cdot 95413\cdot 3754664319237163$	$5$	$122.329697534$	$237742282069512.03$			✓	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$190786487649$
17.3.307...632.1	$x^{17} - 9 x - 2$	$17$	[3,7]	$-\,2^{16}\cdot 46\!\cdots\!87$	$2$	$122.329698366$				✓	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$586018865698$
17.3.307...327.1	$x^{17} - 9 x - 1$	$17$	[3,7]	$-\,101\cdot 374761\cdot 21841751\cdot 372116706329069072557$	$4$	$122.329698367$	$5.546527766851085e+17$			✓	$S_{17}$ (as 17T10)	trivial	$2$	$9$	$299533567462$