Number field search results

Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)

Results (42 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
11.11.41426511213649.1	$x^{11} - x^{10} - 10 x^{9} + 9 x^{8} + 36 x^{7} - 28 x^{6} - 56 x^{5} + 35 x^{4} + 35 x^{3} - 15 x^{2} - 6 x + 1$	$11$	[11,0]	$23^{10}$	$1$	$17.2955507649$	$17.295550764917277$		✓	✓	$C_{11}$ (as 11T1)	trivial	$2$	$10$	$1014.31330506$
11.11.48706494267293.1	$x^{11} - 3 x^{10} - 8 x^{9} + 28 x^{8} + 15 x^{7} - 87 x^{6} + 16 x^{5} + 95 x^{4} - 51 x^{3} - 17 x^{2} + 13 x - 1$	$11$	[11,0]	$421\cdot 115692385433$	$2$	$17.5519785399$	$6979003.816254365$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$10$	$1198.69025149$
11.11.55029067682009.1	$x^{11} - x^{10} - 11 x^{9} + 9 x^{8} + 41 x^{7} - 24 x^{6} - 60 x^{5} + 16 x^{4} + 34 x^{3} + 2 x^{2} - 5 x - 1$	$11$	[11,0]	$55029067682009$	$1$	$17.7478088005$	$7418157.970952694$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$10$	$1235.5779303$
11.11.57451466331409.1	$x^{11} - 12 x^{9} - 5 x^{8} + 46 x^{7} + 32 x^{6} - 57 x^{5} - 43 x^{4} + 23 x^{3} + 16 x^{2} - x - 1$	$11$	[11,0]	$233\cdot 246572816873$	$2$	$17.8174503041$	$7579674.553132806$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$10$	$1321.7181478350058$
11.11.89814305807257.1	$x^{11} - x^{10} - 12 x^{9} + 10 x^{8} + 53 x^{7} - 35 x^{6} - 108 x^{5} + 51 x^{4} + 102 x^{3} - 27 x^{2} - 36 x + 1$	$11$	[11,0]	$2053\cdot 43747835269$	$2$	$18.5560680335$	$9477040.983727833$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$10$	$1627.3698026869433$
11.11.96470357797337.1	$x^{11} - 2 x^{10} - 10 x^{9} + 15 x^{8} + 38 x^{7} - 36 x^{6} - 61 x^{5} + 36 x^{4} + 38 x^{3} - 15 x^{2} - 6 x + 1$	$11$	[11,0]	$137\cdot 293\cdot 11093\cdot 216649$	$4$	$18.6770609217$	$9821932.487924004$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$10$	$1759.2258321328961$
11.11.104215884017569.1	$x^{11} - 3 x^{10} - 8 x^{9} + 26 x^{8} + 15 x^{7} - 60 x^{6} - 11 x^{5} + 49 x^{4} + 4 x^{3} - 14 x^{2} - x + 1$	$11$	[11,0]	$1451\cdot 71823490019$	$2$	$18.8086501658$	$10208618.124779131$			?	$S_{11}$ (as 11T8)	trivial	$2$	$10$	$1786.5712036132677$
11.11.129171716734329.1	$x^{11} - 2 x^{10} - 10 x^{9} + 21 x^{8} + 32 x^{7} - 72 x^{6} - 40 x^{5} + 100 x^{4} + 17 x^{3} - 51 x^{2} + 3$	$11$	[11,0]	$3^{3}\cdot 4784137656827$	$2$	$19.1793287267$	$7880309.912601921$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$10$	$2553.142576310772$
11.11.167643906155581.1	$x^{11} - x^{10} - 13 x^{9} + 19 x^{8} + 42 x^{7} - 73 x^{6} - 40 x^{5} + 88 x^{4} + 8 x^{3} - 34 x^{2} + 3 x + 1$	$11$	[11,0]	$233\cdot 937\cdot 5279\cdot 145459$	$4$	$19.6393070905$	$12947737.491762064$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$10$	$2519.525904095352$
11.11.176300559557501.1	$x^{11} - 13 x^{9} - 7 x^{8} + 53 x^{7} + 53 x^{6} - 55 x^{5} - 86 x^{4} - 18 x^{3} + 16 x^{2} + 8 x + 1$	$11$	[11,0]	$7786721\cdot 22641181$	$2$	$19.7294042685$	$13277822.093909115$			✓	$S_{11}$ (as 11T8)	trivial	$2$	$10$	$2848.1756047880867$
11.11.3670285774226257.1	$x^{11} - 5 x^{10} - 4 x^{9} + 54 x^{8} - 53 x^{7} - 127 x^{6} + 208 x^{5} + 69 x^{4} - 222 x^{3} + 29 x^{2} + 56 x - 5$	$11$	[11,0]	$1297^{5}$	$1$	$25.9999621898$	$36.013886210738214$			?	$D_{11}$ (as 11T2)	trivial	$2$	$10$	$15121.2781703$
11.11.103...049.1	$x^{11} - 5 x^{10} - 18 x^{9} + 114 x^{8} + 37 x^{7} - 856 x^{6} + 746 x^{5} + 2117 x^{4} - 3648 x^{3} + 135 x^{2} + 2677 x - 1301$	$11$	[11,0]	$19^{5}\cdot 211^{5}$	$2$	$43.4253834437$	$63.31666447310692$			?	$D_{11}$ (as 11T2)	trivial	$2$	$10$	$287818.658355$
11.11.182...449.1	$x^{11} - x^{10} - 30 x^{9} + 63 x^{8} + 220 x^{7} - 698 x^{6} - 101 x^{5} + 1960 x^{4} - 1758 x^{3} + 35 x^{2} + 243 x + 29$	$11$	[11,0]	$67^{10}$	$1$	$45.7159766745$	$45.71597667454237$		✓		$C_{11}$ (as 11T1)	trivial	$2$	$10$	$330512.248088$
11.11.348...541.1	$x^{11} - 4 x^{10} - 17 x^{9} + 78 x^{8} + 75 x^{7} - 494 x^{6} - 8 x^{5} + 1260 x^{4} - 522 x^{3} - 1122 x^{2} + 748 x - 9$	$11$	[11,0]	$3^{5}\cdot 7^{5}\cdot 31^{8}$	$3$	$48.4881323872$	$71.48237976311032$			?	$F_{11}$ (as 11T4)	trivial	$2$	$10$	$1374042.48636$
11.11.491...848.1	$x^{11} - 22 x^{9} + 176 x^{7} - 616 x^{5} + 880 x^{3} - 352 x - 88$	$11$	[11,0]	$2^{10}\cdot 7^{5}\cdot 11^{11}$	$3$	$50.0255405753$	$66.49824652345667$			?	$F_{11}$ (as 11T4)	trivial	$2$	$10$	$1966590.40257$
11.11.831...401.1	$x^{11} - 2 x^{10} - 32 x^{9} + 86 x^{8} + 284 x^{7} - 1057 x^{6} - 293 x^{5} + 4084 x^{4} - 3446 x^{3} - 2439 x^{2} + 4158 x - 1323$	$11$	[11,0]	$3^{5}\cdot 2027^{5}$	$2$	$52.4793730328$	$77.9807668595276$				$D_{11}$ (as 11T2)	trivial	$2$	$10$	$5739586.8996353615$
11.11.311...601.1	$x^{11} - x^{10} - 40 x^{9} + 19 x^{8} + 482 x^{7} - 84 x^{6} - 2185 x^{5} - 102 x^{4} + 3152 x^{3} + 781 x^{2} + 57 x + 1$	$11$	[11,0]	$89^{10}$	$1$	$59.1796964646$	$59.17969646456082$		✓		$C_{11}$ (as 11T1)	trivial	$2$	$10$	$846366.485722$
11.11.313...201.1	$x^{11} - 4 x^{10} - 25 x^{9} + 81 x^{8} + 237 x^{7} - 562 x^{6} - 1010 x^{5} + 1574 x^{4} + 1805 x^{3} - 1586 x^{2} - 847 x + 579$	$11$	[11,0]	$74843^{4}$	$1$	$59.2132111445$	$273.57448711456993$			?	$\PSL(2,11)$ (as 11T5)	trivial	$2$	$10$	$2978508.35907$
11.11.313...201.2	$x^{11} - 20 x^{9} + 143 x^{7} - 4 x^{6} - 463 x^{5} + 54 x^{4} + 691 x^{3} - 186 x^{2} - 392 x + 177$	$11$	[11,0]	$74843^{4}$	$1$	$59.2132111445$	$273.57448711456993$			?	$\PSL(2,11)$ (as 11T5)	trivial	$2$	$10$	$2978508.35907$
11.11.123...625.1	$x^{11} - x^{10} - 20 x^{9} + 30 x^{8} + 105 x^{7} - 207 x^{6} - 63 x^{5} + 240 x^{4} - 15 x^{3} - 80 x^{2} + 11 x + 4$	$11$	[11,0]	$3^{10}\cdot 5^{10}\cdot 11^{8}$	$3$	$67.0734074997$	$79.85240853282978$			?	$C_{11}:C_5$ (as 11T3)	trivial	$2$	$10$	$12183336.2677$
11.11.552...152.1	$x^{11} - 33 x^{9} + 396 x^{7} - 2079 x^{5} + 4455 x^{3} - 2673 x - 810$	$11$	[11,0]	$2^{15}\cdot 3^{10}\cdot 11^{11}$	$3$	$76.8483821571$	$102.77538915918468$			?	$F_{11}$ (as 11T4)	trivial	$2$	$10$	$22811054.8299$
11.11.672...201.1	$x^{11} - 55 x^{9} - 33 x^{8} + 825 x^{7} + 396 x^{6} - 4972 x^{5} - 1287 x^{4} + 12760 x^{3} + 924 x^{2} - 10989 x - 243$	$11$	[11,0]	$11^{20}$	$1$	$78.2422346586$	$78.24223465860136$		✓		$C_{11}$ (as 11T1)	trivial	$2$	$10$	$278432564.723$
11.11.271...889.1	$x^{11} - 33 x^{9} + 396 x^{7} - 2079 x^{5} + 4455 x^{3} - 2673 x - 837$	$11$	[11,0]	$3^{10}\cdot 11^{16}$	$2$	$88.8177141494$	$105.73949735950434$			?	$C_{11}:C_5$ (as 11T3)	trivial	$2$	$10$	$48372191.2791$
11.11.285...000.1	$x^{11} - 55 x^{9} + 1100 x^{7} - 9625 x^{5} + 34375 x^{3} - 34375 x - 13900$	$11$	[11,0]	$2^{10}\cdot 5^{10}\cdot 11^{11}$	$3$	$89.2243913869$	$115.62581676361589$			?	$F_{11}$ (as 11T4)	trivial	$2$	$10$	$52622964.70901569$
11.11.973...001.1	$x^{11} - x^{10} - 90 x^{9} + 115 x^{8} + 2349 x^{7} - 943 x^{6} - 26327 x^{5} - 21284 x^{4} + 102168 x^{3} + 217794 x^{2} + 148930 x + 30647$	$11$	[11,0]	$199^{10}$	$1$	$122.989046087$	$122.98904608708088$		✓		$C_{11}$ (as 11T1)	trivial	$2$	$10$	$114390451.519$
11.11.193...000.1	$x^{11} - x^{10} - 53 x^{9} + 31 x^{8} + 996 x^{7} - 28 x^{6} - 7812 x^{5} - 5784 x^{4} + 20673 x^{3} + 36219 x^{2} + 19909 x + 3279$	$11$	[11,0]	$2^{10}\cdot 5^{5}\cdot 7^{10}\cdot 11^{8}$	$4$	$130.925642711$	$167.70025700875578$			?	$F_{11}$ (as 11T4)	trivial	$2$	$10$	$501847260.162$
11.11.448...625.1	$x^{11} - 55 x^{9} + 1100 x^{7} - 9625 x^{5} + 34375 x^{3} - 34375 x - 12675$	$11$	[11,0]	$5^{10}\cdot 11^{16}$	$2$	$141.312400294$	$168.23560841235079$			?	$C_{11}:C_5$ (as 11T3)	trivial	$2$	$10$	$677575079.592$
11.11.157...801.1	$x^{11} - x^{10} - 150 x^{9} + 402 x^{8} + 6577 x^{7} - 28617 x^{6} - 62124 x^{5} + 475464 x^{4} - 343344 x^{3} - 1913488 x^{2} + 4015168 x - 2287616$	$11$	[11,0]	$331^{10}$	$1$	$195.322701164$	$195.32270116363648$		✓		$C_{11}$ (as 11T1)	trivial	$2$	$10$	$1340143683620$
11.11.300...049.1	$x^{11} - x^{10} - 160 x^{9} + 525 x^{8} + 6066 x^{7} - 26034 x^{6} - 48369 x^{5} + 265374 x^{4} - 42966 x^{3} - 405001 x^{2} + 63189 x + 170569$	$11$	[11,0]	$353^{10}$	$1$	$207.08985455$	$207.0898545497219$		✓		$C_{11}$ (as 11T1)	trivial	$2$	$10$	$5373530988.23$
11.11.536...401.1	$x^{11} - 3 x^{10} - 71 x^{9} + 272 x^{8} + 1617 x^{7} - 8190 x^{6} - 9378 x^{5} + 92787 x^{4} - 73516 x^{3} - 274866 x^{2} + 475325 x - 157109$	$11$	[11,0]	$13^{4}\cdot 59^{4}\cdot 3529^{4}$	$3$	$218.30900210472942$	$1645.2182226075665$				$\PSL(2,11)$ (as 11T5)	trivial	$2$	$10$	$9455726475.598814$
11.11.972...049.1	$x^{11} - x^{10} - 180 x^{9} + 13 x^{8} + 11655 x^{7} + 12159 x^{6} - 316973 x^{5} - 720142 x^{4} + 2670510 x^{3} + 10551746 x^{2} + 10752776 x + 3098903$	$11$	[11,0]	$397^{10}$	$1$	$230.428835104$	$230.42883510401091$		✓		$C_{11}$ (as 11T1)	trivial	$2$	$10$	$1592800927.62$
11.11.166...801.1	$x^{11} - x^{10} - 190 x^{9} + 547 x^{8} + 10985 x^{7} - 51221 x^{6} - 141765 x^{5} + 1224028 x^{4} - 2399676 x^{3} + 1263744 x^{2} + 873500 x - 785489$	$11$	[11,0]	$419^{10}$	$1$	$242.008672808$	$242.00867280835675$		✓		$C_{11}$ (as 11T1)	trivial	$2$	$10$	$13726169613.8$
11.11.452...849.1	$x^{11} - x^{10} - 210 x^{9} + 857 x^{8} + 6242 x^{7} - 36336 x^{6} - 8398 x^{5} + 289307 x^{4} - 265801 x^{3} - 519569 x^{2} + 455080 x + 344327$	$11$	[11,0]	$463^{10}$	$1$	$265.005841026$	$265.00584102607024$		✓		$C_{11}$ (as 11T1)	trivial	$2$	$10$	$5780480495.29$
11.11.799...449.1	$x^{11} - x^{10} - 280 x^{9} + 469 x^{8} + 14891 x^{7} - 24713 x^{6} - 271477 x^{5} + 355512 x^{4} + 1733428 x^{3} - 1151536 x^{2} - 2438066 x + 391619$	$11$	[11,0]	$617^{10}$	$1$	$344.051041126$	$344.051041125666$		✓		$C_{11}$ (as 11T1)	trivial	$2$	$10$	$11014089072.5$
11.11.159...601.1	$x^{11} - x^{10} - 300 x^{9} + 2185 x^{8} + 8376 x^{7} - 135886 x^{6} + 437196 x^{5} + 166743 x^{4} - 4024987 x^{3} + 9615051 x^{2} - 9696452 x + 3691321$	$11$	[11,0]	$661^{10}$	$1$	$366.285316023$	$366.2853160227791$		✓		$C_{11}$ (as 11T1)	trivial	$2$	$10$	$17494437669.3$
11.11.220...449.1	$x^{11} - x^{10} - 310 x^{9} + 395 x^{8} + 26441 x^{7} - 57583 x^{6} - 744575 x^{5} + 2220564 x^{4} + 2568726 x^{3} - 5088204 x^{2} - 1360638 x + 996543$	$11$	[11,0]	$683^{10}$	$1$	$377.351511793$	$377.351511792966$		✓		$C_{11}$ (as 11T1)	trivial	$2$	$10$	$2276941413140$
11.11.412...649.1	$x^{11} - x^{10} - 330 x^{9} - 637 x^{8} + 30782 x^{7} + 122078 x^{6} - 616689 x^{5} - 3355168 x^{4} + 183306 x^{3} + 17584739 x^{2} + 19842261 x + 2279191$	$11$	[11,0]	$727^{10}$	$1$	$399.387914504$	$399.387914503562$		✓		$C_{11}$ (as 11T1)	trivial	$2$	$10$	$49130453388.1$
11.11.218...401.1	$x^{11} - x^{10} - 390 x^{9} + 653 x^{8} + 52046 x^{7} - 146438 x^{6} - 2723930 x^{5} + 11558015 x^{4} + 36326009 x^{3} - 250960565 x^{2} + 385923388 x - 145865807$	$11$	[11,0]	$859^{10}$	$1$	$464.80042081$	$464.8004208101595$		✓		$C_{11}$ (as 11T1)	trivial	$2$	$10$	$80664010957.6$
11.11.281...801.1	$x^{11} - x^{10} - 400 x^{9} + 29 x^{8} + 34594 x^{7} - 51208 x^{6} - 648406 x^{5} + 1281923 x^{4} + 1931229 x^{3} - 2774565 x^{2} - 1474244 x + 1306999$	$11$	[11,0]	$881^{10}$	$1$	$475.609834056$	$475.6098340560147$		✓		$C_{11}$ (as 11T1)	trivial	$2$	$10$	$379023342573$
11.11.580...049.1	$x^{11} - x^{10} - 430 x^{9} - 2035 x^{8} + 28780 x^{7} + 141142 x^{6} - 760875 x^{5} - 3028650 x^{4} + 8674010 x^{3} + 20981317 x^{2} - 30077229 x - 47440673$	$11$	[11,0]	$947^{10}$	$1$	$507.893562454$	$507.8935624536204$		✓		$C_{11}$ (as 11T1)	trivial	$2$	$10$	$1104123814020$
11.11.913...401.1	$x^{11} - x^{10} - 450 x^{9} + 393 x^{8} + 65785 x^{7} - 76121 x^{6} - 3728249 x^{5} + 6483322 x^{4} + 89323866 x^{3} - 205338716 x^{2} - 745717454 x + 2032282741$	$11$	[11,0]	$991^{10}$	$1$	$529.301740716$	$529.3017407164167$		✓		$C_{11}$ (as 11T1)	trivial	$2$	$10$	$155801246971$
11.11.118...424.1	$x^{11} - 4 x^{10} - 5541 x^{9} - 17700 x^{8} + 8989656 x^{7} + 88565592 x^{6} - 3982035456 x^{5} - 53992425120 x^{4} + 177164975493 x^{3} + 3011149862548 x^{2} - 789230330881 x - 3422014984884$	$11$	[11,0]	$2^{24}\cdot 3^{10}\cdot 337^{4}\cdot 310501^{4}$	$4$	$10157.6040123$	$303970.38325382833$			?	$M_{11}$ (as 11T6)	trivial	$2$	$10$	$71167879092500000000$
11.11.130...000.1	$x^{11} - 89045 x^{9} - 1016268 x^{8} + 1999274189 x^{7} + 17620911770 x^{6} - 14713278229518 x^{5} - 142840655647272 x^{4} + 38125562570421876 x^{3} + 562256553231789768 x^{2} - 26705329205451737544 x - 432518584183431877728$	$11$	[11,0]	$2^{16}\cdot 3^{4}\cdot 5^{6}\cdot 11^{12}\cdot 13^{4}\cdot 17^{4}\cdot 347^{8}$	$7$	$67406.2536104$	$936774.2546036756$				$M_{11}$ (as 11T6)	trivial	$2$	$10$	$6854659729190000000000000$