Number field search results

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

Results (1-50 of 8287 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
5.1.3825936.1	$x^{5} - 2 x^{4} - 5 x^{3} + 24 x^{2} - 42 x + 36$	$5$	[1,2]	$2^{4}\cdot 3^{2}\cdot 163^{2}$	$3$	$20.7275294171$	$44.22668877499196$				$D_{5}$ (as 5T2)	$[11]$	$2$	$2$	$22.2358434203$
5.1.3965816.1	$x^{5} - 2 x^{4} + 7 x^{3} - 11 x^{2} - 6 x - 1$	$5$	[1,2]	$2^{3}\cdot 337\cdot 1471$	$3$	$20.8769240913$	$1991.4356630330792$			?	$S_5$ (as 5T5)	$[11]$	$2$	$2$	$9.39193242027$
5.1.4532905.1	$x^{5} - x^{4} + 9 x^{3} - x^{2} + 17 x - 1$	$5$	[1,2]	$5\cdot 13\cdot 69737$	$3$	$21.4424952949$	$2129.0620000366357$				$S_5$ (as 5T5)	$[11]$	$2$	$2$	$9.85745901993$
5.1.4604992.1	$x^{5} - 2 x^{4} + 8 x^{3} - 36 x^{2} + 67 x - 30$	$5$	[1,2]	$2^{6}\cdot 7\cdot 19\cdot 541$	$4$	$21.5102657535$	$758.6988862519834$				$S_5$ (as 5T5)	$[11]$	$2$	$2$	$21.7301567016$
5.1.4704080.1	$x^{5} - x^{4} + 6 x^{3} + 4 x^{2} + 7 x - 1$	$5$	[1,2]	$2^{4}\cdot 5\cdot 127\cdot 463$	$4$	$21.6020486488$	$1217.247860173666$			?	$S_5$ (as 5T5)	$[11]$	$2$	$2$	$8.49952501069$
5.1.4718800.1	$x^{5} - 2 x^{4} + 2 x^{3} + 10 x^{2} - 30 x + 20$	$5$	[1,2]	$2^{4}\cdot 5^{2}\cdot 47\cdot 251$	$4$	$21.6155511781$	$712.9637583819549$			?	$S_5$ (as 5T5)	$[11]$	$2$	$2$	$9.6270196687$
5.1.4892116.1	$x^{5} - x^{4} + 4 x^{3} + 12 x^{2} - 38 x + 44$	$5$	[1,2]	$2^{2}\cdot 1223029$	$2$	$21.7720513159$	$1755.5170074549985$				$S_5$ (as 5T5)	$[12]$	$2$	$2$	$12.2449742113$
5.1.4953845.1	$x^{5} - 2 x^{4} + 2 x^{3} + 10 x^{2} + 5 x - 1$	$5$	[1,2]	$5\cdot 13\cdot 76213$	$3$	$21.8267202797$	$2225.7234778830907$			✓	$S_5$ (as 5T5)	$[11]$	$2$	$2$	$4.97731913356$
5.1.4990864.1	$x^{5} - 3 x^{3} - 10 x^{2} + 25 x - 12$	$5$	[1,2]	$2^{4}\cdot 73\cdot 4273$	$3$	$21.8592444671$	$1117.01208587911$			✓	$S_5$ (as 5T5)	$[11]$	$2$	$2$	$10.3688743994$
5.1.5360324.1	$x^{5} - 2 x^{4} + x^{3} - 9 x^{2} + 14 x + 1$	$5$	[1,2]	$2^{2}\cdot 911\cdot 1471$	$3$	$22.173702082$	$1837.605104729616$			✓	$S_5$ (as 5T5)	$[11]$	$2$	$2$	$7.56149966349$
5.1.5415540.1	$x^{5} - 2 x^{3} - 4 x^{2} + 3 x + 18$	$5$	[1,2]	$2^{2}\cdot 3\cdot 5\cdot 13\cdot 53\cdot 131$	$6$	$22.2191966965$	$1847.0453219327999$				$S_5$ (as 5T5)	$[13]$	$2$	$2$	$20.4406870877$
5.1.5439349.1	$x^{5} - x^{4} + 6 x^{3} - 10 x^{2} + 11 x - 6$	$5$	[1,2]	$5439349$	$1$	$22.2386994234$	$2332.2411967890457$			✓	$S_5$ (as 5T5)	$[11]$	$2$	$2$	$7.47312058233$
5.1.5574629.1	$x^{5} - x^{4} + 5 x^{3} - 11 x^{2} + 11 x - 6$	$5$	[1,2]	$113\cdot 49333$	$2$	$22.3482331714$	$2361.0652256979265$			✓	$S_5$ (as 5T5)	$[12]$	$2$	$2$	$7.09502945787$
5.1.5592784.1	$x^{5} - 2 x^{4} + 2 x^{3} + 32 x^{2} - 51 x + 50$	$5$	[1,2]	$2^{4}\cdot 293\cdot 1193$	$3$	$22.3627706289$	$1182.453381744921$				$S_5$ (as 5T5)	$[11]$	$2$	$2$	$14.8626130353$
5.1.5665572.1	$x^{5} - x^{4} + 13 x^{3} - 14 x^{2} + 44 x - 44$	$5$	[1,2]	$2^{2}\cdot 3^{3}\cdot 11\cdot 19\cdot 251$	$5$	$22.420678574$	$828.7768444118636$			?	$S_5$ (as 5T5)	$[11]$	$2$	$2$	$9.99676835926$
5.1.5718864.3	$x^{5} - x^{4} + 10 x^{3} - 4 x^{2} + 24 x + 6$	$5$	[1,2]	$2^{4}\cdot 3\cdot 283\cdot 421$	$4$	$22.4626998349$	$1342.1360898848889$			✓	$S_5$ (as 5T5)	$[11]$	$2$	$2$	$12.2071654654$
5.1.5781873.1	$x^{5} - 2 x^{4} + 7 x^{3} + 9 x^{2} + 30 x + 72$	$5$	[1,2]	$3\cdot 373\cdot 5167$	$3$	$22.5119807961$	$2404.552557129912$			?	$S_5$ (as 5T5)	$[11]$	$2$	$2$	$14.2336951674$
5.1.6017045.1	$x^{5} - 2 x^{4} + 4 x^{3} - 17 x^{2} + 10 x - 16$	$5$	[1,2]	$5\cdot 1097^{2}$	$2$	$22.6922025754$	$237.84247776121794$				$S_5$ (as 5T5)	$[11]$	$2$	$2$	$19.4058527259$
5.1.6076884.1	$x^{5} - 4 x^{3} - 24 x^{2} - 11 x - 34$	$5$	[1,2]	$2^{2}\cdot 3\cdot 11\cdot 19\cdot 2423$	$5$	$22.7371585005$	$1956.5778887344807$				$S_5$ (as 5T5)	$[11]$	$2$	$2$	$18.4065310903$
5.1.6193913.1	$x^{5} - x^{4} + 5 x^{3} - 8 x^{2} + 10 x + 1$	$5$	[1,2]	$11\cdot 263\cdot 2141$	$3$	$22.8240662993$	$2488.757320431223$			?	$S_5$ (as 5T5)	$[13]$	$2$	$2$	$10.369762485$
5.1.6214788.1	$x^{5} + x^{3} - 3 x^{2} + 8 x - 1$	$5$	[1,2]	$2^{2}\cdot 3^{2}\cdot 172633$	$3$	$22.8394301372$	$1142.3763406334226$			✓	$S_5$ (as 5T5)	$[11]$	$2$	$2$	$8.75072634305$
5.1.6223825.1	$x^{5} - 6 x^{3} - 3 x^{2} + 22 x - 15$	$5$	[1,2]	$5^{2}\cdot 241\cdot 1033$	$3$	$22.8460684966$	$1458.9442104703726$			✓	$S_5$ (as 5T5)	$[11]$	$2$	$2$	$6.3673778095$
5.1.6226421.1	$x^{5} + 3 x^{3} - 19 x^{2} - 12 x - 53$	$5$	[1,2]	$977\cdot 6373$	$2$	$22.847974029$	$2495.27974383635$				$S_5$ (as 5T5)	$[11]$	$2$	$2$	$18.6250901605$
5.1.6265888.1	$x^{5} - 2 x^{4} + 3 x^{3} + 6 x^{2} + 10 x + 4$	$5$	[1,2]	$2^{5}\cdot 195809$	$2$	$22.8768658539$	$1770.0124293348904$				$S_5$ (as 5T5)	$[11]$	$2$	$2$	$20.3934336975$
5.1.6289488.2	$x^{5} - 2 x^{4} - 2 x^{3} + 6 x^{2} + 30 x + 24$	$5$	[1,2]	$2^{4}\cdot 3^{4}\cdot 23\cdot 211$	$4$	$22.8940727519$	$563.4407728701549$			?	$S_5$ (as 5T5)	$[13]$	$2$	$2$	$13.6016951437$
5.1.6317352.1	$x^{5} - x^{4} + 4 x^{3} + 3 x^{2} - 12 x + 6$	$5$	[1,2]	$2^{3}\cdot 3^{4}\cdot 9749$	$3$	$22.9143221897$	$1006.1587133184995$			✓	$S_5$ (as 5T5)	$[12]$	$2$	$2$	$8.80806331317$
5.1.6370809.1	$x^{5} - 2 x^{4} + 12 x^{3} - 9 x^{2} + 9 x + 1$	$5$	[1,2]	$3\cdot 2123603$	$2$	$22.9529714762$	$2524.046156471787$			?	$S_5$ (as 5T5)	$[11]$	$2$	$2$	$10.3900893$
5.1.6384096.1	$x^{5} + 12 x^{3} - 10 x^{2} - 12 x - 36$	$5$	[1,2]	$2^{5}\cdot 3^{5}\cdot 821$	$3$	$22.9625376718$	$530.5688955751483$			?	$S_5$ (as 5T5)	$[11]$	$2$	$2$	$17.9274031184$
5.1.6401221.1	$x^{5} - x^{4} - 4 x^{3} + 27 x^{2} - 49 x + 58$	$5$	[1,2]	$31^{2}\cdot 6661$	$2$	$22.9748436335$	$454.41280791808674$				$S_5$ (as 5T5)	$[13]$	$2$	$2$	$13.2196862386$
5.1.6479824.1	$x^{5} - x^{4} + 10 x^{3} + 4 x^{2} + 3 x - 1$	$5$	[1,2]	$2^{4}\cdot 13\cdot 31153$	$3$	$23.0309918696$	$1428.6415450712257$			?	$S_5$ (as 5T5)	$[11]$	$2$	$2$	$12.537258625$
5.1.6495369.1	$x^{5} - 2 x^{4} + 15 x^{3} - 14 x^{2} + 33 x - 48$	$5$	[1,2]	$3\cdot 59\cdot 36697$	$3$	$23.0420314815$	$2548.601381150061$				$S_5$ (as 5T5)	$[11]$	$2$	$2$	$12.1613481408$
5.1.6540321.1	$x^{5} - x^{4} - 8 x^{3} - 3 x^{2} + 26 x + 24$	$5$	[1,2]	$3\cdot 2180107$	$2$	$23.073836601$	$2557.4051302052244$			?	$S_5$ (as 5T5)	$[11]$	$2$	$2$	$16.4006077831$
5.1.6571389.1	$x^{5} - x^{4} + 8 x^{3} - 9 x^{2} + 8 x - 1$	$5$	[1,2]	$3\cdot 11^{2}\cdot 43\cdot 421$	$4$	$23.0957162528$	$1152.650633160811$			✓	$S_5$ (as 5T5)	$[11]$	$2$	$2$	$7.19937117811$
5.1.6721120.1	$x^{5} - x^{4} + 5 x^{3} - 3 x^{2} + 28$	$5$	[1,2]	$2^{5}\cdot 5\cdot 7\cdot 17\cdot 353$	$5$	$23.2000184297$	$1633.1804063241532$			?	$S_5$ (as 5T5)	$[11]$	$2$	$2$	$12.8450413616$
5.1.6763644.1	$x^{5} - x^{4} + 2 x^{3} + 7 x^{2} - 2 x - 6$	$5$	[1,2]	$2^{2}\cdot 3^{2}\cdot 89\cdot 2111$	$4$	$23.2293013549$	$1501.5152346879468$			✓	$S_5$ (as 5T5)	$[11]$	$2$	$2$	$7.16977984789$
5.1.6772340.1	$x^{5} - 2 x^{4} + 4 x^{3} + 4 x^{2} - 7 x + 20$	$5$	[1,2]	$2^{2}\cdot 5\cdot 53\cdot 6389$	$4$	$23.2352714562$	$2065.50402118285$				$S_5$ (as 5T5)	$[13]$	$2$	$2$	$19.4163496124$
5.1.6837360.1	$x^{5} - 2 x^{4} - x^{3} + 4 x^{2} + 15 x + 12$	$5$	[1,2]	$2^{4}\cdot 3\cdot 5\cdot 31\cdot 919$	$5$	$23.2797166183$	$1848.967279321081$			?	$S_5$ (as 5T5)	$[11]$	$2$	$2$	$9.8248442433$
5.1.6865236.1	$x^{5} - x^{4} + 7 x^{3} - 7 x^{2} + 28 x - 64$	$5$	[1,2]	$2^{2}\cdot 3^{5}\cdot 7\cdot 1009$	$4$	$23.298668075$	$693.2073342601075$				$S_5$ (as 5T5)	$[13]$	$2$	$2$	$22.7748479193$
5.1.6914516.1	$x^{5} - x^{4} + 12 x^{3} + 4 x^{2} + 6 x - 8$	$5$	[1,2]	$2^{2}\cdot 7\cdot 246947$	$3$	$23.3320209214$	$2087.0726219078842$				$S_5$ (as 5T5)	$[12]$	$2$	$2$	$18.8673536765$
5.1.6977012.1	$x^{5} - 2 x^{4} - 2 x^{3} - 6 x^{2} + 67 x + 18$	$5$	[1,2]	$2^{2}\cdot 7^{2}\cdot 35597$	$3$	$23.3740459781$	$1095.9533194848398$				$S_5$ (as 5T5)	$[13]$	$2$	$2$	$17.4989007161$
5.1.7145577.1	$x^{5} + 3 x^{3} - 5 x^{2} - 3 x - 6$	$5$	[1,2]	$3^{4}\cdot 19\cdot 4643$	$3$	$23.4859136992$	$1070.0833486669521$			✓	$S_5$ (as 5T5)	$[11]$	$2$	$2$	$16.7730473023$
5.1.7307724.1	$x^{5} + 12 x^{3} - 24 x^{2} + 19 x - 160$	$5$	[1,2]	$2^{2}\cdot 3\cdot 608977$	$3$	$23.5915473747$	$2703.2802296469376$			?	$S_5$ (as 5T5)	$[12]$	$2$	$2$	$15.0827184804$
5.1.7327940.1	$x^{5} - x^{4} + 7 x^{3} - 3 x^{2} + 2 x + 20$	$5$	[1,2]	$2^{2}\cdot 5\cdot 366397$	$3$	$23.6045856298$	$2148.5606645341245$			?	$S_5$ (as 5T5)	$[13]$	$2$	$2$	$9.33229604965$
5.1.7354869.1	$x^{5} - x^{4} + 8 x^{3} + 6 x + 1$	$5$	[1,2]	$3\cdot 997\cdot 2459$	$3$	$23.6219087952$	$2711.986172531121$			✓	$S_5$ (as 5T5)	$[13]$	$2$	$2$	$6.81705374175$
5.1.7415200.1	$x^{5} - x^{4} + 3 x^{3} + 15 x^{2} - 50$	$5$	[1,2]	$2^{5}\cdot 5^{2}\cdot 13\cdot 23\cdot 31$	$5$	$23.660535729$	$1126.0467858751272$				$S_5$ (as 5T5)	$[11]$	$2$	$2$	$20.6114539695$
5.1.7442928.1	$x^{5} - 2 x^{4} + 6 x^{3} - 30 x^{2} + 60 x - 36$	$5$	[1,2]	$2^{4}\cdot 3^{4}\cdot 5743$	$3$	$23.6782043081$	$826.2365610734412$			?	$S_5$ (as 5T5)	$[11]$	$2$	$2$	$21.4313163731$
5.1.7486941.1	$x^{5} - x^{4} - 2 x^{3} + 20 x^{2} + 39 x + 18$	$5$	[1,2]	$3\cdot 7\cdot 11\cdot 32411$	$4$	$23.7061420353$	$2736.227512470409$			?	$S_5$ (as 5T5)	$[11]$	$2$	$2$	$10.3553170257$
5.1.7489752.1	$x^{5} - x^{4} + 9 x^{3} - 6 x^{2} + 2 x + 1$	$5$	[1,2]	$2^{3}\cdot 3\cdot 312073$	$3$	$23.7079218799$	$2736.741127691839$			✓	$S_5$ (as 5T5)	$[11]$	$2$	$2$	$8.92707337839$
5.1.7500080.1	$x^{5} - x^{4} + 2 x^{3} + 16 x^{2} + x + 1$	$5$	[1,2]	$2^{4}\cdot 5\cdot 7\cdot 59\cdot 227$	$5$	$23.7144566883$	$1725.2271503953946$			?	$S_5$ (as 5T5)	$[14]$	$2$	$2$	$10.8878487872$
5.1.7616097.1	$x^{5} - x^{4} + 8 x^{3} - 11 x^{2} - 8 x + 12$	$5$	[1,2]	$3^{2}\cdot 846233$	$2$	$23.7873735869$	$1593.3295327709207$			?	$S_5$ (as 5T5)	$[11]$	$2$	$2$	$10.5966572077$