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Results (1-50 of 322140 matches)

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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
5.5.14641.1	$x^{5} - x^{4} - 4 x^{3} + 3 x^{2} + 3 x - 1$	$5$	[5,0]	$11^{4}$	$1$	$6.80948312752$	$6.809483127522301$	✓	✓	$C_5$ (as 5T1)	trivial	$2$	$4$	$1.63569412559$
5.5.24217.1	$x^{5} - 5 x^{3} - x^{2} + 3 x + 1$	$5$	[5,0]	$61\cdot 397$	$2$	$7.53050443021$	$155.6181223379848$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$2.39942113132$
5.5.36497.1	$x^{5} - 2 x^{4} - 3 x^{3} + 5 x^{2} + x - 1$	$5$	[5,0]	$36497$	$1$	$8.17431620701$	$191.04188022525324$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$3.55065765574$
5.5.38569.1	$x^{5} - 5 x^{3} + 4 x - 1$	$5$	[5,0]	$38569$	$1$	$8.26509168848$	$196.38991827484423$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$3.15543791633$
5.5.65657.1	$x^{5} - x^{4} - 5 x^{3} + 2 x^{2} + 5 x + 1$	$5$	[5,0]	$65657$	$1$	$9.19297770826$	$256.236219141635$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$5.50318166396$
5.5.70601.1	$x^{5} - x^{4} - 5 x^{3} + 2 x^{2} + 3 x - 1$	$5$	[5,0]	$17\cdot 4153$	$2$	$9.327433695$	$265.7084868798887$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$4.61496156169$
5.5.81509.1	$x^{5} - x^{4} - 5 x^{3} + 3 x^{2} + 5 x - 2$	$5$	[5,0]	$81509$	$1$	$9.59933422509$	$285.49781084975064$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$7.63162348973$
5.5.81589.1	$x^{5} - 6 x^{3} + 8 x - 1$	$5$	[5,0]	$83\cdot 983$	$2$	$9.60121780954$	$285.6378826416412$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$7.60787640263$
5.5.89417.1	$x^{5} - 6 x^{3} - x^{2} + 8 x + 3$	$5$	[5,0]	$89417$	$1$	$9.77876521496$	$299.02675465583343$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$6.74148650938$
5.5.101833.1	$x^{5} - x^{4} - 5 x^{3} + 5 x^{2} + 2 x - 1$	$5$	[5,0]	$101833$	$1$	$10.0363941276$	$319.11283270968596$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$6.32919746615$
5.5.106069.1	$x^{5} - 2 x^{4} - 4 x^{3} + 7 x^{2} + 3 x - 4$	$5$	[5,0]	$73\cdot 1453$	$2$	$10.1185363196$	$325.68236059080635$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$9.17408549814$
5.5.117688.1	$x^{5} - x^{4} - 5 x^{3} + 4 x^{2} + 4 x - 1$	$5$	[5,0]	$2^{3}\cdot 47\cdot 313$	$3$	$10.3310969354$	$343.0568466012594$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$9.71347669051$
5.5.122821.1	$x^{5} - 2 x^{4} - 4 x^{3} + 4 x^{2} + 3 x - 1$	$5$	[5,0]	$263\cdot 467$	$2$	$10.4196834623$	$350.4582714104491$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$7.04707403444$
5.5.124817.1	$x^{5} - 7 x^{3} - 6 x^{2} + 2 x + 1$	$5$	[5,0]	$7\cdot 11\cdot 1621$	$3$	$10.4533320988$	$353.2944947207641$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$7.92197613589$
5.5.126032.1	$x^{5} - 6 x^{3} + 6 x - 2$	$5$	[5,0]	$2^{4}\cdot 7877$	$2$	$10.4736043891$	$154.52701637191086$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$12.0598883245$
5.5.135076.1	$x^{5} - x^{4} - 5 x^{3} + 4 x^{2} + 4 x - 2$	$5$	[5,0]	$2^{2}\cdot 33769$	$2$	$10.6197828931$	$291.70626984657$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$11.6288832988$
5.5.138136.1	$x^{5} - x^{4} - 6 x^{3} + 3 x^{2} + 4 x - 2$	$5$	[5,0]	$2^{3}\cdot 31\cdot 557$	$3$	$10.6674686497$	$371.6665171898055$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$11.0050313668$
5.5.138917.1	$x^{5} - 6 x^{3} - 2 x^{2} + 3 x + 1$	$5$	[5,0]	$138917$	$1$	$10.6795039123$	$372.71570935499886$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$9.4150840208$
5.5.144209.1	$x^{5} - 6 x^{3} - x^{2} + 6 x - 1$	$5$	[5,0]	$13\cdot 11093$	$2$	$10.759658142$	$379.74860105074777$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$8.38185695843$
5.5.147109.1	$x^{5} - 2 x^{4} - 4 x^{3} + 5 x^{2} + 3 x - 2$	$5$	[5,0]	$157\cdot 937$	$2$	$10.8025888908$	$383.54791095767945$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$11.6668990641$
5.5.149169.1	$x^{5} - 6 x^{3} - 3 x^{2} + 4 x + 1$	$5$	[5,0]	$3\cdot 19\cdot 2617$	$3$	$10.8326750486$	$386.22402825303345$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$8.79855118605$
5.5.153424.1	$x^{5} - 2 x^{4} - 4 x^{3} + 8 x^{2} - 2$	$5$	[5,0]	$2^{4}\cdot 43\cdot 223$	$3$	$10.8937815003$	$170.49461080203213$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$11.5954695752$
5.5.157457.1	$x^{5} - 2 x^{4} - 4 x^{3} + 5 x^{2} + 4 x - 1$	$5$	[5,0]	$157457$	$1$	$10.9504607918$	$396.80851805373334$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$9.8429578526$
5.5.160801.1	$x^{5} - x^{4} - 5 x^{3} + 4 x^{2} + 3 x - 1$	$5$	[5,0]	$401^{2}$	$1$	$10.9965828103$	$20.024984394500787$		✓	$D_{5}$ (as 5T2)	trivial	$2$	$4$	$9.17494614126$
5.5.161121.1	$x^{5} - x^{4} - 6 x^{3} + 3 x^{2} + 5 x + 1$	$5$	[5,0]	$3\cdot 43\cdot 1249$	$3$	$11.0009560526$	$401.39880418357$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$11.2054995686$
5.5.170701.1	$x^{5} - x^{4} - 6 x^{3} + 4 x + 1$	$5$	[5,0]	$170701$	$1$	$11.1287711835$	$413.1597753896185$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$8.997051159$
5.5.173513.1	$x^{5} - 2 x^{4} - 5 x^{3} + 3 x^{2} + 3 x - 1$	$5$	[5,0]	$167\cdot 1039$	$2$	$11.1651973477$	$416.5489166952664$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$7.25222447496$
5.5.176281.1	$x^{5} - x^{4} - 5 x^{3} + 3 x^{2} + 4 x - 1$	$5$	[5,0]	$7\cdot 25183$	$2$	$11.2005951843$	$419.8583094330753$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$9.26719739114$
5.5.176684.1	$x^{5} - 6 x^{3} - x^{2} + 5 x - 1$	$5$	[5,0]	$2^{2}\cdot 44171$	$2$	$11.2057116947$	$420.3379592661124$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$12.6809122173$
5.5.179024.1	$x^{5} - 8 x^{3} + 6 x - 2$	$5$	[5,0]	$2^{4}\cdot 67\cdot 167$	$3$	$11.2352373438$	$184.17031608098438$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$15.1926139168$
5.5.180769.1	$x^{5} - 2 x^{4} - 4 x^{3} + 7 x^{2} - 1$	$5$	[5,0]	$41\cdot 4409$	$2$	$11.2570550811$	$425.1693780130455$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$9.64320519613$
5.5.181057.1	$x^{5} - 2 x^{4} - 4 x^{3} + 7 x^{2} + 2 x - 3$	$5$	[5,0]	$331\cdot 547$	$2$	$11.2606397308$	$425.50793177096006$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$11.9801284306$
5.5.186037.1	$x^{5} - x^{4} - 6 x^{3} + 2 x^{2} + 5 x - 2$	$5$	[5,0]	$186037$	$1$	$11.3219143597$	$431.3200667717652$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$12.8893052818$
5.5.195829.1	$x^{5} - 2 x^{4} - 5 x^{3} + 6 x^{2} + 7 x + 1$	$5$	[5,0]	$113\cdot 1733$	$2$	$11.4386665825$	$442.52570546805526$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$12.9763440515$
5.5.202817.1	$x^{5} - 2 x^{4} - 4 x^{3} + 5 x^{2} + 2 x - 1$	$5$	[5,0]	$202817$	$1$	$11.5191615986$	$450.35208448501714$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$10.5466728882$
5.5.205225.1	$x^{5} - x^{4} - 6 x^{3} + 3 x^{2} + 7 x - 3$	$5$	[5,0]	$5^{2}\cdot 8209$	$2$	$11.5463854905$	$264.92633453725404$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$13.7910879608$
5.5.207184.1	$x^{5} - x^{4} - 6 x^{3} + 2 x^{2} + 7 x - 1$	$5$	[5,0]	$2^{4}\cdot 23\cdot 563$	$3$	$11.568345285$	$198.12629214590953$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$13.8472207557$
5.5.210557.1	$x^{5} - x^{4} - 6 x^{3} + 4 x^{2} + 8 x - 1$	$5$	[5,0]	$210557$	$1$	$11.6057693921$	$458.8649038660508$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$10.7293738318$
5.5.216637.1	$x^{5} - 2 x^{4} - 4 x^{3} + 7 x^{2} + x - 2$	$5$	[5,0]	$23\cdot 9419$	$2$	$11.6720335329$	$465.44279992282617$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$14.9557752479$
5.5.218524.1	$x^{5} - 2 x^{4} - 4 x^{3} + 5 x^{2} + 3 x - 1$	$5$	[5,0]	$2^{2}\cdot 54631$	$2$	$11.6922967258$	$467.46550674889374$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$14.6003975231$
5.5.220036.1	$x^{5} - 2 x^{4} - 5 x^{3} + 11 x^{2} - 2 x - 1$	$5$	[5,0]	$2^{2}\cdot 55009$	$2$	$11.7084322771$	$372.3090034733704$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$16.188166415$
5.5.220669.1	$x^{5} - 7 x^{3} - 2 x^{2} + 11 x + 5$	$5$	[5,0]	$149\cdot 1481$	$2$	$11.7151611068$	$469.75419104037803$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$16.1498365364$
5.5.223824.1	$x^{5} - 2 x^{4} - 4 x^{3} + 6 x^{2} + 2 x - 2$	$5$	[5,0]	$2^{4}\cdot 3\cdot 4663$	$3$	$11.7484704958$	$205.92891515721612$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$17.8718319712$
5.5.223952.1	$x^{5} - 6 x^{3} - 2 x^{2} + 6 x + 2$	$5$	[5,0]	$2^{4}\cdot 13997$	$2$	$11.7498139266$	$205.98778983933025$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$15.4493023517$
5.5.224773.1	$x^{5} - x^{4} - 6 x^{3} + 2 x^{2} + 7 x + 2$	$5$	[5,0]	$53\cdot 4241$	$2$	$11.7584162009$	$474.10230963369077$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$15.2067902478$
5.5.230224.1	$x^{5} - 2 x^{4} - 4 x^{3} + 6 x^{2} + 3 x - 2$	$5$	[5,0]	$2^{4}\cdot 14389$	$2$	$11.814901874$	$269.28797958273094$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$22.6110814528$
5.5.233489.1	$x^{5} - x^{4} - 6 x^{3} + x^{2} + 5 x - 1$	$5$	[5,0]	$233489$	$1$	$11.8482247846$	$483.2069949824816$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$8.87058361542$
5.5.236549.1	$x^{5} - x^{4} - 6 x^{3} + 7 x^{2} + 2 x - 1$	$5$	[5,0]	$236549$	$1$	$11.8791187361$	$486.3630331347151$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$14.655875922$
5.5.240133.1	$x^{5} - 2 x^{4} - 4 x^{3} + 6 x^{2} + 2 x - 1$	$5$	[5,0]	$439\cdot 547$	$2$	$11.9148991107$	$490.03367231242385$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$15.8564126109$
5.5.240881.1	$x^{5} - 2 x^{4} - 5 x^{3} + 9 x^{2} + 5 x - 7$	$5$	[5,0]	$240881$	$1$	$11.9223127196$	$490.7962917545323$		✓	$S_5$ (as 5T5)	trivial	$2$	$4$	$10.6079997587$

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