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Results (1-50 of 868 matches)

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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Narrow class group	Unit group torsion	Unit group rank	Regulator
7.1.653069599.1	$x^{7} + 7 x - 4$	$7$	[1,3]	$-\,7^{7}\cdot 13\cdot 61$	$3$	$18.1668622812$	$248.50866893993384$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$108.303924404$
7.1.1581202560.1	$x^{7} - 14 x^{4} + 14 x^{2} - 4$	$7$	[1,3]	$-\,2^{7}\cdot 3\cdot 5\cdot 7^{7}$	$4$	$20.6129938025$	$127.5579616909212$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$281.305240321$
7.1.1950149824.1	$x^{7} + 7 x^{5} - 14 x^{4} - 7 x^{3} - 28 x^{2} - 28 x - 10$	$7$	[1,3]	$-\,2^{6}\cdot 7^{7}\cdot 37$	$3$	$21.2399049202$	$135.26303852868134$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$145.686508467$
7.1.2134623456.1	$x^{7} - 7 x^{4} + 7 x^{3} - 9$	$7$	[1,3]	$-\,2^{5}\cdot 3^{4}\cdot 7^{7}$	$3$	$21.5159329623$	$136.06766994305872$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$553.417911671$
7.3.2846164608.1	$x^{7} + 7 x^{3} - 28 x - 16$	$7$	[3,2]	$2^{7}\cdot 3^{3}\cdot 7^{7}$	$3$	$22.4186043978$	$95.68930071445884$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$4$	$565.980673187$
7.3.3201935184.1	$x^{7} - 7 x^{5} + 7 x^{3} + 21 x - 6$	$7$	[3,2]	$2^{4}\cdot 3^{5}\cdot 7^{7}$	$3$	$22.7990145963$	$55.35672771723257$				$S_7$ (as 7T7)	trivial	trivial	$2$	$4$	$1013.56380949$
7.3.4216540160.1	$x^{7} - 21 x^{3} - 14 x - 4$	$7$	[3,2]	$2^{10}\cdot 5\cdot 7^{7}$	$3$	$23.7133957214$	$99.44736375512461$				$S_7$ (as 7T7)	trivial	trivial	$2$	$4$	$1271.08951123$
7.1.5403265623.1	$x^{7} - 14 x^{4} + 42 x^{2} - 28 x + 9$	$7$	[1,3]	$-\,3^{8}\cdot 7^{7}$	$2$	$24.5685470679$	$38.18269887824235$			?	$F_7$ (as 7T4)	trivial	trivial	$2$	$3$	$400.835066484$
7.1.5403265623.2	$x^{7} - 7 x^{4} - 21 x^{3} - 42 x^{2} - 63 x - 36$	$7$	[1,3]	$-\,3^{8}\cdot 7^{7}$	$2$	$24.5685470679$	$72.47485488010228$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$828.338400691$
7.5.6746464256.1	$x^{7} - 14 x^{5} + 35 x^{3} - 28 x^{2} + 4$	$7$	[5,1]	$-\,2^{13}\cdot 7^{7}$	$2$	$25.3602625994$	$74.79641274736187$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$5$	$943.766732975$
7.3.12807740736.1	$x^{7} - 7 x^{3} - 7 x - 2$	$7$	[3,2]	$2^{6}\cdot 3^{5}\cdot 7^{7}$	$3$	$27.7923100953$	$187.05625850806678$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$4$	$890.503599416$
7.3.12807740736.2	$x^{7} - 7 x^{5} + 14 x^{3} - 28 x^{2} - 7 x + 2$	$7$	[3,2]	$2^{6}\cdot 3^{5}\cdot 7^{7}$	$3$	$27.7923100953$	$129.69756577441493$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$4$	$1150.98279613$
7.1.13341396600.1	$x^{7} + 7 x^{5} - 7 x^{4} - 35 x^{3} - 35 x^{2} - 14 x - 2$	$7$	[1,3]	$-\,2^{3}\cdot 3^{4}\cdot 5^{2}\cdot 7^{7}$	$4$	$27.9548603981$	$241.48859133520403$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$501.744849279$
7.1.15232251328.1	$x^{7} - 28 x^{4} + 42 x^{3} - 14 x^{2} + 14 x + 14$	$7$	[1,3]	$-\,2^{6}\cdot 7^{7}\cdot 17^{2}$	$3$	$28.4892217261$	$65.91057809321941$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$361.665496262$
7.1.15232251328.2	$x^{7} - 7 x^{5} + 14 x^{3} - 14 x^{2} - 35 x - 14$	$7$	[1,3]	$-\,2^{6}\cdot 7^{7}\cdot 17^{2}$	$3$	$28.4892217261$	$102.91398703713477$			✓	$S_7$ (as 7T7)	$[2]$	$[2]$	$2$	$3$	$214.840870163$
7.3.21926008832.1	$x^{7} - 7 x^{3} - 4$	$7$	[3,2]	$2^{11}\cdot 7^{7}\cdot 13$	$3$	$30.0109636402$	$226.7748804889756$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$4$	$1418.29893921$
7.1.23521211623.1	$x^{7} - 14 x^{4} - 7 x^{3} + 56 x^{2} - 28 x + 5$	$7$	[1,3]	$-\,7^{7}\cdot 13^{4}$	$2$	$30.3135708831$	$48.790340734004666$			?	$F_7$ (as 7T4)	trivial	trivial	$2$	$3$	$306.92601284$
7.1.23718038400.1	$x^{7} - 28 x^{4} + 14 x^{3} + 56 x^{2} + 21 x - 2$	$7$	[1,3]	$-\,2^{7}\cdot 3^{2}\cdot 5^{2}\cdot 7^{7}$	$4$	$30.3496795359$	$212.59990691447746$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$1216.5111274$
7.1.27881871808.1	$x^{7} - 7 x^{5} - 14 x^{4} + 21 x^{3} + 42 x^{2} - 14 x - 40$	$7$	[1,3]	$-\,2^{6}\cdot 7^{7}\cdot 23^{2}$	$3$	$31.059098539$	$119.70543275823796$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$1672.52877845$
7.3.28817416656.4	$x^{7} - 21 x^{5} - 21 x^{4} + 105 x^{3} + 231 x^{2} + 140 x + 9$	$7$	[3,2]	$2^{4}\cdot 3^{7}\cdot 7^{7}$	$3$	$31.2058800719$	$92.91812571124727$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$4$	$2382.7904441$
7.1.30464502656.1	$x^{7} - 14 x^{4} + 14 x^{3} - 14 x^{2} + 49 x - 30$	$7$	[1,3]	$-\,2^{7}\cdot 7^{7}\cdot 17^{2}$	$3$	$31.4546509605$	$173.08000555798776$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$2494.81084892$
7.3.32108294484.1	$x^{7} + 7 x^{5} - 7 x^{4} - 21 x^{3} + 42 x^{2} - 21 x + 3$	$7$	[3,2]	$2^{2}\cdot 3^{3}\cdot 7^{7}\cdot 19^{2}$	$4$	$31.6916842004$	$139.19042305462258$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$4$	$2831.91309773$
7.3.33353491500.1	$x^{7} - 7 x^{5} - 7 x^{3} - 63 x^{2} + 189 x + 69$	$7$	[3,2]	$2^{2}\cdot 3^{4}\cdot 5^{3}\cdot 7^{7}$	$4$	$31.8644113911$	$170.75822051230972$			?	$S_7$ (as 7T7)	trivial	$[2]$	$2$	$4$	$1592.99351962$
7.3.33820440381.1	$x^{7} - 7 x^{4} + 21 x^{2} - 9$	$7$	[3,2]	$3^{5}\cdot 7^{7}\cdot 13^{2}$	$3$	$31.9277611221$	$175.7823697292858$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$4$	$1393.77333517$
7.1.37105553408.1	$x^{7} - 14 x^{3} + 28 x - 16$	$7$	[1,3]	$-\,2^{12}\cdot 7^{7}\cdot 11$	$3$	$32.3533938607$	$196.89458856827093$				$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$1601.02536619$
7.1.38423222208.2	$x^{7} - 14 x^{4} + 112 x - 72$	$7$	[1,3]	$-\,2^{6}\cdot 3^{6}\cdot 7^{7}$	$3$	$32.5150799383$	$148.46665076647034$				$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$3968.54528661$
7.1.38423222208.3	$x^{7} - 14 x^{4} + 49 x + 18$	$7$	[1,3]	$-\,2^{6}\cdot 3^{6}\cdot 7^{7}$	$3$	$32.5150799383$	$114.79377881944359$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$3784.45528452$
7.1.38423222208.6	$x^{7} - 28 x^{4} - 42 x^{3} - 126 x^{2} - 84 x - 126$	$7$	[1,3]	$-\,2^{6}\cdot 3^{6}\cdot 7^{7}$	$3$	$32.5150799383$	$119.79893588004386$				$S_7$ (as 7T7)	$[7]$	$[7]$	$2$	$3$	$395.733248637$
7.1.38423222208.9	$x^{7} - 14 x^{4} + 42 x^{3} - 14 x - 114$	$7$	[1,3]	$-\,2^{6}\cdot 3^{6}\cdot 7^{7}$	$3$	$32.5150799383$	$73.51891167878458$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$1559.12640386$
7.1.38423222208.10	$x^{7} - 21 x^{4} - 126 x^{3} + 63 x^{2} + 315 x - 243$	$7$	[1,3]	$-\,2^{6}\cdot 3^{6}\cdot 7^{7}$	$3$	$32.5150799383$	$89.92726948552361$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$570.028029145$
7.1.38423222208.11	$x^{7} - 14 x^{4} + 84 x^{3} - 168 x^{2} + 168 x - 72$	$7$	[1,3]	$-\,2^{6}\cdot 3^{6}\cdot 7^{7}$	$3$	$32.5150799383$	$91.11188262869479$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$2795.36022949$
7.1.38423222208.12	$x^{7} - 7 x^{4} - 63 x^{3} - 126 x^{2} - 42 x - 51$	$7$	[1,3]	$-\,2^{6}\cdot 3^{6}\cdot 7^{7}$	$3$	$32.5150799383$	$98.5488388175451$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$3079.0610721$
7.1.38424045751.1	$x^{7} + 7 x - 1$	$7$	[1,3]	$-\,7^{7}\cdot 13\cdot 37\cdot 97$	$4$	$32.5151794961$	$1906.177569842242$			✓	$S_7$ (as 7T7)	$[2]$	$[2]$	$2$	$3$	$160.061613247$
7.1.38475928960.1	$x^{7} + 7 x - 2$	$7$	[1,3]	$-\,2^{7}\cdot 5\cdot 7^{7}\cdot 73$	$4$	$32.5214479533$	$674.3903901412205$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$2264.29200617$
7.1.43423775304.1	$x^{7} + 35 x^{3} - 21 x^{2} + 14 x - 2$	$7$	[1,3]	$-\,2^{3}\cdot 3\cdot 7^{7}\cdot 13^{3}$	$4$	$33.0883696135$	$155.87707456750547$			?	$S_7$ (as 7T7)	$[2]$	$[2]$	$2$	$3$	$911.284028448$
7.1.60036284700.1	$x^{7} - 21 x^{4} - 21 x^{3} - 42 x^{2} - 56 x - 36$	$7$	[1,3]	$-\,2^{2}\cdot 3^{6}\cdot 5^{2}\cdot 7^{7}$	$4$	$34.6555983178$	$188.38226987529606$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$1693.73849449$
7.1.60036284700.2	$x^{7} - 7 x^{4} + 28 x - 24$	$7$	[1,3]	$-\,2^{2}\cdot 3^{6}\cdot 5^{2}\cdot 7^{7}$	$4$	$34.6555983178$	$152.1480701870832$				$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$7313.21168216$
7.1.60036284700.3	$x^{7} - 7 x^{4} - 21 x^{3} + 84 x^{2} + 126 x - 162$	$7$	[1,3]	$-\,2^{2}\cdot 3^{6}\cdot 5^{2}\cdot 7^{7}$	$4$	$34.6555983178$	$306.9685738593459$				$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$3213.19980727$
7.1.64572359544.1	$x^{7} - 7 x^{5} + 28 x^{3} - 21 x^{2} + 6$	$7$	[1,3]	$-\,2^{3}\cdot 3^{4}\cdot 7^{7}\cdot 11^{2}$	$4$	$35.0180839448$	$358.1854651422006$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$1064.53300044$
7.1.68307950592.1	$x^{7} - 14 x^{4} + 21 x^{3} + 112 x + 42$	$7$	[1,3]	$-\,2^{10}\cdot 3^{4}\cdot 7^{7}$	$3$	$35.300561053$	$95.41872531570051$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$3983.96244215$
7.1.68307950592.2	$x^{7} + 7 x^{5} + 35 x^{3} - 84 x^{2} + 63 x - 84$	$7$	[1,3]	$-\,2^{10}\cdot 3^{4}\cdot 7^{7}$	$3$	$35.300561053$	$171.4345215714076$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$1763.95926824$
7.1.72643904487.1	$x^{7} - 7 x^{4} + 28 x - 27$	$7$	[1,3]	$-\,3^{6}\cdot 7^{7}\cdot 11^{2}$	$3$	$35.6122884737$	$157.25635442981533$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$995.873391166$
7.1.76108549888.1	$x^{7} - 7 x^{5} - 14 x^{4} - 7 x^{3} + 14 x - 14$	$7$	[1,3]	$-\,2^{8}\cdot 7^{7}\cdot 19^{2}$	$3$	$35.8501099925$	$137.07873102674878$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$1440.86418105$
7.1.76846444416.1	$x^{7} + 7 x - 6$	$7$	[1,3]	$-\,2^{7}\cdot 3^{6}\cdot 7^{7}$	$3$	$35.8995587961$	$162.34291888251445$			✓	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$2908.66643304$
7.1.76846444416.7	$x^{7} + 21 x^{5} - 14 x^{4} + 84 x^{3} - 84 x^{2} + 112 x - 48$	$7$	[1,3]	$-\,2^{7}\cdot 3^{6}\cdot 7^{7}$	$3$	$35.8995587961$	$182.22376525738957$				$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$4553.00914478$
7.1.86452249968.1	$x^{7} + 21 x^{3} - 54$	$7$	[1,3]	$-\,2^{4}\cdot 3^{8}\cdot 7^{7}$	$3$	$36.5087206353$	$115.04666087791696$				$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$5953.56007964$
7.1.86986729375.1	$x^{7} - 28 x^{4} + 49 x^{3} - 56 x^{2} + 63 x + 37$	$7$	[1,3]	$-\,5^{4}\cdot 7^{7}\cdot 13^{2}$	$3$	$36.5408798489$	$93.03719935120803$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$2205.88942796$
7.1.102942875000.1	$x^{7} - 7 x^{2} - 10$	$7$	[1,3]	$-\,2^{3}\cdot 5^{6}\cdot 7^{7}$	$3$	$37.4307080019$	$158.87861600603665$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$2070.66238709$
7.3.105413504000.2	$x^{7} - 35 x^{4} + 105 x^{3} - 42 x^{2} - 70 x + 25$	$7$	[3,2]	$2^{10}\cdot 5^{3}\cdot 7^{7}$	$3$	$37.5577411339$	$226.99298776076898$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$4$	$5848.15810594$
7.1.106731172800.3	$x^{7} - 14 x^{4} - 42 x^{3} - 126 x^{2} - 126 x - 216$	$7$	[1,3]	$-\,2^{6}\cdot 3^{4}\cdot 5^{2}\cdot 7^{7}$	$4$	$37.6244519948$	$191.66962196191074$			?	$S_7$ (as 7T7)	trivial	trivial	$2$	$3$	$3260.47214421$

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