Number field search results

Results (1-50 of 570 matches)

 

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
10.0.9300278979.1	x^10 - 4x^9 + 7x^8 - 11x^7 + 18x^6 - 19x^5 + 16x^4 - 17x^3 + 10x^2 - 3x + 3	$10$	[0,5]	$-\,3^{5}\cdot 337^{3}$	$2$	$9.92772177703$			✓	$F_5 \wr C_2$ (as 10T33)	trivial	$6$	$4$	$21.6645741104$
10.0.19911454263.1	x^10 - 2x^9 + 6x^8 - 10x^7 + 16x^6 - 17x^5 + 19x^4 - 12x^3 + 6x^2 - x + 1	$10$	[0,5]	$-\,3^{5}\cdot 19^{2}\cdot 61^{3}$	$3$	$10.7129800968$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$6$	$4$	$32.6108769459$
10.0.21141825471.1	x^10 - 2x^9 + 6x^8 - 12x^7 + 21x^6 - 29x^5 + 32x^4 - 29x^3 + 22x^2 - 12x + 3	$10$	[0,5]	$-\,3^{5}\cdot 13^{3}\cdot 199^{2}$	$3$	$10.7774061163$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$6$	$4$	$42.3340333761$
10.2.47280848896.1	x^10 - 4x^9 + 6x^8 - 17x^6 + 34x^5 - 36x^4 + 22x^3 - 6x^2 + 1	$10$	[2,4]	$2^{15}\cdot 113^{3}$	$2$	$11.6806907646$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$2$	$5$	$19.9288656356$
10.0.50316807879.1	x^10 - x^9 + 5x^8 - x^7 + 9x^6 + 3x^5 + 12x^4 + 2x^3 + 16x^2 - 3x + 9	$10$	[0,5]	$-\,3^{5}\cdot 13^{3}\cdot 307^{2}$	$3$	$11.7536108656$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$6$	$4$	$68.9524885099$
10.0.52750877643.1	x^10 - x^9 - x^8 + 3x^7 - x^6 - 9x^5 + 5x^4 + 32x^3 + 34x^2 + 15x + 3	$10$	[0,5]	$-\,3^{5}\cdot 601^{3}$	$2$	$11.8092677376$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$6$	$4$	$63.8325503351$
10.0.60897409375.1	x^10 - 3x^9 + x^8 + 5x^7 - 6x^6 - x^5 + 11x^4 - 17x^3 + 15x^2 - 8x + 3	$10$	[0,5]	$-\,5^{5}\cdot 11^{7}$	$2$	$11.9800845131$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$2$	$4$	$29.501052045$
10.0.80561164032.1	x^10 - 2x^9 - 5x^8 + 10x^7 + 5x^6 - 22x^5 + 29x^4 - 12x^3 + 7x^2 + 1	$10$	[0,5]	$-\,2^{8}\cdot 3^{5}\cdot 109^{3}$	$3$	$12.3200529188$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$6$	$4$	$85.4450012777$
10.0.90731184128.1	x^10 - 4x^9 + 9x^8 - 8x^7 - 2x^6 + 16x^5 - 14x^4 + 10x^2 - 8x + 2	$10$	[0,5]	$-\,2^{29}\cdot 13^{2}$	$2$	$12.4673932372$			✓	$F_5 \wr C_2$ (as 10T33)	trivial	$4$	$4$	$129.161083872$
10.0.101928170799.1	x^10 - x^9 + 7x^8 - 3x^7 + 17x^6 + 3x^5 + 22x^4 + 6x^3 + 10x^2 + x + 1	$10$	[0,5]	$-\,3^{5}\cdot 7^{2}\cdot 13^{2}\cdot 37^{3}$	$4$	$12.6133202649$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$6$	$4$	$75.155539666$
10.0.102294880256.1	x^10 - 2x^9 + 8x^8 - 8x^7 + 20x^6 - 8x^5 + 24x^4 + 18x^2 + 4x + 4	$10$	[0,5]	$-\,2^{22}\cdot 29^{3}$	$2$	$12.6178508596$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$4$	$4$	$124.32431863$
10.0.103010321491.1	x^10 - x^9 + 4x^7 + 6x^6 - 7x^5 - 3x^4 + 2x^2 + 5x + 2	$10$	[0,5]	$-\,7^{5}\cdot 11^{2}\cdot 37^{3}$	$3$	$12.62664802$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$2$	$4$	$39.1664588566$
10.0.103737344000.1	x^10 - 4x^9 + 4x^8 + 2x^6 - 6x^5 + 8x^4 - 4x^3 - 6x^2 - 4x + 10	$10$	[0,5]	$-\,2^{14}\cdot 5^{3}\cdot 37^{3}$	$3$	$12.6355314325$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$4$	$4$	$101.062761051$
10.0.107150045184.1	x^10 - 2x^9 + 2x^8 + 2x^7 - 4x^5 + 6x^4 + 2x^3 - 2x^2 - 2x + 1	$10$	[0,5]	$-\,2^{12}\cdot 3^{5}\cdot 7^{2}\cdot 13^{3}$	$4$	$12.676496354$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$6$	$4$	$105.528408969$
10.0.114445392399.1	x^10 - x^9 + 8x^8 - 5x^7 + 24x^6 - 11x^5 + 42x^4 - 17x^3 + 40x^2 - 10x + 13	$10$	[0,5]	$-\,3^{5}\cdot 13^{3}\cdot 463^{2}$	$3$	$12.7602690407$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$6$	$4$	$109.22995726$
10.0.209715200000.1	x^10 - 4x^9 + 5x^8 + 4x^6 - 8x^5 - 4x^4 + 5x^2 + 4x + 1	$10$	[0,5]	$-\,2^{26}\cdot 5^{5}$	$2$	$13.5569811094$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$4$	$4$	$208.253170812$
10.2.265306590625.1	x^10 - 2x^9 - 2x^8 + 5x^7 + 5x^6 - 8x^5 - 4x^4 + 7x^3 + 5x^2 - 2x - 1	$10$	[2,4]	$5^{5}\cdot 29^{3}\cdot 59^{2}$	$3$	$13.8795314041$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$2$	$5$	$65.9162636915$
10.0.265420800000.1	x^10 - 4x^9 + 7x^8 - 12x^7 + 14x^6 - 4x^5 - 4x^4 + 12x^3 - 2x^2 - 16x + 10	$10$	[0,5]	$-\,2^{20}\cdot 3^{4}\cdot 5^{5}$	$3$	$13.8801287754$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$4$	$4$	$264.332701262$
10.0.327680000000.1	x^10 - 2x^9 + 11x^8 - 12x^7 + 34x^6 - 12x^5 + 28x^4 + 16x^3 - 2x^2 + 4x + 2	$10$	[0,5]	$-\,2^{22}\cdot 5^{7}$	$2$	$14.1757156617$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$4$	$4$	$303.206408045$
10.0.327680000000.2	x^10 - 4x^9 + 7x^8 - 8x^7 + 18x^6 - 52x^5 + 100x^4 - 120x^3 + 90x^2 - 40x + 10	$10$	[0,5]	$-\,2^{22}\cdot 5^{7}$	$2$	$14.1757156617$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$4$	$4$	$298.181459297$
10.0.512000000000.1	x^10 - 4x^9 - x^8 + 16x^7 + 2x^6 - 20x^5 - 2x^4 + 12x^3 + 3x^2 - 4x + 1	$10$	[0,5]	$-\,2^{18}\cdot 5^{9}$	$2$	$14.8226889821$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$4$	$4$	$382.919458552$
10.0.560163396123.1	x^10 - 4x^9 + 6x^8 - 3x^7 - x^6 + 21x^4 - 16x^3 + 10x^2 - 3x + 1	$10$	[0,5]	$-\,3^{5}\cdot 1321^{3}$	$2$	$14.9565515662$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$6$	$4$	$280.4368291288231$
10.0.597196800000.1	x^10 - 2x^8 - 4x^7 + 16x^6 + 44x^5 + 70x^4 + 56x^3 + 37x^2 + 12x + 4	$10$	[0,5]	$-\,2^{18}\cdot 3^{6}\cdot 5^{5}$	$3$	$15.0526078375$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$4$	$4$	$384.461617828$
10.0.679477248000.1	x^10 - 2x^9 + 5x^8 + 4x^6 - 24x^5 + 4x^4 + 20x^2 - 8x + 4	$10$	[0,5]	$-\,2^{26}\cdot 3^{4}\cdot 5^{3}$	$3$	$15.2481618087$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$4$	$4$	$453.142676197$
10.0.1322306994176.1	x^10 - 5x^9 + 6x^8 + 6x^7 - 14x^6 + 14x^4 - 4x^3 - 8x^2 + 4x + 4	$10$	[0,5]	$-\,2^{15}\cdot 7^{9}$	$2$	$16.2979593217$				$F_5 \wr C_2$ (as 10T33)	trivial	$2$	$4$	$490.5591677684269$
10.0.1677721600000.1	x^10 - 4x^9 + 5x^8 + 2x^6 - 8x^5 - 6x^4 + 10x^2 + 8x + 2	$10$	[0,5]	$-\,2^{29}\cdot 5^{5}$	$2$	$16.6906015546$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$4$	$4$	$691.362501818$
10.0.1677721600000.2	x^10 - 4x^9 + 5x^8 - 6x^6 + 8x^5 + 2x^4 + 10x^2 + 8x + 2	$10$	[0,5]	$-\,2^{29}\cdot 5^{5}$	$2$	$16.6906015546$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$4$	$4$	$594.97342001$
10.2.1852746653125.1	x^10 + x^8 - 6x^7 - 10x^5 + 7x^4 - 4x^3 - 6x + 1	$10$	[2,4]	$5^{5}\cdot 29^{2}\cdot 89^{3}$	$3$	$16.8570511162$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$2$	$5$	$190.921457098$
10.0.2048000000000.1	x^10 - 4x^9 + 13x^8 - 16x^7 + 12x^6 + 16x^5 - 12x^4 - 16x^3 + 12x^2 + 16x + 4	$10$	[0,5]	$-\,2^{20}\cdot 5^{9}$	$2$	$17.0267984504$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$4$	$4$	$960.785628248$
10.0.2830974609375.1	x^10 - 3x^9 + 11x^8 - 22x^7 + 44x^6 - 61x^5 + 80x^4 - 75x^3 + 65x^2 - 35x + 15	$10$	[0,5]	$-\,3^{2}\cdot 5^{9}\cdot 11^{5}$	$3$	$17.5870742625$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$2$	$4$	$290.541651662$
10.0.3110400000000.2	x^10 - 3x^9 + 4x^8 - 10x^7 + 31x^6 - 45x^5 + 22x^4 + 4x^3 - 10x^2 + 6x + 4	$10$	[0,5]	$-\,2^{15}\cdot 3^{5}\cdot 5^{8}$	$3$	$17.7534035196$				$F_5 \wr C_2$ (as 10T33)	$[2]$	$2$	$4$	$429.229407245$
10.0.5435817984000.1	x^10 - 2x^9 - 6x^8 + 8x^7 + 38x^6 - 60x^5 + 36x^4 - 24x^3 + 21x^2 - 10x + 2	$10$	[0,5]	$-\,2^{29}\cdot 3^{4}\cdot 5^{3}$	$3$	$18.7726892246$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$4$	$4$	$1606.39678312$
10.0.6115295232000.2	x^10 - 4x^9 + 8x^8 - 16x^7 + 18x^6 - 16x^5 + 36x^4 + 8x^3 + 34x^2 + 8x + 8	$10$	[0,5]	$-\,2^{26}\cdot 3^{6}\cdot 5^{3}$	$3$	$18.9951069374$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$4$	$4$	$1867.58681577$
10.0.8388608000000.2	x^10 - 2x^9 + x^8 - 16x^7 + 64x^6 - 104x^5 + 84x^4 - 32x^3 + 12x^2 - 8x + 4	$10$	[0,5]	$-\,2^{29}\cdot 5^{6}$	$2$	$19.6050967576$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$4$	$4$	$1839.9530215$
10.0.8388608000000.3	x^10 - 2x^9 + 9x^8 - 8x^7 + 36x^6 - 24x^5 + 88x^4 - 16x^3 + 117x^2 - 34x + 65	$10$	[0,5]	$-\,2^{29}\cdot 5^{6}$	$2$	$19.6050967576$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$4$	$4$	$2331.14845802$
10.2.9023189417984.1	x^10 - 2x^9 - 2x^8 + 8x^7 - 2x^6 + 4x^5 - 8x^4 + 8x^3 + 9x^2 + 14x - 14	$10$	[2,4]	$2^{29}\cdot 7^{5}$	$2$	$19.748586085$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$2$	$5$	$1286.7287828658853$
10.0.9784472371200.4	x^10 - 4x^9 + 12x^8 - 32x^7 + 60x^6 - 72x^5 + 96x^4 - 184x^3 + 249x^2 - 164x + 40	$10$	[0,5]	$-\,2^{29}\cdot 3^{6}\cdot 5^{2}$	$3$	$19.9091968714$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$4$	$4$	$2016.29270729$
10.6.9932496465625.1	x^10 - 4x^9 + x^8 + 16x^7 - 31x^6 + 22x^5 + 32x^4 - 87x^3 + 36x^2 + 22x + 1	$10$	[6,2]	$5^{5}\cdot 19^{4}\cdot 29^{3}$	$3$	$19.9391133347$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$2$	$7$	$970.442963618$
10.0.12800000000000.4	x^10 - 4x^9 + 5x^8 - 10x^6 - 10x^4 + 125x^2 + 100x + 25	$10$	[0,5]	$-\,2^{18}\cdot 5^{11}$	$2$	$20.4513036513$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$4$	$4$	$2596.18843424$
10.0.12800000000000.5	x^10 - 20x^7 + 10x^6 + 16x^5 + 100x^4 - 100x^3 - 135x^2 + 80x + 68	$10$	[0,5]	$-\,2^{18}\cdot 5^{11}$	$2$	$20.4513036513$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$4$	$4$	$2424.71004544$
10.0.38060880859375.1	x^10 + 6x^8 - 16x^7 + 36x^6 - 73x^5 + 145x^4 - 170x^3 + 110x^2 - 35x + 5	$10$	[0,5]	$-\,5^{9}\cdot 11^{7}$	$2$	$22.80593506945785$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$2$	$4$	$1444.5760423293254$
10.0.41472000000000.1	x^10 - 4x^9 + 3x^8 - 8x^7 + 38x^6 - 52x^5 + 90x^4 - 100x^3 + 175x^2 - 100x + 25	$10$	[0,5]	$-\,2^{18}\cdot 3^{4}\cdot 5^{9}$	$3$	$23.0025242905$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$4$	$4$	$3779.66867664$
10.0.41472000000000.2	x^10 - 2x^9 + 3x^8 + 8x^7 - 22x^6 + 40x^5 + 54x^4 - 116x^3 + 19x^2 + 154x + 61	$10$	[0,5]	$-\,2^{18}\cdot 3^{4}\cdot 5^{9}$	$3$	$23.0025242905$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$4$	$4$	$5015.07769189$
10.0.41943040000000.1	x^10 - 4x^9 + 5x^8 + 6x^6 - 8x^5 - 2x^4 + 10x^2 + 8x + 2	$10$	[0,5]	$-\,2^{29}\cdot 5^{7}$	$2$	$23.0285180325$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$4$	$4$	$2997.36851938$
10.0.41943040000000.2	x^10 - 4x^9 + 5x^8 - 2x^6 + 8x^5 + 6x^4 + 10x^2 + 8x + 2	$10$	[0,5]	$-\,2^{29}\cdot 5^{7}$	$2$	$23.0285180325$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$4$	$4$	$3738.4769374$
10.0.41943040000000.3	x^10 - 4x^9 + 5x^8 + 4x^6 - 16x^5 - 12x^4 + 40x^2 + 32x + 8	$10$	[0,5]	$-\,2^{29}\cdot 5^{7}$	$2$	$23.0285180325$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$4$	$4$	$2926.30902181$
10.0.41943040000000.4	x^10 - 4x^9 + 5x^8 - 12x^6 + 16x^5 + 4x^4 + 40x^2 + 32x + 8	$10$	[0,5]	$-\,2^{29}\cdot 5^{7}$	$2$	$23.0285180325$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$4$	$4$	$3915.39655163$
10.0.41943040000000.5	x^10 - 2x^9 - 3x^8 + 16x^7 - 4x^6 - 16x^5 + 8x^4 - 8x^3 + 141x^2 + 86x + 13	$10$	[0,5]	$-\,2^{29}\cdot 5^{7}$	$2$	$23.0285180325$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$4$	$4$	$5818.23582375$
10.0.41943040000000.9	x^10 - 4x^9 + 13x^8 - 32x^7 + 80x^6 - 152x^5 + 260x^4 - 320x^3 + 385x^2 - 300x + 185	$10$	[0,5]	$-\,2^{29}\cdot 5^{7}$	$2$	$23.0285180325$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$4$	$4$	$3767.62437539$
10.0.48922361856000.2	x^10 - 4x^9 + 32x^7 - 52x^6 - 24x^5 + 184x^4 - 280x^3 + 225x^2 - 100x + 20	$10$	[0,5]	$-\,2^{29}\cdot 3^{6}\cdot 5^{3}$	$3$	$23.3857197868$			?	$F_5 \wr C_2$ (as 10T33)	trivial	$4$	$4$	$5791.3465542$