Number field search results

Results (13 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
15.3.132...125.1	x^15 - 14x^10 + 35x^5 + 7	$15$	[3,6]	$5^{9}\cdot 7^{14}$	$2$	$16.1487969276$			?	$F_5\times C_3$ (as 15T8)	trivial	$2$	$8$	$1272.85837366$
15.15.150...125.1	x^15 - 35x^13 + 455x^11 - 70x^10 - 2800x^9 + 1225x^8 + 8575x^7 - 6475x^6 - 11375x^5 + 12250x^4 + 3500x^3 - 6125x^2 + 875	$15$	[15,0]	$3^{6}\cdot 5^{15}\cdot 7^{14}$	$3$	$47.7064034771$			?	$F_5\times C_3$ (as 15T8)	trivial	$2$	$14$	$63554489.595$
15.1.190...375.1	x^15 - 7	$15$	[1,7]	$-\,3^{15}\cdot 5^{9}\cdot 7^{14}$	$3$	$48.4463907827$			?	$F_5 \times S_3$ (as 15T11)	$[3]$	$2$	$7$	$6961795.7233$
15.1.244...287.1	x^15 - 7x - 7	$15$	[1,7]	$-\,7^{14}\cdot 360109842601953263$	$2$	$91.030550716$			✓	$S_{15}$ (as 15T104)	$[3]$	$2$	$7$	$184152421.262$
15.1.349...463.1	x^15 + 7x - 7	$15$	[1,7]	$-\,7^{14}\cdot 227\cdot 431\cdot 911\cdot 5785715141$	$5$	$93.2359515383$			✓	$S_{15}$ (as 15T104)	$[3]$	$2$	$7$	$285284378.359$
15.15.141...704.1	x^15 - 5x^14 - 196x^13 + 1169x^12 + 11263x^11 - 81613x^10 - 202566x^9 + 2212053x^8 - 621438x^7 - 21624778x^6 + 33584838x^5 + 40476996x^4 - 93826187x^3 + 7159929x^2 + 37429270x - 2390177	$15$	[15,0]	$2^{12}\cdot 7^{14}\cdot 139^{2}\cdot 181^{3}\cdot 6679^{2}$	$5$	$189.153645042$			?	$F_5\wr C_3$ (as 15T75)	trivial	$2$	$14$	$2364264785700$
15.15.610...000.1	x^15 - 1386x^13 - 11088x^12 + 599872x^11 + 9930592x^10 - 30585240x^9 - 1986852672x^8 - 21167338976x^7 - 115110115456x^6 - 371202419840x^5 - 748349521920x^4 - 954137766400x^3 - 748821964800x^2 - 330710016000x - 62992384000	$15$	[15,0]	$2^{18}\cdot 5^{6}\cdot 7^{14}\cdot 13^{4}\cdot 113^{2}\cdot 139\cdot 2081603^{2}$	$7$	$967.605275802$				$S_5\wr C_3$ (as 15T101)	trivial	$2$	$14$	$700629720200000000$
15.9.483...000.1	x^15 - 126x^13 - 1008x^12 - 72268x^11 - 1126048x^10 - 2073960x^9 + 91965888x^8 + 1073983904x^7 + 5909943424x^6 + 19089311360x^5 + 38490439680x^4 + 49074905600x^3 + 38514739200x^2 + 17009664000x + 3239936000	$15$	[9,3]	$-\,2^{15}\cdot 5^{6}\cdot 7^{14}\cdot 113^{4}\cdot 292113919^{2}$	$5$	$1110.71862196$				$S_5\wr C_3$ (as 15T101)	trivial	$2$	$11$	$432308459235000000$
15.9.509...000.1	x^15 + 378x^13 - 3024x^12 + 61040x^11 - 598528x^10 + 3949848x^9 - 33288192x^8 + 67412352x^7 + 486419584x^6 - 1876640640x^5 + 409167360x^4 + 4110937600x^3 - 2003456000x^2 - 2157568000x + 1232896000	$15$	[9,3]	$-\,2^{18}\cdot 5^{6}\cdot 7^{14}\cdot 43^{4}\cdot 20509^{2}\cdot 356999^{2}$	$6$	$1515.14880159$				$A_5^3:C_6$ (as 15T95)	trivial	$2$	$11$	$2962071577270000000$
18.0.205...904.1	x^18 - 6x^17 + 25x^16 - 56x^15 + 99x^14 - 84x^13 + 182x^12 - 576x^11 + 1370x^10 - 652x^9 - 1687x^8 - 296x^7 + 4585x^6 + 322x^5 + 1345x^4 + 1968x^3 - 1900x^2 - 140x + 883	$18$	[0,9]	$-\,2^{18}\cdot 7^{16}\cdot 11^{9}$	$3$	$37.4045639315$			?	$C_3\times S_5$ (as 18T144)	$[2]$	$2$	$8$	$2301587.82409$
18.10.294...000.1	x^18 - 8x^17 - 1156x^16 + 14154x^15 + 423940x^14 - 5125470x^13 - 93649612x^12 + 707709382x^11 + 13267262503x^10 - 22767247498x^9 - 956927787788x^8 - 2079511561696x^7 + 26371202953424x^6 + 116524442366080x^5 - 240413334218560x^4 - 2025645894140800x^3 - 904755223448000x^2 + 12306082210800000x + 19770512585440000	$18$	[10,4]	$2^{18}\cdot 5^{4}\cdot 7^{14}\cdot 11^{6}\cdot 12220878786283^{2}$	$5$	$822.069483586$				$C_3^6.(C_2^5.S_6)$ (as 18T959)	$[3]$	$2$	$13$	$275838095689000000000$
18.8.620...000.1	x^18 - 6x^17 - 259x^16 + 1104x^15 + 27702x^14 - 78092x^13 - 1133860x^12 + 749496x^11 - 24909067x^10 + 179283762x^9 + 3952514393x^8 - 7642151520x^7 - 83225330671x^6 + 39650978542x^5 - 2237560061623x^4 + 140148607132x^3 + 61196564097655x^2 - 8286020351802x - 118147417799503	$18$	[8,5]	$-\,2^{33}\cdot 5^{6}\cdot 7^{16}\cdot 113^{4}\cdot 292113919^{2}$	$5$	$856.90594434$			?	$S_5\wr C_3$ (as 18T953)	$[4]$	$2$	$12$	$20490928721400000000$
18.0.102...000.1	x^18 - 2x^17 - 105x^16 + 226x^15 + 11703x^14 + 14378x^13 - 232120x^12 + 1499850x^11 + 5839935x^10 - 56215138x^9 - 148536524x^8 + 476327430x^7 + 1716133097x^6 - 569605554x^5 - 4456285196x^4 + 3043182798x^3 + 18185858208x^2 + 20721671532x + 10691052217	$18$	[0,9]	$-\,2^{30}\cdot 5^{6}\cdot 7^{16}\cdot 43^{4}\cdot 20509^{2}\cdot 356999^{2}$	$6$	$880.979599107$			?	$A_5^3:C_6$ (as 18T933)	$[2, 4]$	$2$	$8$	$2229041780230000000$