Number field search results

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

Results (1-50 of 105747 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
12.0.7086244000000.1	$x^{12} - x^{11} + 5 x^{10} - 10 x^{9} + 9 x^{8} - 9 x^{7} + 14 x^{6} + 9 x^{5} + 9 x^{4} + 10 x^{3} + 5 x^{2} + x + 1$	$12$	[0,6]	$2^{8}\cdot 5^{6}\cdot 11^{6}$	$3$	$11.77248128$	$11.772481280020624$		✓		$D_6$ (as 12T3)	$[2]$	$2$	$5$	$18.6432813936$
12.0.8067775586689.1	$x^{12} - 5 x^{11} + 18 x^{10} - 48 x^{9} + 100 x^{8} - 178 x^{7} + 267 x^{6} - 336 x^{5} + 364 x^{4} - 329 x^{3} + 245 x^{2} - 147 x + 49$	$12$	[0,6]	$7^{10}\cdot 13^{4}$	$2$	$11.9004344759$	$18.248200448594663$				$A_4 \times C_2$ (as 12T7)	$[2]$	$14$	$5$	$118.411290819$
12.0.8916100448256.2	$x^{12} - 4 x^{11} + 4 x^{10} + 12 x^{9} - 37 x^{8} + 32 x^{7} + 22 x^{6} - 80 x^{5} + 88 x^{4} - 48 x^{3} + 10 x^{2} + 1$	$12$	[0,6]	$2^{24}\cdot 3^{12}$	$2$	$12.0$	$20.784609690826528$			?	$C_6\times S_3$ (as 12T18)	$[2]$	$2$	$5$	$20.761295793$
12.0.11709207984384.1	$x^{12} - 6 x^{11} + 15 x^{10} - 20 x^{9} + 22 x^{8} - 34 x^{7} + 47 x^{6} - 40 x^{5} + 38 x^{4} - 42 x^{3} + 27 x^{2} - 8 x + 1$	$12$	[0,6]	$2^{8}\cdot 3^{6}\cdot 89^{4}$	$3$	$12.2756348091$	$28.44982682753188$				$S_5$ (as 12T74)	$[2]$	$6$	$5$	$73.1160095474$
12.0.12745792515625.1	$x^{12} - 5 x^{11} + 12 x^{10} - 24 x^{9} + 48 x^{8} - 66 x^{7} + 53 x^{6} - 36 x^{5} + 42 x^{4} - 41 x^{3} + 23 x^{2} - 7 x + 1$	$12$	[0,6]	$5^{6}\cdot 13^{8}$	$2$	$12.3627163157$	$12.362716315674692$		✓		$A_4$ (as 12T4)	$[2]$	$2$	$5$	$21.2498556899$
12.0.12993941393521.1	$x^{12} - 2 x^{11} + 4 x^{10} + 3 x^{9} + 7 x^{8} + 11 x^{7} + 22 x^{6} + 3 x^{5} + 22 x^{4} - 14 x^{3} + 11 x^{2} - 5 x + 1$	$12$	[0,6]	$11^{4}\cdot 31^{6}$	$2$	$12.3825970919$	$18.466185312619388$				$S_4$ (as 12T9)	$[2]$	$2$	$5$	$19.9903874862$
12.0.13867245015625.1	$x^{12} - 3 x^{11} + 12 x^{10} - 15 x^{9} + 17 x^{8} - 12 x^{7} + 21 x^{6} + 12 x^{5} + 17 x^{4} + 15 x^{3} + 12 x^{2} + 3 x + 1$	$12$	[0,6]	$5^{6}\cdot 31^{6}$	$2$	$12.449899598$	$12.449899597988733$		✓		$D_6$ (as 12T3)	$[2]$	$2$	$5$	$19.9824474015$
12.0.14412774445056.1	$x^{12} - x^{11} - x^{10} - 4 x^{9} + 7 x^{8} - 3 x^{7} + 2 x^{6} + 3 x^{5} + 7 x^{4} + 4 x^{3} - x^{2} + x + 1$	$12$	[0,6]	$2^{12}\cdot 3^{6}\cdot 13^{6}$	$3$	$12.4899959968$	$17.663521732655695$				$S_3 \times C_2^2$ (as 12T10)	$[2]$	$6$	$5$	$102.897388412$
12.0.14512627712000.1	$x^{12} - 4 x^{11} + 7 x^{10} - 2 x^{9} - 16 x^{8} + 20 x^{7} + x^{6} - 40 x^{5} + 18 x^{4} + 74 x^{3} + 49 x^{2} + 12 x + 1$	$12$	[0,6]	$2^{16}\cdot 5^{3}\cdot 11^{6}$	$3$	$12.497184204$	$18.687649168180677$			?	$(C_6\times C_2):C_2$ (as 12T15)	$[2]$	$2$	$5$	$23.2188740371$
12.0.19292185090369.1	$x^{12} - 2 x^{11} + 9 x^{10} - 18 x^{9} + 47 x^{8} - 50 x^{7} + 119 x^{6} - 82 x^{5} + 145 x^{4} - 70 x^{3} + 61 x^{2} + 12 x + 1$	$12$	[0,6]	$19^{4}\cdot 23^{6}$	$2$	$12.7972047438$	$20.904544960366874$				$S_4$ (as 12T9)	$[2]$	$2$	$5$	$23.1491000918$
12.0.23086477815921.1	$x^{12} - 3 x^{11} - x^{9} + 33 x^{8} - 66 x^{7} + 81 x^{6} - 66 x^{5} + 33 x^{4} - x^{3} - 3 x + 1$	$12$	[0,6]	$3^{14}\cdot 13^{6}$	$2$	$12.9901193115$	$12.99011931146003$		✓	?	$D_6$ (as 12T3)	$[2]$	$6$	$5$	$125.397415321$
12.0.27825593350009.1	$x^{12} - 3 x^{11} + 5 x^{10} - 13 x^{9} + 36 x^{8} - 72 x^{7} + 115 x^{6} - 150 x^{5} + 144 x^{4} - 92 x^{3} + 38 x^{2} - 9 x + 1$	$12$	[0,6]	$7^{8}\cdot 13^{6}$	$2$	$13.1938143701$	$13.193814370085985$		✓		$A_4$ (as 12T4)	$[2]$	$2$	$5$	$39.6447347937$
12.0.29365647704064.1	$x^{12} - 2 x^{10} + x^{8} + 2 x^{6} + 22 x^{4} + 1$	$12$	[0,6]	$2^{24}\cdot 3^{6}\cdot 7^{4}$	$3$	$13.253175999778417$	$25.352413640746768$				$C_6\times S_3$ (as 12T18)	$[2]$	$4$	$5$	$107.78321771793813$
12.0.29365647704064.2	$x^{12} - 4 x^{11} + 10 x^{10} - 16 x^{9} + 20 x^{8} - 20 x^{7} + 18 x^{6} - 20 x^{5} + 7 x^{4} + 4 x^{3} + 4 x^{2} - 4 x + 1$	$12$	[0,6]	$2^{24}\cdot 3^{6}\cdot 7^{4}$	$3$	$13.253175999778417$	$25.352413640746768$			?	$C_6\times S_3$ (as 12T18)	$[2]$	$2$	$5$	$29.848139323999433$
12.0.29721861554176.5	$x^{12} - 4 x^{11} + 12 x^{10} - 32 x^{9} + 49 x^{8} - 52 x^{7} + 38 x^{6} + 8 x^{5} + 15 x^{4} + 12 x^{3} + 26 x^{2} + 8 x + 1$	$12$	[0,6]	$2^{24}\cdot 11^{6}$	$2$	$13.2664991614$	$16.714741551887755$			?	$C_2 \times S_4$ (as 12T24)	$[2]$	$4$	$5$	$94.0085507311$
12.0.29721861554176.8	$x^{12} - 4 x^{11} + 6 x^{10} - 4 x^{9} + 6 x^{8} - 12 x^{7} + 30 x^{6} - 88 x^{5} + 184 x^{4} - 236 x^{3} + 180 x^{2} - 76 x + 14$	$12$	[0,6]	$2^{24}\cdot 11^{6}$	$2$	$13.2664991614$	$16.714741551887755$			?	$C_2 \times S_4$ (as 12T24)	$[2]$	$2$	$5$	$56.5731936552$
12.0.30576476160000.1	$x^{12} - 4 x^{9} + 11 x^{8} - 8 x^{7} + 8 x^{6} - 16 x^{5} + 23 x^{4} - 16 x^{3} + 8 x^{2} - 4 x + 1$	$12$	[0,6]	$2^{26}\cdot 3^{6}\cdot 5^{4}$	$3$	$13.29787621895837$	$22.739048476302873$			?	$S_3\times D_6$ (as 12T37)	$[2]$	$4$	$5$	$143.03962332369602$
12.0.30667140235264.4	$x^{12} - 9 x^{8} + 23 x^{4} + 1$	$12$	[0,6]	$2^{30}\cdot 13^{4}$	$2$	$13.3011576202$	$24.255161140409015$			?	$C_2^2\times S_4$ (as 12T48)	$[2]$	$4$	$5$	$159.454020061$
12.0.32357746661769.1	$x^{12} - 6 x^{11} + 12 x^{10} - 3 x^{9} - 18 x^{8} - 3 x^{7} + 67 x^{6} - 39 x^{5} - 39 x^{4} - 12 x^{3} + 36 x^{2} + 12 x + 1$	$12$	[0,6]	$3^{18}\cdot 17^{4}$	$2$	$13.3607710668$	$21.42428528562855$			?	$A_4 \times C_2$ (as 12T7)	$[2]$	$18$	$5$	$404.15700628$
12.0.34012224000000.2	$x^{12} - 2 x^{11} + 2 x^{10} + 4 x^{9} - 11 x^{8} + 16 x^{7} - 4 x^{6} - 14 x^{5} + 31 x^{4} - 20 x^{3} + 9 x^{2} - 4 x + 1$	$12$	[0,6]	$2^{12}\cdot 3^{12}\cdot 5^{6}$	$3$	$13.416407864998739$	$23.2379000772445$			?	$C_6\times S_3$ (as 12T18)	$[2]$	$6$	$5$	$158.3481109354468$
12.0.34012224000000.3	$x^{12} - 2 x^{11} + 8 x^{10} - 14 x^{9} + 22 x^{8} - 38 x^{7} + 29 x^{6} - 38 x^{5} + 28 x^{4} + 4 x^{3} + 15 x^{2} + 8 x + 1$	$12$	[0,6]	$2^{12}\cdot 3^{12}\cdot 5^{6}$	$3$	$13.416407864998739$	$23.2379000772445$			?	$C_6\times S_3$ (as 12T18)	$[2]$	$2$	$5$	$38.643470623377944$
12.0.38806720086016.1	$x^{12} - 4 x^{11} + 6 x^{10} + 2 x^{9} + 9 x^{8} - 30 x^{7} - 32 x^{5} + 22 x^{4} + 46 x^{3} + 24 x^{2} + 4 x + 1$	$12$	[0,6]	$2^{18}\cdot 23^{6}$	$2$	$13.5646599663$	$16.131190144457708$			?	$C_2 \times S_4$ (as 12T24)	$[2]$	$2$	$5$	$45.0203706198$
12.0.38806720086016.3	$x^{12} - 2 x^{11} + 2 x^{10} + 9 x^{8} - 24 x^{7} + 30 x^{6} - 4 x^{5} + 6 x^{4} - 46 x^{3} + 98 x^{2} - 70 x + 25$	$12$	[0,6]	$2^{18}\cdot 23^{6}$	$2$	$13.5646599663$	$16.131190144457708$			?	$C_2 \times S_4$ (as 12T24)	$[2]$	$4$	$5$	$103.136133603$
12.0.38806720086016.10	$x^{12} + 2 x^{10} + 20 x^{8} + 72 x^{6} + 80 x^{4} + 32 x^{2} + 64$	$12$	[0,6]	$2^{18}\cdot 23^{6}$	$2$	$13.5646599663$	$13.564659966250536$		✓	?	$D_6$ (as 12T3)	$[2]$	$2$	$5$	$30.2165763179$
12.0.39357658203125.1	$x^{12} - 4 x^{11} + 7 x^{10} - 10 x^{9} + 9 x^{8} - 8 x^{7} + 21 x^{6} - 14 x^{5} + 6 x^{4} - 31 x^{3} + 16 x^{2} + 7 x + 1$	$12$	[0,6]	$5^{9}\cdot 67^{4}$	$2$	$13.580604576842257$	$27.369376545007917$			?	$S_3 \times C_4$ (as 12T11)	$[2]$	$10$	$5$	$172.1554240836862$
12.0.40060837890625.1	$x^{12} - 4 x^{11} + 8 x^{10} - 12 x^{9} + 7 x^{8} + x^{7} - x^{6} + 7 x^{5} + 8 x^{4} - x^{3} + 4 x^{2} + x + 1$	$12$	[0,6]	$5^{9}\cdot 29^{5}$	$2$	$13.6006605782$	$55.32131584893095$				$C_6^2:C_4$ (as 12T82)	$[2]$	$2$	$5$	$54.025980927$
12.0.40122452017152.1	$x^{12} - 6 x^{9} + 36 x^{7} - 55 x^{6} - 6 x^{5} + 99 x^{4} - 120 x^{3} + 72 x^{2} - 24 x + 4$	$12$	[0,6]	$2^{23}\cdot 3^{14}$	$2$	$13.6024025177$	$24.23672593327708$			?	$C_4\times S_4$ (as 12T53)	$[2]$	$2$	$5$	$55.0386255568$
12.0.40400838383661.1	$x^{12} - 2 x^{11} + 5 x^{10} - 3 x^{9} + 5 x^{8} + 4 x^{7} + x^{6} + 4 x^{5} + 5 x^{4} - 3 x^{3} + 5 x^{2} - 2 x + 1$	$12$	[0,6]	$3^{3}\cdot 7^{3}\cdot 257^{4}$	$3$	$13.6102425469$	$157.26462102353685$			?	$C_4^3:S_4$ (as 12T221)	$[2]$	$2$	$5$	$57.3231784803$
12.0.41326975008000.1	$x^{12} - 4 x^{11} + 2 x^{10} + 13 x^{9} - 19 x^{8} - 12 x^{7} + 39 x^{6} - 24 x^{5} + 41 x^{4} - 59 x^{3} - 73 x^{2} + 77 x + 121$	$12$	[0,6]	$2^{8}\cdot 3^{6}\cdot 5^{3}\cdot 11^{6}$	$4$	$13.6359730681$	$20.390535708149212$			?	$(C_6\times C_2):C_2$ (as 12T15)	$[2]$	$2$	$5$	$32.841606571$
12.0.42988165993728.1	$x^{12} - 2 x^{11} + 7 x^{10} - 10 x^{9} + 18 x^{8} + 6 x^{7} + 13 x^{6} + 24 x^{5} + 48 x^{4} + 4 x^{3} + 153 x^{2} + 170 x + 52$	$12$	[0,6]	$2^{8}\cdot 3^{6}\cdot 613^{3}$	$3$	$13.680828848387218$	$144.24253855791977$				$S_4^2:C_2^2$ (as 12T235)	$[2]$	$6$	$5$	$137.68594827081117$
12.0.45056958152704.1	$x^{12} + 3 x^{10} + 6 x^{8} + 7 x^{6} - 5 x^{4} + 4$	$12$	[0,6]	$2^{14}\cdot 229^{4}$	$2$	$13.7345200932$	$111.01431377060545$				$C_2\wr S_4$ (as 12T226)	$[2]$	$2$	$5$	$88.7875105726$
12.0.47464824438784.2	$x^{12} - x^{10} + 11 x^{8} - 6 x^{6} + 11 x^{4} - x^{2} + 1$	$12$	[0,6]	$2^{26}\cdot 29^{4}$	$2$	$13.7942361489$	$39.50574321172675$			?	$C_2^2\wr S_3$ (as 12T139)	$[2]$	$2$	$5$	$90.3115436211$
12.0.47464824438784.6	$x^{12} - x^{10} - 2 x^{9} - 4 x^{8} + 8 x^{7} - 10 x^{6} + 4 x^{5} + 38 x^{4} - 64 x^{3} + 50 x^{2} - 20 x + 4$	$12$	[0,6]	$2^{26}\cdot 29^{4}$	$2$	$13.7942361489$	$39.50574321172675$				$C_2^2\wr S_3$ (as 12T139)	$[2]$	$2$	$5$	$172.555606426$
12.0.47464824438784.7	$x^{12} + 9 x^{8} - 28 x^{6} + 52 x^{4} - 24 x^{2} + 4$	$12$	[0,6]	$2^{26}\cdot 29^{4}$	$2$	$13.7942361489$	$25.616305216426433$			?	$C_2^2\times S_4$ (as 12T48)	$[2]$	$2$	$5$	$128.296321684$
12.0.47464824438784.13	$x^{12} + 9 x^{8} + 28 x^{6} + 52 x^{4} + 24 x^{2} + 4$	$12$	[0,6]	$2^{26}\cdot 29^{4}$	$2$	$13.7942361489$	$25.616305216426433$			?	$C_2^2\times S_4$ (as 12T48)	$[2]$	$2$	$5$	$98.5165623303$
12.0.49772243044593.1	$x^{12} - x^{11} - 11 x^{10} + 5 x^{9} + 58 x^{8} - 8 x^{7} - 170 x^{6} + 9 x^{5} + 273 x^{4} - 36 x^{3} - 184 x^{2} + 16 x + 49$	$12$	[0,6]	$3^{6}\cdot 29^{2}\cdot 433^{3}$	$3$	$13.84891026068896$	$194.0901852232616$			?	$S_4^2:C_2^2$ (as 12T235)	$[2]$	$6$	$5$	$113.47188748459872$
12.0.52716660869376.1	$x^{12} - 3 x^{11} + 7 x^{10} - 8 x^{9} + 3 x^{8} + 21 x^{7} - 20 x^{6} + 21 x^{5} + 19 x^{4} - 22 x^{3} + 21 x^{2} - 5 x + 1$	$12$	[0,6]	$2^{8}\cdot 3^{6}\cdot 7^{10}$	$3$	$13.9153988181$	$13.915398818088354$		✓		$D_6$ (as 12T3)	$[3]$	$6$	$5$	$129.556705727$
12.0.54203275126125.1	$x^{12} - x^{11} + x^{10} - 3 x^{9} + 9 x^{8} - x^{7} + 13 x^{6} - x^{5} + 9 x^{4} - 3 x^{3} + x^{2} - x + 1$	$12$	[0,6]	$3^{6}\cdot 5^{3}\cdot 29^{6}$	$3$	$13.947684899$	$20.85665361461421$			?	$S_3\times D_4$ (as 12T28)	$[2]$	$2$	$5$	$49.8680904603$
12.0.56035644604416.1	$x^{12} - 4 x^{11} + 10 x^{10} - 12 x^{9} + 13 x^{8} - 8 x^{7} - 2 x^{6} - 14 x^{5} + x^{4} + 12 x^{3} + 14 x^{2} + 6 x + 1$	$12$	[0,6]	$2^{16}\cdot 3^{8}\cdot 19^{4}$	$3$	$13.986381314361736$	$28.927150259359184$			?	$C_4^2:D_6$ (as 12T95)	$[2]$	$2$	$5$	$61.11632021519273$
12.0.56192894500864.1	$x^{12} - 6 x^{9} - 5 x^{8} - 14 x^{7} + 18 x^{6} + 26 x^{5} + 7 x^{4} + 30 x^{3} + 32 x^{2} - 8 x + 1$	$12$	[0,6]	$2^{18}\cdot 11^{8}$	$2$	$13.9896478859$	$18.09986519556776$			?	$C_2 \times S_4$ (as 12T23)	$[2]$	$4$	$5$	$122.749535419$
12.0.56192894500864.2	$x^{12} - 2 x^{11} + 8 x^{10} - 4 x^{9} + 5 x^{8} + 10 x^{7} - 14 x^{6} - 10 x^{5} + 5 x^{4} + 4 x^{3} + 8 x^{2} + 2 x + 1$	$12$	[0,6]	$2^{18}\cdot 11^{8}$	$2$	$13.9896478859$	$18.09986519556776$			?	$C_2 \times S_4$ (as 12T24)	$[2]$	$2$	$5$	$73.6545271447$
12.0.60236288000000.1	$x^{12} - 5 x^{11} + 9 x^{10} - 3 x^{9} - 14 x^{8} + 36 x^{7} - 26 x^{6} - 4 x^{5} + 46 x^{4} - 54 x^{3} + 40 x^{2} - 16 x + 4$	$12$	[0,6]	$2^{15}\cdot 5^{6}\cdot 7^{6}$	$3$	$14.070888342$	$21.082511580717696$				$S_3\times D_4$ (as 12T28)	$[2]$	$2$	$5$	$215.015036463$
12.0.64793042714624.1	$x^{12} - 14 x^{10} + 77 x^{8} - 203 x^{6} + 280 x^{4} - 196 x^{2} + 56$	$12$	[0,6]	$2^{15}\cdot 7^{11}$	$2$	$14.1566566156$	$23.80856360004096$			?	$D_4 \times C_3$ (as 12T14)	$[2]$	$14$	$5$	$285.656284225$
12.0.66461218140625.1	$x^{12} - 3 x^{11} + 7 x^{10} - 5 x^{9} + 2 x^{8} - 2 x^{7} - 4 x^{6} + 2 x^{5} + 2 x^{4} + 5 x^{3} + 7 x^{2} + 3 x + 1$	$12$	[0,6]	$5^{6}\cdot 7^{4}\cdot 11^{6}$	$3$	$14.18667734359471$	$27.138137470492882$				$C_6\times S_3$ (as 12T18)	$[2]$	$2$	$5$	$58.48592416953988$
12.0.67834724548608.1	$x^{12} - 6 x^{11} + 20 x^{10} - 44 x^{9} + 66 x^{8} - 56 x^{7} + 4 x^{6} + 40 x^{5} - 16 x^{4} - 40 x^{3} + 52 x^{2} - 24 x + 4$	$12$	[0,6]	$2^{16}\cdot 3^{6}\cdot 17^{5}$	$3$	$14.2108810899$	$17.995272006877602$			?	$S_3\times D_4$ (as 12T28)	$[2]$	$4$	$5$	$247.52822708$
12.0.70955197267968.1	$x^{12} - 2 x^{10} - 2 x^{9} + 6 x^{8} + 10 x^{7} - 23 x^{6} - 10 x^{5} + 63 x^{4} - 72 x^{3} + 39 x^{2} - 10 x + 1$	$12$	[0,6]	$2^{18}\cdot 3^{6}\cdot 13^{5}$	$3$	$14.2642415423$	$17.663521732655695$			?	$S_3\times D_4$ (as 12T28)	$[2]$	$6$	$5$	$157.300416399$
12.0.72964670628096.1	$x^{12} - x^{11} - x^{10} + 12 x^{9} - 5 x^{8} - 5 x^{7} + 52 x^{6} - 35 x^{5} + 37 x^{4} + 24 x^{3} + 23 x^{2} + 5 x + 1$	$12$	[0,6]	$2^{8}\cdot 3^{10}\cdot 13^{6}$	$3$	$14.297476307$	$20.620529060204074$				$S_3^2$ (as 12T16)	$[2]$	$6$	$5$	$530.218430458$
12.0.74049191673856.2	$x^{12} + 2 x^{10} + 4 x^{8} + 8 x^{6} + 16 x^{4} + 32 x^{2} + 64$	$12$	[0,6]	$2^{18}\cdot 7^{10}$	$2$	$14.3150661808$	$14.315066180821045$	✓	✓	?	$C_6\times C_2$ (as 12T2)	$[2]$	$14$	$5$	$279.150027194$
12.0.74049191673856.3	$x^{12} - 6 x^{11} + 18 x^{10} - 28 x^{9} + 26 x^{8} - 16 x^{7} + 20 x^{6} - 22 x^{5} + 17 x^{4} - 14 x^{3} + 2 x^{2} + 2 x + 1$	$12$	[0,6]	$2^{18}\cdot 7^{10}$	$2$	$14.3150661808$	$17.023578553967216$			?	$C_2^2 \times A_4$ (as 12T25)	$[2]$	$4$	$5$	$100.980899762$
12.0.74049191673856.4	$x^{12} - 4 x^{11} + 6 x^{10} - 12 x^{9} + 30 x^{8} - 56 x^{7} + 120 x^{6} - 224 x^{5} + 284 x^{4} - 240 x^{3} + 136 x^{2} - 48 x + 8$	$12$	[0,6]	$2^{18}\cdot 7^{10}$	$2$	$14.3150661808$	$17.023578553967216$			?	$A_4\times C_2$ (as 12T6)	$[2]$	$2$	$5$	$52.5042907936$