Number field search results

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

Results (1-50 of 3075 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
12.8.16135716339712.1	$x^{12} - 2 x^{11} - 3 x^{10} + 10 x^{9} - 11 x^{8} + 2 x^{7} + 24 x^{6} - 38 x^{5} + 31 x^{4} - 20 x^{3} - 2 x^{2} + 8 x - 1$	$12$	[8,2]	$2^{18}\cdot 367^{2}\cdot 457$	$3$	$12.6080818889$	$1158.3401918262182$			?	$S_4^2:D_4$ (as 12T260)	trivial	$2$	$9$	$119.057952469$
12.8.17497403356237.1	$x^{12} - x^{11} - 9 x^{10} + 9 x^{9} + 30 x^{8} - 29 x^{7} - 46 x^{6} + 39 x^{5} + 33 x^{4} - 19 x^{3} - 10 x^{2} + 2 x + 1$	$12$	[8,2]	$7^{2}\cdot 373\cdot 30941^{2}$	$3$	$12.693492584$	$8988.156151291543$			✓	$C_2^6.S_6$ (as 12T293)	trivial	$2$	$9$	$124.895743469$
12.8.18137291911168.1	$x^{12} - 4 x^{10} - 2 x^{9} + 9 x^{8} + 2 x^{7} - 15 x^{6} + 8 x^{5} + 14 x^{4} - 10 x^{3} - 7 x^{2} + 2 x + 1$	$12$	[8,2]	$2^{12}\cdot 151\cdot 2237\cdot 13109$	$4$	$12.7315428744$	$244082.97569768157$			✓	$S_{12}$ (as 12T301)	trivial	$2$	$9$	$127.640680383$
12.8.18172175140625.1	$x^{12} - x^{11} - 4 x^{10} + 5 x^{9} - 2 x^{8} + 15 x^{6} - 15 x^{5} - 10 x^{4} + 14 x^{3} - x^{2} - 4 x + 1$	$12$	[8,2]	$5^{6}\cdot 11^{2}\cdot 109^{2}\cdot 809$	$4$	$12.7335816128$	$2202.2613378071187$			?	$S_4^2:D_4$ (as 12T260)	trivial	$2$	$9$	$127.537100962$
12.8.18277154559581.1	$x^{12} - 2 x^{11} - 3 x^{10} + 6 x^{9} - 3 x^{7} + 3 x^{6} - x^{5} + 4 x^{4} - 4 x^{3} - 3 x^{2} + 4 x - 1$	$12$	[8,2]	$18277154559581$	$1$	$12.7396955277$	$4275178.892114458$			✓	$S_{12}$ (as 12T301)	trivial	$2$	$9$	$127.989315487$
12.8.18308160781573.1	$x^{12} - x^{11} - 7 x^{10} + 7 x^{9} + 10 x^{8} - 14 x^{7} + 2 x^{6} + 19 x^{5} - 8 x^{4} - 17 x^{3} + x^{2} + 5 x + 1$	$12$	[8,2]	$13^{2}\cdot 397\cdot 16519^{2}$	$3$	$12.7414951469$	$9233.339536700683$			?	$C_2^6.S_6$ (as 12T293)	trivial	$2$	$9$	$128.463455261$
12.8.18319482619417.1	$x^{12} - x^{11} - 8 x^{10} + 6 x^{9} + 26 x^{8} - 15 x^{7} - 39 x^{6} + 19 x^{5} + 20 x^{4} - 6 x^{3} - 3 x + 1$	$12$	[8,2]	$7^{8}\cdot 97\cdot 181^{2}$	$3$	$12.7421515767$	$484.86836299303326$			✓	$D_4\wr C_3$ (as 12T222)	trivial	$2$	$9$	$128.232202134$
12.8.19063047515625.1	$x^{12} - 2 x^{11} - 5 x^{10} + 7 x^{9} + 10 x^{8} + 2 x^{7} - 20 x^{6} - 19 x^{5} + 20 x^{4} + 19 x^{3} - 5 x^{2} - 6 x - 1$	$12$	[8,2]	$3^{4}\cdot 5^{6}\cdot 3881^{2}$	$3$	$12.7844689936$	$241.2778481336403$			?	$S_4\wr C_2$ (as 12T203)	trivial	$2$	$9$	$131.311224905$
12.8.20290998443009.1	$x^{12} - 2 x^{11} - 7 x^{10} + 10 x^{9} + 21 x^{8} - 18 x^{7} - 24 x^{6} + 16 x^{5} + 7 x^{4} - 10 x^{3} + 4 x + 1$	$12$	[8,2]	$7^{8}\cdot 41\cdot 293^{2}$	$3$	$12.8511487783$	$401.0739284602191$			?	$D_4\wr C_3$ (as 12T222)	trivial	$2$	$9$	$136.470116005$
12.8.20802722533376.1	$x^{12} - 2 x^{11} - 6 x^{10} + 14 x^{9} + 10 x^{8} - 46 x^{7} - 18 x^{6} + 58 x^{5} + 22 x^{4} - 28 x^{3} - 9 x^{2} + 4 x + 1$	$12$	[8,2]	$2^{12}\cdot 7^{8}\cdot 881$	$3$	$12.8778495812$	$365.3331991872269$			?	$D_4\wr C_3$ (as 12T222)	trivial	$2$	$9$	$138.21501334$
12.8.21426070716181.1	$x^{12} - 2 x^{11} - 2 x^{10} + 2 x^{9} - x^{8} + 18 x^{7} + 3 x^{6} - 44 x^{5} + x^{4} + 32 x^{3} - 3 x^{2} - 5 x + 1$	$12$	[8,2]	$61\cdot 592661^{2}$	$2$	$12.9095730044$	$6012.680018095092$			✓	$C_2^6.S_6$ (as 12T293)	trivial	$2$	$9$	$140.499080957$
12.8.24302560546048.1	$x^{12} - x^{11} - 4 x^{10} + 10 x^{9} - 5 x^{8} - 26 x^{7} + 29 x^{6} + 10 x^{5} - 23 x^{4} + 12 x^{3} + 2 x^{2} - 5 x + 1$	$12$	[8,2]	$2^{8}\cdot 37^{7}$	$2$	$13.0458086084$	$23.81430748424474$			?	$A_4:C_4$ (as 12T30)	trivial	$2$	$9$	$152.927532449$
12.8.24805630328125.1	$x^{12} - 3 x^{11} + x^{9} + 5 x^{8} + 8 x^{7} - 8 x^{6} - 8 x^{5} - 5 x^{4} - 2 x^{3} + 6 x^{2} + 5 x + 1$	$12$	[8,2]	$5^{6}\cdot 2731\cdot 581311$	$3$	$13.0681022007$	$89094.3415992284$			?	$S_6\wr C_2$ (as 12T299)	trivial	$2$	$9$	$154.471906261$
12.8.24952387024669.1	$x^{12} - 6 x^{11} + 14 x^{10} - 15 x^{9} + 24 x^{7} - 30 x^{6} + 9 x^{5} + 13 x^{4} - 16 x^{3} + 3 x^{2} + 3 x - 1$	$12$	[8,2]	$13^{10}\cdot 181$	$2$	$13.0745276594$	$114.05791132835279$			✓	$C_2\wr C_6$ (as 12T134)	trivial	$2$	$9$	$154.283337179$
12.8.25438761101997.1	$x^{12} - 3 x^{10} - x^{9} - 9 x^{8} + 12 x^{7} + 21 x^{6} - 12 x^{5} - 9 x^{4} + x^{3} - 3 x^{2} + 1$	$12$	[8,2]	$3^{16}\cdot 19^{2}\cdot 1637$	$3$	$13.0955777411$	$763.0672475840189$			?	$D_4\wr C_3$ (as 12T222)	trivial	$2$	$9$	$155.078927319$
12.8.25641035447233.1	$x^{12} - 5 x^{11} + 6 x^{10} + 6 x^{9} - 18 x^{8} + 17 x^{7} - 15 x^{6} + 17 x^{5} - 18 x^{4} + 6 x^{3} + 6 x^{2} - 5 x + 1$	$12$	[8,2]	$73\cdot 592661^{2}$	$2$	$13.1042236499$	$6577.556765243459$			✓	$C_2^6.S_6$ (as 12T293)	trivial	$2$	$9$	$156.046592372$
12.8.25652742953125.1	$x^{12} - 5 x^{11} + 3 x^{10} + 22 x^{9} - 41 x^{8} + 6 x^{7} + 39 x^{6} - 35 x^{5} + 3 x^{4} + 18 x^{3} - 5 x^{2} - 6 x - 1$	$12$	[8,2]	$5^{6}\cdot 109\cdot 3881^{2}$	$3$	$13.1047221532$	$1454.3538083973926$			✓	$S_4^2:D_4$ (as 12T260)	trivial	$2$	$9$	$156.335074574$
12.8.25652742953125.2	$x^{12} - 4 x^{11} + 16 x^{9} - 9 x^{8} - 30 x^{7} + 22 x^{6} + 31 x^{5} - 23 x^{4} - 13 x^{3} + 10 x^{2} + x - 1$	$12$	[8,2]	$5^{6}\cdot 109\cdot 3881^{2}$	$3$	$13.1047221532$	$1454.3538083973926$			✓	$S_4^2:D_4$ (as 12T260)	trivial	$2$	$9$	$156.402949424$
12.8.26641409828125.1	$x^{12} - x^{11} - 2 x^{10} + 6 x^{9} - 4 x^{8} - 2 x^{7} - 4 x^{6} - 10 x^{5} + 20 x^{4} + 7 x^{3} - 11 x^{2} + 1$	$12$	[8,2]	$5^{6}\cdot 1705050229$	$2$	$13.1460849274$	$92332.28657950588$			?	$S_6\wr C_2$ (as 12T299)	trivial	$2$	$9$	$159.465807194$
12.8.28866785588221.1	$x^{12} - 6 x^{10} - 4 x^{9} + 13 x^{8} + 16 x^{7} - 9 x^{6} - 21 x^{5} - 4 x^{4} + 11 x^{3} + 5 x^{2} - 2 x - 1$	$12$	[8,2]	$7^{8}\cdot 5007421$	$2$	$13.2342662878$	$8188.526267478483$			✓	$S_4\wr C_3$ (as 12T292)	trivial	$2$	$9$	$168.173115475$
12.8.30967526064128.1	$x^{12} - 6 x^{10} - 2 x^{9} + 9 x^{8} + 8 x^{7} - x^{6} - 14 x^{5} - 6 x^{4} + 10 x^{3} + 5 x^{2} - 2 x - 1$	$12$	[8,2]	$2^{18}\cdot 118131737$	$2$	$13.3119662942$	$30741.728903885676$			✓	$S_6\wr C_2$ (as 12T299)	trivial	$2$	$9$	$175.399901193$
12.8.31436180453125.1	$x^{12} - 2 x^{11} - 2 x^{10} + 2 x^{9} - 7 x^{8} + 6 x^{7} + 23 x^{6} - x^{5} - 24 x^{4} - 9 x^{3} + 9 x^{2} + 4 x - 1$	$12$	[8,2]	$5^{6}\cdot 7^{8}\cdot 349$	$3$	$13.3286392753$	$152.86089885109513$			?	$C_2\wr C_6$ (as 12T134)	trivial	$2$	$9$	$175.632791501$
12.8.34183776846541.1	$x^{12} - 4 x^{11} + 3 x^{10} + 2 x^{9} - 7 x^{8} + 11 x^{7} - 11 x^{6} - x^{5} + 21 x^{4} - 9 x^{3} - 8 x^{2} + 2 x + 1$	$12$	[8,2]	$7^{8}\cdot 181^{3}$	$2$	$13.4220340756$	$180.57500040015438$			?	$C_4\wr C_3$ (as 12T94)	trivial	$2$	$9$	$185.527083784$
12.8.34282488765625.1	$x^{12} - x^{11} - 5 x^{10} + 7 x^{9} + x^{8} - 11 x^{7} + 19 x^{6} - 14 x^{5} - 5 x^{4} + 30 x^{3} - 27 x^{2} + 5 x + 1$	$12$	[8,2]	$5^{6}\cdot 31^{2}\cdot 1511^{2}$	$3$	$13.4252596905$	$483.9473111817029$			?	$S_4\wr C_2$ (as 12T203)	trivial	$2$	$9$	$185.208174005$
12.8.34801233152049.1	$x^{12} - 3 x^{11} - 4 x^{10} + 16 x^{9} + 4 x^{8} - 24 x^{7} - x^{6} - 4 x^{5} - 10 x^{4} + 26 x^{3} + 31 x^{2} + 10 x + 1$	$12$	[8,2]	$3^{6}\cdot 7^{10}\cdot 13^{2}$	$3$	$13.442072066$	$31.606810323667133$			?	$C_2^2 \times A_4$ (as 12T25)	trivial	$2$	$9$	$185.836401127$
12.8.35258133876736.1	$x^{12} - 3 x^{10} + x^{8} - 6 x^{6} + 11 x^{4} - 6 x^{2} + 1$	$12$	[8,2]	$2^{12}\cdot 92779^{2}$	$2$	$13.4566909027$	$1117.2647207234238$			✓	$C_2^5:S_6$ (as 12T285)	trivial	$2$	$9$	$188.34728076$
12.8.36472323149824.1	$x^{12} - 6 x^{10} + 13 x^{8} - 15 x^{6} + 14 x^{4} - 9 x^{2} + 1$	$12$	[8,2]	$2^{12}\cdot 197^{2}\cdot 479^{2}$	$3$	$13.4947119538$	$1126.761791560834$			✓	$C_2^5:S_6$ (as 12T285)	trivial	$2$	$9$	$192.752697995$
12.8.36767438995456.1	$x^{12} - 4 x^{11} - 2 x^{10} + 20 x^{9} + x^{8} - 46 x^{7} - 2 x^{6} + 58 x^{5} + 3 x^{4} - 34 x^{3} + x^{2} + 6 x - 1$	$12$	[8,2]	$2^{18}\cdot 13^{2}\cdot 911^{2}$	$3$	$13.5037777544$	$307.80513316057613$			?	$S_4^2:C_2^2$ (as 12T236)	trivial	$2$	$9$	$196.084738415$
12.8.37921581578125.1	$x^{12} - x^{11} - 5 x^{10} + 9 x^{9} + 9 x^{8} - 20 x^{7} - 11 x^{6} + 9 x^{5} + 9 x^{4} + 7 x^{3} - x^{2} - 4 x - 1$	$12$	[8,2]	$5^{6}\cdot 7^{8}\cdot 421$	$3$	$13.5386035236$	$167.8899668775688$			?	$C_2\wr C_6$ (as 12T134)	trivial	$2$	$9$	$196.536532311$
12.8.38509781640625.1	$x^{12} - x^{11} - 7 x^{10} + 4 x^{9} + 8 x^{8} - 13 x^{7} + 9 x^{6} + 21 x^{5} - 18 x^{4} - 12 x^{3} + 8 x^{2} + 2 x - 1$	$12$	[8,2]	$5^{8}\cdot 9929^{2}$	$2$	$13.5559800598$	$333.1810239839254$			?	$S_4\wr C_2$ (as 12T203)	trivial	$2$	$9$	$198.646945236$
12.8.39358370640625.1	$x^{12} - 2 x^{11} - 8 x^{10} + 20 x^{9} + 8 x^{8} - 38 x^{7} + 2 x^{6} + 20 x^{5} + 3 x^{4} + x^{3} - 6 x^{2} - x + 1$	$12$	[8,2]	$5^{6}\cdot 31^{2}\cdot 1619^{2}$	$3$	$13.5806250626$	$500.9441086588403$			?	$S_4\wr C_2$ (as 12T203)	trivial	$2$	$9$	$202.073516984$
12.8.40147924665121.1	$x^{12} - 5 x^{11} + 6 x^{10} + 9 x^{9} - 33 x^{8} + 36 x^{7} + 6 x^{6} - 51 x^{5} + 22 x^{4} + 19 x^{3} - 2 x^{2} - 8 x + 1$	$12$	[8,2]	$7^{10}\cdot 13^{2}\cdot 29^{2}$	$3$	$13.6031219578$	$98.26956684930803$			?	$C_2^2\wr C_3$ (as 12T90)	trivial	$2$	$9$	$209.650751578$
12.8.40419192196881.1	$x^{12} - 6 x^{11} + 12 x^{10} - 45 x^{8} + 81 x^{7} - 25 x^{6} - 69 x^{5} + 48 x^{4} + 21 x^{3} - 18 x^{2} + 1$	$12$	[8,2]	$3^{18}\cdot 17^{2}\cdot 19^{2}$	$3$	$13.6107576926$	$93.38629449764028$			?	$C_2^2\wr C_3$ (as 12T90)	trivial	$2$	$9$	$210.44327278$
12.8.41524582203125.1	$x^{12} - 3 x^{11} - 5 x^{10} + 20 x^{9} + 3 x^{8} - 40 x^{7} + 11 x^{6} + 15 x^{5} + 3 x^{4} + 13 x^{3} - 26 x^{2} + 10 x - 1$	$12$	[8,2]	$5^{6}\cdot 7^{8}\cdot 461$	$3$	$13.6413946261$	$175.6847877137702$			?	$C_2\wr C_6$ (as 12T134)	trivial	$2$	$9$	$208.277047451$
12.8.42597674078125.1	$x^{12} - x^{11} - 5 x^{10} + 5 x^{9} + 3 x^{8} + x^{7} + 6 x^{6} - 17 x^{5} - 8 x^{4} + 15 x^{3} + 5 x^{2} - 3 x - 1$	$12$	[8,2]	$5^{6}\cdot 181\cdot 3881^{2}$	$3$	$13.6704294268$	$1874.114457550552$			?	$S_4^2:D_4$ (as 12T260)	trivial	$2$	$9$	$211.394191552$
12.8.44804009850925.1	$x^{12} - 4 x^{11} + 3 x^{10} + x^{9} - 4 x^{8} + 3 x^{7} + x^{6} + 9 x^{5} + 3 x^{4} - 12 x^{3} - 4 x^{2} + 3 x + 1$	$12$	[8,2]	$5^{2}\cdot 13^{11}$	$2$	$13.7280780714$	$23.474683296117743$			?	$C_4\times A_4$ (as 12T29)	trivial	$2$	$9$	$219.591054766$
12.8.44962053890625.1	$x^{12} - 5 x^{11} + 4 x^{10} + 14 x^{9} - 22 x^{8} - 7 x^{7} + 29 x^{6} - 7 x^{5} - 22 x^{4} + 14 x^{3} + 4 x^{2} - 5 x + 1$	$12$	[8,2]	$3^{2}\cdot 5^{6}\cdot 17881^{2}$	$3$	$13.7321069909$	$517.8947769576364$			?	$S_4^2:C_2^2$ (as 12T236)	trivial	$2$	$9$	$225.044091621$
12.8.45358541265625.1	$x^{12} - 5 x^{11} + 3 x^{10} + 14 x^{9} - 11 x^{8} - 19 x^{7} + 3 x^{6} + 26 x^{5} + 9 x^{4} - 21 x^{3} - 7 x^{2} + 5 x + 1$	$12$	[8,2]	$5^{6}\cdot 7^{2}\cdot 43^{2}\cdot 179^{2}$	$4$	$13.7421575489$	$519.0327542650849$			?	$S_6\times C_2$ (as 12T219)	trivial	$2$	$9$	$216.664760258$
12.8.47211387828125.1	$x^{12} - 6 x^{10} - 3 x^{9} + 11 x^{8} + 16 x^{7} - 6 x^{6} - 24 x^{5} - 4 x^{4} + 11 x^{3} + 5 x^{2} - x - 1$	$12$	[8,2]	$5^{6}\cdot 29^{3}\cdot 229\cdot 541$	$4$	$13.7880832604$	$4238.384715902982$			?	$S_3\wr D_4$ (as 12T274)	trivial	$2$	$9$	$225.817592693$
12.8.47466656328125.1	$x^{12} - x^{11} - 7 x^{10} + 8 x^{9} + 17 x^{8} - 15 x^{7} - 32 x^{6} - 4 x^{5} + 49 x^{4} + 26 x^{3} - 30 x^{2} - 12 x - 1$	$12$	[8,2]	$5^{7}\cdot 157^{4}$	$2$	$13.7942805134$	$41.89646002154997$			?	$C_4\times S_4$ (as 12T53)	trivial	$2$	$9$	$249.254034357$
12.8.51942673828125.1	$x^{12} - 2 x^{11} - 6 x^{10} + 11 x^{9} + 15 x^{8} - 17 x^{7} - 27 x^{6} + 4 x^{5} + 29 x^{4} + 4 x^{3} - 12 x^{2} + 1$	$12$	[8,2]	$3^{6}\cdot 5^{9}\cdot 191^{2}$	$3$	$13.8982576497$	$80.03958242980093$			?	$S_3^2:C_4$ (as 12T79)	trivial	$2$	$9$	$245.622566038$
12.8.52649684000000.1	$x^{12} - 8 x^{10} - 3 x^{9} + 21 x^{8} + 14 x^{7} - 21 x^{6} - 18 x^{5} + 5 x^{4} + 3 x^{3} + x^{2} + 3 x + 1$	$12$	[8,2]	$2^{8}\cdot 5^{6}\cdot 19^{4}\cdot 101$	$4$	$13.9139246589$	$254.00060640965427$			?	$A_4^2:D_4$ (as 12T208)	trivial	$2$	$9$	$238.420109994$
12.8.53626953329261.1	$x^{12} - x^{11} - 2 x^{10} + 8 x^{9} - 10 x^{8} - 19 x^{7} + 26 x^{6} + 23 x^{5} - 22 x^{4} - 12 x^{3} + 8 x^{2} + 2 x - 1$	$12$	[8,2]	$13^{10}\cdot 389$	$2$	$13.9352659137$	$167.20949205345389$			?	$C_2\wr C_6$ (as 12T134)	trivial	$2$	$9$	$240.048042471$
12.8.53894294828125.1	$x^{12} - 5 x^{11} + 5 x^{10} + 9 x^{9} - 17 x^{8} + x^{7} + 12 x^{6} - 4 x^{5} - 2 x^{4} - 5 x^{3} + x^{2} + 4 x + 1$	$12$	[8,2]	$5^{6}\cdot 229\cdot 3881^{2}$	$3$	$13.9410419109$	$2108.0192124361674$			?	$S_4^2:D_4$ (as 12T260)	trivial	$2$	$9$	$238.451434556$
12.8.54738442953125.1	$x^{12} - 6 x^{11} + 12 x^{10} - 5 x^{9} - 21 x^{8} + 48 x^{7} - 48 x^{6} + 21 x^{5} + 10 x^{4} - 22 x^{3} + 6 x^{2} + 4 x - 1$	$12$	[8,2]	$5^{6}\cdot 29^{3}\cdot 379^{2}$	$3$	$13.9591091556$	$234.42482803662244$			?	$D_6\wr C_2$ (as 12T125)	trivial	$2$	$9$	$244.611008736$
12.8.55336169149373.1	$x^{12} - 3 x^{11} + 4 x^{9} + 2 x^{7} - 10 x^{6} + 3 x^{5} + 21 x^{4} - 4 x^{3} - 14 x^{2} - 2 x + 1$	$12$	[8,2]	$7^{8}\cdot 181^{2}\cdot 293$	$3$	$13.9717484372$	$842.6976657804249$			?	$D_4\wr C_3$ (as 12T222)	trivial	$2$	$9$	$242.797003084$
12.8.56034909078125.1	$x^{12} - x^{11} - 2 x^{10} - 2 x^{9} + 6 x^{8} + 5 x^{7} - 16 x^{6} + 8 x^{5} + 17 x^{4} - 14 x^{3} - 8 x^{2} + 4 x + 1$	$12$	[8,2]	$5^{6}\cdot 9649\cdot 371669$	$3$	$13.9863660154$	$133907.3220738881$			?	$S_6\wr C_2$ (as 12T299)	trivial	$2$	$9$	$246.984429478$
12.8.56819956000000.1	$x^{12} - x^{11} - 5 x^{10} + x^{9} + 9 x^{8} + 12 x^{7} - 5 x^{6} - 32 x^{5} - 3 x^{4} + 27 x^{3} + 2 x^{2} - 6 x + 1$	$12$	[8,2]	$2^{8}\cdot 5^{6}\cdot 19^{4}\cdot 109$	$4$	$14.0025911294$	$263.86835860861856$			✓	$A_4^2:D_4$ (as 12T208)	trivial	$2$	$9$	$248.524487865$
12.8.58003456000000.1	$x^{12} - 4 x^{11} + 2 x^{10} + 4 x^{9} + 12 x^{8} - 26 x^{7} - 22 x^{6} + 72 x^{5} - 32 x^{4} - 32 x^{3} + 27 x^{2} - 2 x - 1$	$12$	[8,2]	$2^{18}\cdot 5^{6}\cdot 7^{2}\cdot 17^{2}$	$4$	$14.0266670802$	$68.99275324264136$			?	$S_3^2:C_2^2$ (as 12T77)	trivial	$2$	$9$	$251.0296206$
12.8.58599345953125.1	$x^{12} - x^{11} - 7 x^{10} + 8 x^{9} + 12 x^{8} - 13 x^{7} - 14 x^{5} + 34 x^{3} - 13 x^{2} - 9 x + 1$	$12$	[8,2]	$5^{6}\cdot 61\cdot 7841^{2}$	$3$	$14.038619313531752$	$1546.4491585564654$			?	$S_4^2:D_4$ (as 12T260)	trivial	$2$	$9$	$265.6642429284124$