Number field search results

Note: Search results may be incomplete. Given $p$-adic completions contain an unramified field and completions are only searched for ramified primes.

Results (1-50 of 128 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
12.0.43712183505898313.1	$x^{12} + x^{10} - 4 x^{9} + x^{8} - 5 x^{7} + 15 x^{6} - 10 x^{5} + 4 x^{4} - 32 x^{3} + 16 x^{2} + 64$	$12$	[0,6]	$7\cdot 71\cdot 9378277^{2}$	$3$	$24.3622208051$	$68271.54362543738$	✓		?	$C_2^6.S_6$ (as 12T293)	$[4]$	$2$	$5$	$1090.39910049$
12.0.55727154111410752.1	$x^{12} - 4 x^{11} + 11 x^{10} - 21 x^{9} + 33 x^{8} - 45 x^{7} + 61 x^{6} - 90 x^{5} + 132 x^{4} - 168 x^{3} + 176 x^{2} - 128 x + 64$	$12$	[0,6]	$2^{6}\cdot 47\cdot 71\cdot 510817^{2}$	$4$	$24.860254602$	$116776.58426242822$	✓		?	$C_2^6.S_6$ (as 12T293)	$[8]$	$2$	$5$	$855.966217482$
12.0.164765793052061537.1	$x^{12} - x^{11} + 4 x^{10} - 2 x^{9} + 9 x^{8} + x^{7} + 13 x^{6} + 2 x^{5} + 36 x^{4} - 16 x^{3} + 64 x^{2} - 32 x + 64$	$12$	[0,6]	$7^{2}\cdot 71\cdot 127\cdot 610667^{2}$	$4$	$27.2106503061$	$196328.0172899426$	✓		?	$C_2^6.S_6$ (as 12T293)	$[8]$	$2$	$5$	$542.4922644$
12.0.330258075592223457.1	$x^{12} - 2 x^{11} + 6 x^{10} - 10 x^{9} + 16 x^{8} - 23 x^{7} + 31 x^{6} - 46 x^{5} + 64 x^{4} - 80 x^{3} + 96 x^{2} - 64 x + 64$	$12$	[0,6]	$3^{2}\cdot 7\cdot 71\cdot 8592653^{2}$	$4$	$28.8339707679$	$113188.54015756189$	✓		?	$C_2^6.S_6$ (as 12T293)	$[2, 2]$	$2$	$5$	$1131.48199948$
12.0.365797447951045273.1	$x^{12} - x^{11} + 2 x^{10} - 6 x^{9} + 6 x^{8} - 8 x^{7} + 23 x^{6} - 16 x^{5} + 24 x^{4} - 48 x^{3} + 32 x^{2} - 32 x + 64$	$12$	[0,6]	$23\cdot 71\cdot 14966741^{2}$	$3$	$29.0806017738$	$156335.17855236548$	✓		?	$C_2^6.S_6$ (as 12T293)	$[2]$	$2$	$5$	$1913.53678891$
12.0.680744762871802313.1	$x^{12} - 2 x^{11} + 6 x^{10} - 10 x^{9} + 23 x^{8} - 31 x^{7} + 53 x^{6} - 62 x^{5} + 92 x^{4} - 80 x^{3} + 96 x^{2} - 64 x + 64$	$12$	[0,6]	$71\cdot 223\cdot 6557081^{2}$	$3$	$30.6254180517$	$322208.4162044809$	✓		?	$C_2^6.S_6$ (as 12T293)	$[20]$	$2$	$5$	$1157.87678886$
12.0.167...336.1	$x^{12} - 2 x^{11} + 6 x^{10} - 12 x^{9} + 23 x^{8} - 36 x^{7} + 58 x^{6} - 72 x^{5} + 92 x^{4} - 96 x^{3} + 96 x^{2} - 64 x + 64$	$12$	[0,6]	$2^{14}\cdot 31\cdot 71\cdot 215273^{2}$	$4$	$33.0053943181$	$92246.6550356444$	✓		?	$C_2^6.S_6$ (as 12T293)	$[2, 4]$	$2$	$5$	$5344.28064338$
12.0.168...617.1	$x^{12} - x^{11} - 4 x^{9} + 7 x^{8} - 5 x^{7} + 9 x^{6} - 10 x^{5} + 28 x^{4} - 32 x^{3} - 32 x + 64$	$12$	[0,6]	$7\cdot 71\cdot 58276469^{2}$	$3$	$33.0327885503$	$170186.38339479454$	✓		?	$C_2^6.S_6$ (as 12T293)	$[2, 2]$	$2$	$5$	$3144.85184365$
12.0.242...328.1	$x^{12} - 2 x^{11} + 6 x^{10} - 7 x^{9} + 15 x^{8} - 14 x^{7} + 30 x^{6} - 28 x^{5} + 60 x^{4} - 56 x^{3} + 96 x^{2} - 64 x + 64$	$12$	[0,6]	$2^{4}\cdot 47\cdot 71\cdot 1861^{2}\cdot 3623^{2}$	$5$	$34.048041344$	$299995.9920465605$	✓		?	$C_2^6.S_6$ (as 12T293)	$[8]$	$2$	$5$	$2458.87018868$
12.0.312...921.1	$x^{12} - 3 x^{11} + 6 x^{10} - 9 x^{9} + 13 x^{8} - 14 x^{7} + 17 x^{6} - 28 x^{5} + 52 x^{4} - 72 x^{3} + 96 x^{2} - 96 x + 64$	$12$	[0,6]	$31\cdot 71\cdot 971^{2}\cdot 38791^{2}$	$4$	$34.770428096$	$287928.8110992021$	✓		?	$C_2^6.S_6$ (as 12T293)	$[2, 6]$	$2$	$5$	$2789.41953296$
12.0.383...008.1	$x^{12} - 3 x^{11} + 6 x^{10} - 12 x^{9} + 24 x^{8} - 38 x^{7} + 54 x^{6} - 76 x^{5} + 96 x^{4} - 96 x^{3} + 96 x^{2} - 96 x + 64$	$12$	[0,6]	$2^{8}\cdot 7\cdot 71\cdot 5490413^{2}$	$4$	$35.3712601042$	$90950.41770897784$	✓			$C_2^6.S_6$ (as 12T293)	$[26]$	$2$	$5$	$10598.9086662$
12.0.423...673.1	$x^{12} - x^{11} + x^{10} - 4 x^{9} + 2 x^{8} - x^{7} + 11 x^{6} - 2 x^{5} + 8 x^{4} - 32 x^{3} + 16 x^{2} - 32 x + 64$	$12$	[0,6]	$7\cdot 71\cdot 92317853^{2}$	$3$	$35.6651439862$	$214200.77717179272$	✓		?	$C_2^6.S_6$ (as 12T293)	$[6]$	$2$	$5$	$3410.8701481$
12.0.520...537.1	$x^{12} - x^{11} + 3 x^{10} - x^{9} + 8 x^{8} - 5 x^{7} + 19 x^{6} - 10 x^{5} + 32 x^{4} - 8 x^{3} + 48 x^{2} - 32 x + 64$	$12$	[0,6]	$67^{2}\cdot 71\cdot 103\cdot 131^{2}\cdot 3041^{2}$	$5$	$36.2856620048$	$441803.39206597314$	✓		?	$C_2^6.S_6$ (as 12T293)	$[16]$	$2$	$5$	$3696.39405435$
12.0.557...912.1	$x^{12} + x^{10} - 2 x^{9} + 5 x^{8} - 4 x^{7} + 6 x^{6} - 8 x^{5} + 20 x^{4} - 16 x^{3} + 16 x^{2} + 64$	$12$	[0,6]	$2^{6}\cdot 7\cdot 71\cdot 13236283^{2}$	$4$	$36.4898746018$	$229406.75929013078$	✓		?	$C_2^6.S_6$ (as 12T293)	$[6]$	$2$	$5$	$6973.66482629$
12.0.559...116.1	$x^{12} - 2 x^{9} - x^{8} - x^{7} + 10 x^{6} - 2 x^{5} - 4 x^{4} - 16 x^{3} + 64$	$12$	[0,6]	$2^{2}\cdot 71\cdot 631^{2}\cdot 222347^{2}$	$4$	$36.4994763607$	$199613.3056386773$	✓			$C_2^6.S_6$ (as 12T293)	$[2, 6]$	$2$	$5$	$8390.56932752$
12.0.571...548.1	$x^{12} - x^{11} + 5 x^{10} - 8 x^{9} + 15 x^{8} - 27 x^{7} + 34 x^{6} - 54 x^{5} + 60 x^{4} - 64 x^{3} + 80 x^{2} - 32 x + 64$	$12$	[0,6]	$2^{2}\cdot 17\cdot 71\cdot 199^{2}\cdot 172871^{2}$	$5$	$36.5659175132$	$407540.93832644593$	✓		?	$C_2^6.S_6$ (as 12T293)	$[2, 6]$	$2$	$5$	$3510.16735607$
12.0.587...273.1	$x^{12} - 2 x^{11} + 2 x^{10} - x^{9} + 2 x^{8} + 6 x^{7} - 15 x^{6} + 12 x^{5} + 8 x^{4} - 8 x^{3} + 32 x^{2} - 64 x + 64$	$12$	[0,6]	$7\cdot 37^{2}\cdot 71\cdot 2937881^{2}$	$4$	$36.6495815012$	$232432.1271016552$	✓		?	$C_2^6.S_6$ (as 12T293)	$[4]$	$2$	$5$	$4444.35525967$
12.0.589...816.1	$x^{12} - 4 x^{11} + 8 x^{10} - 11 x^{9} + 11 x^{8} - 9 x^{7} + 10 x^{6} - 18 x^{5} + 44 x^{4} - 88 x^{3} + 128 x^{2} - 128 x + 64$	$12$	[0,6]	$2^{8}\cdot 19^{2}\cdot 71\cdot 479^{2}\cdot 1979^{2}$	$5$	$36.6618191661$	$143039.70967532057$	✓			$C_2^6.S_6$ (as 12T293)	$[12]$	$2$	$5$	$12634.7869797$
12.0.104...048.1	$x^{12} + x^{10} + 4 x^{8} - 2 x^{7} + 8 x^{6} - 4 x^{5} + 16 x^{4} + 16 x^{2} + 64$	$12$	[0,6]	$2^{11}\cdot 29^{2}\cdot 71\cdot 292879^{2}$	$4$	$38.464792761$	$110256.43527395422$	✓			$C_2^6.S_6$ (as 12T293)	$[38]$	$2$	$5$	$18390.3017949$
12.0.131...336.1	$x^{12} - x^{11} + x^{8} - x^{7} + 2 x^{6} - 2 x^{5} + 4 x^{4} - 32 x + 64$	$12$	[0,6]	$2^{10}\cdot 3^{2}\cdot 71\cdot 4489999^{2}$	$4$	$39.2064730176$	$81612.16854328742$	✓			$C_2^6.S_6$ (as 12T293)	$[20]$	$2$	$5$	$19789.9609333$
12.0.177...369.1	$x^{12} - 2 x^{11} + 3 x^{10} - 5 x^{9} + 10 x^{8} - 16 x^{7} + 27 x^{6} - 32 x^{5} + 40 x^{4} - 40 x^{3} + 48 x^{2} - 64 x + 64$	$12$	[0,6]	$7^{2}\cdot 17^{2}\cdot 23^{2}\cdot 31\cdot 71\cdot 32801^{2}$	$6$	$40.1863581522$	$444519.6483137725$	✓		?	$C_2^6.S_6$ (as 12T293)	$[2, 14]$	$2$	$5$	$6024.70639934$
12.0.180...288.1	$x^{12} + 3 x^{10} - 3 x^{9} + 8 x^{8} - 8 x^{7} + 18 x^{6} - 16 x^{5} + 32 x^{4} - 24 x^{3} + 48 x^{2} + 64$	$12$	[0,6]	$2^{4}\cdot 23\cdot 71\cdot 26284189^{2}$	$4$	$40.2446304855$	$328872.11161739286$	✓		?	$C_2^6.S_6$ (as 12T293)	$[2, 20]$	$2$	$5$	$8096.33593456$
12.0.317...297.1	$x^{12} - 2 x^{11} + 2 x^{10} - 5 x^{9} + 9 x^{8} - 11 x^{7} + 17 x^{6} - 22 x^{5} + 36 x^{4} - 40 x^{3} + 32 x^{2} - 64 x + 64$	$12$	[0,6]	$7\cdot 71\cdot 252865201^{2}$	$3$	$42.186925576$	$354505.29600698495$	✓			$C_2^6.S_6$ (as 12T293)	$[20]$	$2$	$5$	$9244.80047583$
12.0.408...368.1	$x^{12} - 4 x^{11} + 9 x^{10} - 16 x^{9} + 25 x^{8} - 34 x^{7} + 45 x^{6} - 68 x^{5} + 100 x^{4} - 128 x^{3} + 144 x^{2} - 128 x + 64$	$12$	[0,6]	$2^{12}\cdot 7\cdot 71\cdot 353^{2}\cdot 12689^{2}$	$5$	$43.0784476761$	$105920.71588348411$	✓		?	$C_2^6.S_6$ (as 12T293)	$[2, 12]$	$2$	$5$	$12454.3420413$
12.0.503...889.1	$x^{12} - x^{11} + 5 x^{10} - 5 x^{9} + 12 x^{8} - 12 x^{7} + 23 x^{6} - 24 x^{5} + 48 x^{4} - 40 x^{3} + 80 x^{2} - 32 x + 64$	$12$	[0,6]	$71\cdot 151\cdot 68559097^{2}$	$3$	$43.8393180179$	$857334.2865749625$	✓			$C_2^6.S_6$ (as 12T293)	$[30]$	$2$	$5$	$4474.31547311$
12.0.605...625.1	$x^{12} - x^{11} + 2 x^{10} - 5 x^{9} + 7 x^{8} - 10 x^{7} + 19 x^{6} - 20 x^{5} + 28 x^{4} - 40 x^{3} + 32 x^{2} - 32 x + 64$	$12$	[0,6]	$3^{8}\cdot 5^{4}\cdot 23\cdot 31^{2}\cdot 71\cdot 3067^{2}$	$6$	$44.5142367855$	$120552.85565639587$	✓		?	$C_2^6.S_6$ (as 12T293)	$[20]$	$2$	$5$	$7457.47174095$
12.0.637...552.1	$x^{12} - x^{10} + 4 x^{8} - 2 x^{7} - x^{6} - 4 x^{5} + 16 x^{4} - 16 x^{2} + 64$	$12$	[0,6]	$2^{12}\cdot 7\cdot 71\cdot 5596639^{2}$	$4$	$44.7075540714$	$177396.20876265827$	✓		?	$C_2^6.S_6$ (as 12T293)	$[2, 6]$	$2$	$5$	$7686.67063026$
12.0.640...297.1	$x^{12} + 4 x^{10} - 3 x^{9} + 9 x^{8} - 13 x^{7} + 17 x^{6} - 26 x^{5} + 36 x^{4} - 24 x^{3} + 64 x^{2} + 64$	$12$	[0,6]	$71\cdot 103\cdot 93558937^{2}$	$3$	$44.7220988891$	$827161.71712731$	✓			$C_2^6.S_6$ (as 12T293)	$[52]$	$2$	$5$	$5049.70714643$
12.0.722...808.1	$x^{12} + 2 x^{10} - x^{9} + 3 x^{8} - 6 x^{7} + 6 x^{6} - 12 x^{5} + 12 x^{4} - 8 x^{3} + 32 x^{2} + 64$	$12$	[0,6]	$2^{4}\cdot 3^{2}\cdot 7\cdot 71\cdot 139^{2}\cdot 228619^{2}$	$6$	$45.1766919755$	$435343.8141561219$	✓		?	$C_2^6.S_6$ (as 12T293)	$[20]$	$2$	$5$	$16970.8785246$
12.0.751...604.1	$x^{12} - x^{11} - x^{10} + x^{9} + 3 x^{8} - 3 x^{7} + 2 x^{6} - 6 x^{5} + 12 x^{4} + 8 x^{3} - 16 x^{2} - 32 x + 64$	$12$	[0,6]	$2^{2}\cdot 71\cdot 5009^{2}\cdot 102701^{2}$	$4$	$45.3242694089$	$382227.5811031956$	✓			$C_2^6.S_6$ (as 12T293)	$[2, 10]$	$2$	$5$	$34746.0777768$
12.0.755...644.1	$x^{12} - x^{11} + 2 x^{10} + 2 x^{9} - 2 x^{8} + 5 x^{7} - 2 x^{6} + 10 x^{5} - 8 x^{4} + 16 x^{3} + 32 x^{2} - 32 x + 64$	$12$	[0,6]	$2^{2}\cdot 3^{6}\cdot 71\cdot 19107623^{2}$	$4$	$45.3459251006$	$167920.39339635507$	✓			$C_2^6.S_6$ (as 12T293)	$[18]$	$2$	$5$	$23448.4150215$
12.0.106...316.1	$x^{12} - 3 x^{11} + 5 x^{10} - 8 x^{9} + 12 x^{8} - 19 x^{7} + 30 x^{6} - 38 x^{5} + 48 x^{4} - 64 x^{3} + 80 x^{2} - 96 x + 64$	$12$	[0,6]	$2^{2}\cdot 7^{2}\cdot 71\cdot 97^{2}\cdot 900283^{2}$	$5$	$46.6463856996$	$416661.7004093369$	✓			$C_2^6.S_6$ (as 12T293)	$[2, 10]$	$2$	$5$	$28477.508179$
12.0.247...833.1	$x^{12} - 3 x^{11} + 7 x^{10} - 13 x^{9} + 20 x^{8} - 28 x^{7} + 39 x^{6} - 56 x^{5} + 80 x^{4} - 104 x^{3} + 112 x^{2} - 96 x + 64$	$12$	[0,6]	$23\cdot 71\cdot 7237^{2}\cdot 53773^{2}$	$4$	$50.0536772104$	$797176.544582817$	✓			$C_2^6.S_6$ (as 12T293)	$[2, 16]$	$2$	$5$	$10397.0185599$
12.0.267...952.1	$x^{12} - 2 x^{11} + 2 x^{10} - 4 x^{9} + 7 x^{8} - 11 x^{7} + 20 x^{6} - 22 x^{5} + 28 x^{4} - 32 x^{3} + 32 x^{2} - 64 x + 64$	$12$	[0,6]	$2^{3}\cdot 71\cdot 686440333^{2}$	$3$	$50.3844080098$	$624418.2165376024$	✓			$C_2^6.S_6$ (as 12T293)	$[2, 10]$	$2$	$5$	$26538.0686047$
12.0.273...017.1	$x^{12} - 2 x^{11} + 2 x^{10} - 4 x^{9} + 8 x^{8} - 13 x^{7} + 21 x^{6} - 26 x^{5} + 32 x^{4} - 32 x^{3} + 32 x^{2} - 64 x + 64$	$12$	[0,6]	$7\cdot 71\cdot 619^{2}\cdot 1197751^{2}$	$4$	$50.4706886953$	$607025.2967488258$	✓		?	$C_2^6.S_6$ (as 12T293)	$[22]$	$2$	$5$	$11271.8097485$
12.0.305...408.1	$x^{12} - x^{11} + x^{10} + x^{9} + 3 x^{8} - 2 x^{7} + 10 x^{6} - 4 x^{5} + 12 x^{4} + 8 x^{3} + 16 x^{2} - 32 x + 64$	$12$	[0,6]	$2^{4}\cdot 7\cdot 71\cdot 195849827^{2}$	$4$	$50.9362415444$	$623978.7304676338$	✓		?	$C_2^6.S_6$ (as 12T293)	$[14]$	$2$	$5$	$19902.7511461$
12.0.316...596.1	$x^{12} - x^{11} + 2 x^{10} - 3 x^{9} - x^{8} + 5 x^{7} - 6 x^{6} + 10 x^{5} - 4 x^{4} - 24 x^{3} + 32 x^{2} - 32 x + 64$	$12$	[0,6]	$2^{2}\cdot 13^{2}\cdot 71\cdot 81183301^{2}$	$4$	$51.0910550855$	$547474.8827955489$	✓		?	$C_2^6.S_6$ (as 12T293)	$[2, 8]$	$2$	$5$	$21037.0098938$
12.0.327...192.1	$x^{12} - 3 x^{11} + 4 x^{10} - 4 x^{9} + 8 x^{8} - 17 x^{7} + 27 x^{6} - 34 x^{5} + 32 x^{4} - 32 x^{3} + 64 x^{2} - 96 x + 64$	$12$	[0,6]	$2^{6}\cdot 7\cdot 71\cdot 101457943^{2}$	$4$	$51.2380239543$	$635135.2465168344$	✓		?	$C_2^6.S_6$ (as 12T293)	$[40]$	$2$	$5$	$18602.3097274$
12.0.366...192.1	$x^{12} + 3 x^{10} - x^{9} + 2 x^{8} - 2 x^{7} - 2 x^{6} - 4 x^{5} + 8 x^{4} - 8 x^{3} + 48 x^{2} + 64$	$12$	[0,6]	$2^{4}\cdot 7\cdot 71\cdot 214682261^{2}$	$4$	$51.7216523763$	$518516.9268933153$	✓		?	$C_2^6.S_6$ (as 12T293)	$[62]$	$2$	$5$	$15907.3392875$
12.0.379...016.1	$x^{12} + 2 x^{10} - x^{9} + 2 x^{8} + 3 x^{7} + 7 x^{6} + 6 x^{5} + 8 x^{4} - 8 x^{3} + 32 x^{2} + 64$	$12$	[0,6]	$2^{4}\cdot 23^{2}\cdot 31\cdot 71\cdot 107^{2}\cdot 42209^{2}$	$6$	$51.8777479641$	$759023.1526371368$	✓		?	$C_2^6.S_6$ (as 12T293)	$[44]$	$2$	$5$	$13598.9641651$
12.0.585...713.1	$x^{12} - 2 x^{11} + 4 x^{10} - 5 x^{9} + 3 x^{8} + x^{7} - 7 x^{6} + 2 x^{5} + 12 x^{4} - 40 x^{3} + 64 x^{2} - 64 x + 64$	$12$	[0,6]	$3^{2}\cdot 7\cdot 17^{2}\cdot 71\cdot 3881^{2}\cdot 5483^{2}$	$6$	$53.7797001549$	$734419.5459551713$	✓			$C_2^6.S_6$ (as 12T293)	$[36]$	$2$	$5$	$20760.2660916$
12.0.619...681.1	$x^{12} - x^{11} + 4 x^{10} - 5 x^{9} + 9 x^{8} - 11 x^{7} + 19 x^{6} - 22 x^{5} + 36 x^{4} - 40 x^{3} + 64 x^{2} - 32 x + 64$	$12$	[0,6]	$13^{2}\cdot 71\cdot 79\cdot 25563581^{2}$	$4$	$54.0341047651$	$1365291.044348054$	✓		?	$C_2^6.S_6$ (as 12T293)	$[84]$	$2$	$5$	$11448.8627536$
12.0.629...400.1	$x^{12} - x^{11} + x^{10} - 2 x^{9} + 4 x^{8} - 2 x^{7} + 4 x^{6} - 4 x^{5} + 16 x^{4} - 16 x^{3} + 16 x^{2} - 32 x + 64$	$12$	[0,6]	$2^{6}\cdot 5^{2}\cdot 71\cdot 74435573^{2}$	$4$	$54.105940459$	$409616.810904239$	✓			$C_2^6.S_6$ (as 12T293)	$[2, 20]$	$2$	$5$	$62317.5212621$
12.0.668...976.1	$x^{12} - x^{11} + 3 x^{10} - 3 x^{9} + 3 x^{8} - 4 x^{7} - 8 x^{5} + 12 x^{4} - 24 x^{3} + 48 x^{2} - 32 x + 64$	$12$	[0,6]	$2^{4}\cdot 7^{2}\cdot 59^{2}\cdot 71\cdot 1857517^{2}$	$5$	$54.3786809837$	$660108.9061117113$	✓		?	$C_2^6.S_6$ (as 12T293)	$[24]$	$2$	$5$	$19091.2369478$
12.0.679...492.1	$x^{12} - 2 x^{11} + 5 x^{10} - 8 x^{9} + 15 x^{8} - 23 x^{7} + 34 x^{6} - 46 x^{5} + 60 x^{4} - 64 x^{3} + 80 x^{2} - 64 x + 64$	$12$	[0,6]	$2^{2}\cdot 17\cdot 71\cdot 375133117^{2}$	$4$	$54.4517078914$	$1345787.0146780284$	✓			$C_2^6.S_6$ (as 12T293)	$[2, 44]$	$2$	$5$	$18837.7363992$
12.0.695...873.1	$x^{12} - 2 x^{11} + 2 x^{10} + x^{8} - 9 x^{7} + 17 x^{6} - 18 x^{5} + 4 x^{4} + 32 x^{2} - 64 x + 64$	$12$	[0,6]	$3^{2}\cdot 7^{3}\cdot 11^{2}\cdot 71\cdot 5119463^{2}$	$5$	$54.5551512051$	$471326.5219683372$	✓		?	$C_2^6.S_6$ (as 12T293)	$[42]$	$2$	$5$	$31643.2467974$
12.0.717...800.1	$x^{12} - 3 x^{11} + 4 x^{10} - 5 x^{9} + 10 x^{8} - 15 x^{7} + 19 x^{6} - 30 x^{5} + 40 x^{4} - 40 x^{3} + 64 x^{2} - 96 x + 64$	$12$	[0,6]	$2^{8}\cdot 5^{2}\cdot 7\cdot 71\cdot 103^{2}\cdot 145823^{2}$	$6$	$54.7001569513$	$306677.19827933505$	✓			$C_2^6.S_6$ (as 12T293)	$[18]$	$2$	$5$	$24417.2090028$
12.0.746...512.1	$x^{12} - 2 x^{11} + 2 x^{10} - 3 x^{9} + 8 x^{8} - 13 x^{7} + 16 x^{6} - 26 x^{5} + 32 x^{4} - 24 x^{3} + 32 x^{2} - 64 x + 64$	$12$	[0,6]	$2^{3}\cdot 71\cdot 3557^{2}\cdot 322229^{2}$	$4$	$54.8786950851$	$806860.4204594498$	✓		?	$C_2^6.S_6$ (as 12T293)	$[36]$	$2$	$5$	$19750.3807326$
12.0.856...600.1	$x^{12} - x^{11} + 2 x^{10} - x^{8} + 9 x^{7} - 6 x^{6} + 18 x^{5} - 4 x^{4} + 32 x^{2} - 32 x + 64$	$12$	[0,6]	$2^{10}\cdot 3^{10}\cdot 5^{2}\cdot 47^{2}\cdot 71\cdot 1901^{2}$	$6$	$55.5144320313$	$111382.88385511184$	✓			$C_2^6.S_6$ (as 12T293)	$[30]$	$2$	$5$	$64636.9600878$
12.0.857...097.1	$x^{12} - x^{11} + 3 x^{10} - 3 x^{9} + 4 x^{8} - 8 x^{7} + 9 x^{6} - 16 x^{5} + 16 x^{4} - 24 x^{3} + 48 x^{2} - 32 x + 64$	$12$	[0,6]	$23\cdot 71\cdot 107^{2}\cdot 6771379^{2}$	$4$	$55.5169585188$	$1087736.1003703978$	✓			$C_2^6.S_6$ (as 12T293)	$[34]$	$2$	$5$	$13102.9109485$