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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
10.0.21144617347.1	$x^{10} - 3 x^{9} + 3 x^{8} - 6 x^{7} + 11 x^{6} - 5 x^{5} + 7 x^{4} - 11 x^{3} + 3 x + 1$	$10$	[0,5]	$-\,7^{2}\cdot 23\cdot 101\cdot 431^{2}$	$4$	$10.7775484285$	$2647.3554729200987$		?	$C_2 \wr S_5$ (as 10T39)	$[2]$	$2$	$4$	$6.29553270718$
10.0.23863536599.2	$x^{10} - x^{9} + 6 x^{8} + 3 x^{7} - x^{6} + 37 x^{5} - 2 x^{4} + 12 x^{3} + 48 x^{2} - 16 x + 32$	$10$	[0,5]	$-\,7^{5}\cdot 17^{5}$	$2$	$10.9087121146$	$10.908712114635714$	✓	?	$D_5$ (as 10T2)	$[2]$	$2$	$4$	$6.25954076332$
10.0.25786890999.1	$x^{10} - 3 x^{9} + x^{8} + 5 x^{7} - 8 x^{6} + 3 x^{5} + 13 x^{4} - 23 x^{3} + 17 x^{2} - 6 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 2251\cdot 47143$	$3$	$10.9935991711$	$17842.55247995645$		?	$S_5^2 \wr C_2$ (as 10T43)	$[2]$	$6$	$4$	$20.6335620213$
10.0.26642567991.1	$x^{10} - x^{8} - 5 x^{7} + 5 x^{6} - 2 x^{5} + 9 x^{4} - 5 x^{3} + 7 x^{2} - x + 1$	$10$	[0,5]	$-\,3\cdot 13\cdot 59^{2}\cdot 443^{2}$	$4$	$11.0295452881$	$1009.6251779744798$		?	$C_2 \wr S_5$ (as 10T39)	$[2]$	$2$	$4$	$8.82283422552$
10.0.27521121875.1	$x^{10} - x^{9} + 4 x^{8} - 3 x^{7} + 10 x^{6} - x^{5} + 20 x^{4} + x^{3} + 21 x^{2} - 4 x + 1$	$10$	[0,5]	$-\,5^{5}\cdot 13^{2}\cdot 31\cdot 41^{2}$	$4$	$11.0653871489$	$287.42825191689144$		?	$C_2 \wr S_5$ (as 10T39)	$[2]$	$2$	$4$	$7.0589268774$
10.0.27996690715.1	$x^{10} - x^{9} + 5 x^{8} - x^{7} + 13 x^{6} + x^{5} + 13 x^{4} - x^{3} + 5 x^{2} - x + 1$	$10$	[0,5]	$-\,5\cdot 7^{3}\cdot 41\cdot 631^{2}$	$4$	$11.0843612128$	$1547.8010614737673$		✓	$C_2 \wr S_5$ (as 10T39)	$[2]$	$2$	$4$	$6.89117563691$
10.0.28023421888.1	$x^{10} - 4 x^{9} + 7 x^{8} - 10 x^{7} + 16 x^{6} - 18 x^{5} + 12 x^{4} - 10 x^{3} + 8 x^{2} - 2 x + 1$	$10$	[0,5]	$-\,2^{6}\cdot 7\cdot 11^{2}\cdot 719^{2}$	$4$	$11.0854190905$	$665.5103304983327$		?	$C_2 \wr S_5$ (as 10T39)	$[2]$	$2$	$4$	$7.13577131236$
10.0.28049553895.1	$x^{10} - 3 x^{9} + 6 x^{8} - 7 x^{7} + 7 x^{6} - 7 x^{5} + 7 x^{4} - 7 x^{3} + 6 x^{2} - 3 x + 1$	$10$	[0,5]	$-\,5\cdot 11^{3}\cdot 2053^{2}$	$3$	$11.0864523789$	$336.0282726200282$		✓	$C_2 \wr S_5$ (as 10T39)	$[2]$	$2$	$4$	$6.72160467904$
10.0.28752750191.1	$x^{10} - 5 x^{9} + 10 x^{8} - 10 x^{7} + 6 x^{6} - 4 x^{5} + 2 x^{4} + x^{3} - 2 x^{2} + x + 1$	$10$	[0,5]	$-\,11\cdot 59^{2}\cdot 83^{2}\cdot 109$	$4$	$11.113937217$	$2423.11844530968$		✓	$C_2 \wr S_5$ (as 10T39)	$[2]$	$2$	$4$	$7.23711181714$
10.0.29730115179.1	$x^{10} - 2 x^{9} + 5 x^{8} - 11 x^{7} + 6 x^{6} + 13 x^{5} - 16 x^{4} + 8 x^{2} - 4 x + 1$	$10$	[0,5]	$-\,3^{8}\cdot 4531339$	$2$	$11.1511500358$	$7906.9339144625865$		?	$S_5^2 \wr C_2$ (as 10T43)	$[2]$	$6$	$4$	$24.9513196667$
10.0.29807896987.1	$x^{10} - 2 x^{9} + 5 x^{6} - 4 x^{5} + 6 x^{4} - 10 x^{3} + 5 x^{2} - x + 1$	$10$	[0,5]	$-\,11\cdot 59^{2}\cdot 83^{2}\cdot 113$	$4$	$11.1540640411$	$2467.1787531510563$		?	$C_2 \wr S_5$ (as 10T39)	$[2]$	$2$	$4$	$7.35204169756$
10.0.30042615123.1	$x^{10} - 2 x^{9} + 3 x^{8} - 4 x^{7} + 6 x^{6} - 10 x^{5} + 6 x^{4} - 5 x^{3} + 8 x^{2} - 3 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 11119^{2}$	$2$	$11.1628161853$	$182.6389881706532$		?	$S_5\times C_2$ (as 10T22)	$[2]$	$6$	$4$	$20.2686416139$
10.0.30401192960.1	$x^{10} - 4 x^{9} + 7 x^{8} - 8 x^{7} + 8 x^{6} - 10 x^{5} + 10 x^{4} - 6 x^{3} + 6 x^{2} - 4 x + 1$	$10$	[0,5]	$-\,2^{10}\cdot 5\cdot 853\cdot 6961$	$4$	$11.1760686959$	$10897.46117221805$		?	$S_5^2 \wr C_2$ (as 10T43)	$[2]$	$4$	$4$	$16.3074615531$
10.0.30569276799.1	$x^{10} - 3 x^{9} + x^{8} + 9 x^{7} - 17 x^{6} + 4 x^{5} + 21 x^{4} - 28 x^{3} + 18 x^{2} - 6 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 349\cdot 360457$	$3$	$11.1822324642$	$19426.746485194068$		?	$S_5^2 \wr C_2$ (as 10T43)	$[2]$	$6$	$4$	$22.0356654809$
10.0.30987265024.2	$x^{10} - 2 x^{8} + 2 x^{4} - x^{2} + 1$	$10$	[0,5]	$-\,2^{10}\cdot 5501^{2}$	$2$	$11.1974291876$	$272.052088551018$		✓	$C_2 \wr S_5$ (as 10T39)	$[2]$	$2$	$4$	$7.56245359551$
10.0.31634094491.1	$x^{10} - 2 x^{9} + 6 x^{8} - 8 x^{7} + 13 x^{6} - 6 x^{5} + 14 x^{4} + 8 x^{3} + 9 x^{2} - x + 1$	$10$	[0,5]	$-\,31\cdot 149\cdot 2617^{2}$	$3$	$11.2205860522$	$3476.769046111634$		?	$C_2 \wr S_5$ (as 10T39)	$[2]$	$2$	$4$	$7.45864702971$
10.0.32356789675.1	$x^{10} - 3 x^{9} + 6 x^{8} - 8 x^{7} + 12 x^{6} - 19 x^{5} + 25 x^{4} - 22 x^{3} + 13 x^{2} - 5 x + 1$	$10$	[0,5]	$-\,5^{2}\cdot 7\cdot 61\cdot 1741^{2}$	$4$	$11.2459602105$	$1927.9613585339307$		✓	$C_2 \wr S_5$ (as 10T39)	$[2]$	$2$	$4$	$7.50430908501$
10.0.32938746880.1	$x^{10} - 2 x^{9} + 3 x^{8} - 10 x^{7} + 15 x^{6} - 14 x^{5} + 19 x^{4} - 14 x^{3} + 4 x^{2} - 2 x + 1$	$10$	[0,5]	$-\,2^{10}\cdot 5\cdot 13\cdot 494873$	$4$	$11.2660249134$	$11343.146829694131$		?	$S_5^2 \wr C_2$ (as 10T43)	$[2]$	$4$	$4$	$14.9534094677$
10.0.33175452528.1	$x^{10} - 4 x^{9} + 4 x^{8} - x^{7} + 9 x^{6} - 25 x^{5} + 29 x^{4} - 17 x^{3} + 8 x^{2} - 4 x + 1$	$10$	[0,5]	$-\,2^{4}\cdot 3^{5}\cdot 31\cdot 275251$	$4$	$11.2740948836$	$8031.4246791125515$		?	$S_5^2 \wr C_2$ (as 10T43)	$[2]$	$6$	$4$	$23.4111032857$
10.0.33191669588.1	$x^{10} + 2 x^{8} + 6 x^{6} - 4 x^{5} + 6 x^{4} + 2 x^{2} + 1$	$10$	[0,5]	$-\,2^{2}\cdot 7^{3}\cdot 11\cdot 1483^{2}$	$4$	$11.2746458707$	$1099.3106712149695$		?	$C_2 \wr S_5$ (as 10T39)	$[2]$	$2$	$4$	$11.4871428263$
10.0.33849995499.1	$x^{10} - x^{9} + 5 x^{8} + 2 x^{7} + 15 x^{6} + 13 x^{5} + 22 x^{4} + 16 x^{3} + 12 x^{2} + 5 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 61\cdot 103\cdot 22171$	$4$	$11.2968109642$	$20442.631410853155$		✓	$S_5^2 \wr C_2$ (as 10T43)	$[2]$	$6$	$4$	$26.5188409529$
10.0.34395934307.1	$x^{10} - 3 x^{9} + 8 x^{8} - 18 x^{7} + 27 x^{6} - 23 x^{5} + 3 x^{4} + 9 x^{3} - x^{2} - 3 x + 1$	$10$	[0,5]	$-\,7^{2}\cdot 41\cdot 43\cdot 631^{2}$	$4$	$11.3148997662$	$2790.550304151495$		?	$C_2 \wr S_5$ (as 10T39)	$[2]$	$2$	$4$	$7.820740513$
10.0.34566529075.1	$x^{10} - 4 x^{9} + 11 x^{8} - 17 x^{7} + 22 x^{6} - 12 x^{5} + 10 x^{4} + 2 x^{3} + 13 x^{2} - 2 x + 1$	$10$	[0,5]	$-\,5^{2}\cdot 13^{2}\cdot 31\cdot 41^{2}\cdot 157$	$5$	$11.3204991724$	$3601.4656738611297$		?	$C_2 \wr S_5$ (as 10T39)	$[2]$	$2$	$4$	$7.79353272783$
10.0.35236014039.1	$x^{10} - 2 x^{9} - x^{7} + 16 x^{6} - 35 x^{5} + 37 x^{4} - 24 x^{3} + 12 x^{2} - 4 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 1951\cdot 74323$	$3$	$11.3422359463$	$20856.953732508493$		?	$S_5^2 \wr C_2$ (as 10T43)	$[2]$	$6$	$4$	$23.8540294082$
10.0.35619686959.1	$x^{10} - 3 x^{9} + 9 x^{8} - 9 x^{7} + 14 x^{6} - x^{5} + 13 x^{4} + 2 x^{3} + 15 x^{2} + 3 x + 1$	$10$	[0,5]	$-\,43\cdot 157\cdot 2297^{2}$	$3$	$11.3545260191$	$3937.89880520056$		?	$C_2 \wr S_5$ (as 10T39)	$[2]$	$2$	$4$	$7.68989820187$
10.0.36483460371.1	$x^{10} - 4 x^{9} + 5 x^{8} + 6 x^{7} - 22 x^{6} + 13 x^{5} + 27 x^{4} - 47 x^{3} + 29 x^{2} - 8 x + 1$	$10$	[0,5]	$-\,3^{6}\cdot 50045899$	$2$	$11.3817646824$	$16125.945533065074$		?	$S_5^2 \wr C_2$ (as 10T43)	$[2]$	$6$	$4$	$34.2453210656$
10.0.36567430479.1	$x^{10} - 4 x^{9} + 7 x^{8} - 2 x^{7} - 13 x^{6} + 17 x^{5} - 4 x^{4} - 7 x^{3} + 9 x^{2} - 4 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 150483253$	$2$	$11.3843815932$	$21247.34710499172$		✓	$S_5^2 \wr C_2$ (as 10T43)	$[2]$	$6$	$4$	$23.7817373022$
10.0.36729519107.1	$x^{10} + 6 x^{8} - x^{7} + 13 x^{6} - 10 x^{5} + 19 x^{4} - 22 x^{3} + 29 x^{2} - 7 x + 25$	$10$	[0,5]	$-\,31\cdot 173\cdot 2617^{2}$	$3$	$11.3894177916$	$3746.3276685308774$		?	$C_2 \wr S_5$ (as 10T39)	$[2]$	$2$	$4$	$8.1121886951$
10.0.36915460911.1	$x^{10} - 2 x^{9} - x^{8} + 9 x^{7} - 15 x^{6} + x^{5} + 23 x^{4} - 26 x^{3} + 16 x^{2} - 6 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 7\cdot 21702211$	$3$	$11.3951705481$	$21348.218450259497$		?	$S_5^2 \wr C_2$ (as 10T43)	$[2]$	$6$	$4$	$23.4163695733$
10.0.36927700335.1	$x^{10} - x^{9} - 2 x^{8} + 3 x^{7} + 5 x^{6} - 11 x^{5} + 5 x^{4} + 3 x^{3} - 2 x^{2} - x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 5\cdot 37^{2}\cdot 149^{2}$	$4$	$11.3955483018$	$287.567383407785$		✓	$C_2 \wr S_5$ (as 10T39)	$[2]$	$2$	$4$	$9.33070264981$
10.0.37148024304.1	$x^{10} - 2 x^{9} - 3 x^{8} + 7 x^{7} + 8 x^{6} - 26 x^{5} + 20 x^{4} - 4 x^{3} - 2 x^{2} + x + 1$	$10$	[0,5]	$-\,2^{4}\cdot 3^{5}\cdot 9554533$	$3$	$11.402329111$	$8498.690692788583$		?	$S_5^2 \wr C_2$ (as 10T43)	$[2]$	$6$	$4$	$24.7788415691$
10.0.37378282599.1	$x^{10} - 2 x^{9} + 3 x^{8} - 2 x^{7} + 7 x^{6} - 7 x^{5} + 7 x^{4} + 2 x^{3} + 3 x^{2} + 3 x + 1$	$10$	[0,5]	$-\,3^{5}\cdot 7\cdot 21974299$	$3$	$11.4093770935$	$21481.626544561284$		?	$S_5^2 \wr C_2$ (as 10T43)	$[2]$	$6$	$4$	$24.5132077358$
10.0.37651630819.1	$x^{10} - 3 x^{9} + 4 x^{8} - 5 x^{7} + 10 x^{6} - 11 x^{5} + 5 x^{4} - 6 x^{3} + 11 x^{2} - 6 x + 1$	$10$	[0,5]	$-\,11\cdot 41\cdot 9137^{2}$	$3$	$11.4176934652$	$2029.972167296882$		?	$C_2 \wr S_5$ (as 10T39)	$[2]$	$2$	$4$	$7.2688497443$
10.0.38249071355.1	$x^{10} - 3 x^{9} + x^{8} + 12 x^{7} - 21 x^{6} + x^{5} + 29 x^{4} - 31 x^{3} + 14 x^{2} - 3 x + 1$	$10$	[0,5]	$-\,5\cdot 11\cdot 29\cdot 59^{2}\cdot 83^{2}$	$5$	$11.4356825113$	$2794.76564312645$		?	$C_2 \wr S_5$ (as 10T39)	$[2]$	$2$	$4$	$8.21638552006$
10.0.38748886528.1	$x^{10} + 3 x^{8} - 2 x^{7} + 13 x^{6} - 16 x^{5} + 24 x^{4} - 18 x^{3} + 12 x^{2} - 4 x + 1$	$10$	[0,5]	$-\,2^{9}\cdot 11\cdot 43^{2}\cdot 61^{2}$	$4$	$11.4505388011$	$1142.6888138442719$		?	$C_2 \wr S_5$ (as 10T39)	$[2]$	$2$	$4$	$12.4492937616$
10.0.39187298043.1	$x^{10} - x^{8} - 2 x^{7} - 2 x^{6} + 2 x^{5} - 2 x^{4} + x^{3} + 8 x^{2} + 3 x + 1$	$10$	[0,5]	$-\,3^{9}\cdot 17^{2}\cdot 83^{2}$	$3$	$11.4634286444$	$135.33339311985708$		?	$S_5\times C_2$ (as 10T22)	$[2]$	$6$	$4$	$28.061841438$
10.0.39304218151.1	$x^{10} - 5 x^{9} + 12 x^{8} - 18 x^{7} + 15 x^{6} - 3 x^{5} - 3 x^{4} - x^{2} + 2 x + 1$	$10$	[0,5]	$-\,11\cdot 59^{2}\cdot 83^{2}\cdot 149$	$4$	$11.4668443154$	$2833.0518879822866$		✓	$C_2 \wr S_5$ (as 10T39)	$[2]$	$2$	$4$	$7.79043343538$
10.0.39529556496.1	$x^{10} - 2 x^{9} - x^{8} + 7 x^{7} - 2 x^{6} - 14 x^{5} + 12 x^{4} + 6 x^{3} - 6 x^{2} - x + 1$	$10$	[0,5]	$-\,2^{4}\cdot 3^{5}\cdot 241\cdot 42187$	$4$	$11.4734015696$	$15620.806893371418$			$S_5^2 \wr C_2$ (as 10T43)	$[2]$	$6$	$4$	$33.8464977748$
10.0.39876183727.1	$x^{10} + 3 x^{8} - 6 x^{7} + 2 x^{6} - 10 x^{5} + 8 x^{4} + 6 x^{2} - 4 x + 1$	$10$	[0,5]	$-\,41\cdot 47\cdot 4549^{2}$	$3$	$11.4834228987$	$2960.7301464334773$			$C_2 \wr S_5$ (as 10T39)	$[2]$	$2$	$4$	$9.34152465944$
10.0.40115792695.1	$x^{10} - 2 x^{9} + 6 x^{8} - 6 x^{7} + 9 x^{6} - 7 x^{5} + 9 x^{4} - 6 x^{3} + 6 x^{2} - 2 x + 1$	$10$	[0,5]	$-\,5\cdot 11\cdot 113^{2}\cdot 239^{2}$	$4$	$11.4903044981$	$1218.7637178715158$		?	$C_2 \wr S_5$ (as 10T39)	$[2]$	$2$	$4$	$11.9889381694$
10.0.40925637499.1	$x^{10} - 2 x^{9} + 3 x^{8} - 2 x^{7} + x^{6} - x^{5} + x^{4} - 2 x^{3} + 3 x^{2} - 2 x + 1$	$10$	[0,5]	$-\,19\cdot 46411^{2}$	$2$	$11.5132926877$	$939.0468571908433$		✓	$C_2 \wr S_5$ (as 10T39)	$[2]$	$2$	$4$	$8.29469915349$
10.0.41432389727.1	$x^{10} - x^{9} + 2 x^{8} - 4 x^{7} + 3 x^{6} - x^{5} + 3 x^{4} - 4 x^{3} + 2 x^{2} - x + 1$	$10$	[0,5]	$-\,23\cdot 42443^{2}$	$2$	$11.527469938$	$988.0227730168976$			$C_2 \wr S_5$ (as 10T39)	$[2]$	$2$	$4$	$11.677349814$
10.0.41485819491.1	$x^{10} + 6 x^{8} - 3 x^{7} + 12 x^{6} - 7 x^{5} + 12 x^{4} - 3 x^{3} + 6 x^{2} + 1$	$10$	[0,5]	$-\,3^{5}\cdot 17\cdot 3169^{2}$	$3$	$11.5289556184$	$402.0186562835113$		?	$C_2 \wr S_5$ (as 10T39)	$[2]$	$2$	$4$	$10.4528168998$
10.0.41554926747.1	$x^{10} - x^{9} + 2 x^{8} - 7 x^{7} + 6 x^{6} - 7 x^{5} + 14 x^{4} - 6 x^{3} + 5 x^{2} + x + 1$	$10$	[0,5]	$-\,3^{9}\cdot 1453^{2}$	$2$	$11.5308746786$	$137.33279881699775$		?	$S_5\times C_2$ (as 10T22)	$[2]$	$6$	$4$	$30.9143518257$
10.0.41824943723.1	$x^{10} - 3 x^{9} + 4 x^{8} + 2 x^{6} - 20 x^{5} + 55 x^{4} - 62 x^{3} + 27 x^{2} - 4 x + 1$	$10$	[0,5]	$-\,31\cdot 197\cdot 2617^{2}$	$3$	$11.5383454297$	$3997.751743167652$		?	$C_2 \wr S_5$ (as 10T39)	$[2]$	$2$	$4$	$8.60885930098$
10.0.41984245539.1	$x^{10} - x^{9} - 4 x^{8} + 9 x^{7} + 3 x^{6} - 12 x^{5} + 18 x^{4} - 8 x^{3} + 2 x^{2} + 1$	$10$	[0,5]	$-\,3^{5}\cdot 137\cdot 1123^{2}$	$3$	$11.5427326122$	$679.3769204204688$		?	$C_2 \wr S_5$ (as 10T39)	$[2]$	$2$	$4$	$11.567127326$
10.0.42555104784.1	$x^{10} - 3 x^{9} + 12 x^{7} - 8 x^{6} - 16 x^{5} + 12 x^{4} + 9 x^{3} - 5 x^{2} - 2 x + 1$	$10$	[0,5]	$-\,2^{4}\cdot 3^{5}\cdot 10945243$	$3$	$11.5583320398$	$16207.585631425798$			$S_5^2 \wr C_2$ (as 10T43)	$[2]$	$6$	$4$	$30.1740112924$
10.0.42573587456.1	$x^{10} - 4 x^{9} + 7 x^{8} - 8 x^{7} + 8 x^{6} - 6 x^{5} + 4 x^{4} - 6 x^{3} + 9 x^{2} - 8 x + 4$	$10$	[0,5]	$-\,2^{10}\cdot 41575769$	$2$	$11.558833947$	$12895.854992981273$		?	$S_5^2 \wr C_2$ (as 10T43)	$[2]$	$4$	$4$	$27.9211161708$
10.0.42917292635.1	$x^{10} - 3 x^{9} + 8 x^{8} - 19 x^{7} + 38 x^{6} - 56 x^{5} + 82 x^{4} - 101 x^{3} + 86 x^{2} - 70 x + 35$	$10$	[0,5]	$-\,5\cdot 7^{2}\cdot 23\cdot 41\cdot 431^{2}$	$5$	$11.5681318982$	$3771.624981357505$		?	$C_2 \wr S_5$ (as 10T39)	$[2]$	$2$	$4$	$8.28396501261$
10.0.43428021875.1	$x^{10} - 2 x^{9} + 2 x^{8} - 5 x^{7} + 6 x^{6} - 3 x^{5} + 6 x^{4} - 5 x^{3} + 2 x^{2} - 2 x + 1$	$10$	[0,5]	$-\,5^{5}\cdot 7\cdot 1409^{2}$	$3$	$11.5818251675$	$222.06980884397592$		✓	$C_2 \wr S_5$ (as 10T39)	$[2]$	$2$	$4$	$9.17348911496$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.