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Label Polynomial Discriminant Galois group Class group Regulator
10.0.138240000000000.2 $x^{10} - 10 x^{7} + 40 x^{6} - 102 x^{5} + 175 x^{4} - 210 x^{3} + 245 x^{2} - 150 x + 129$ $-\,2^{19}\cdot 3^{3}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $3140.11614328$
10.4.262440000000000.1 $x^{10} - 10 x^{8} - 10 x^{7} + 25 x^{6} + 52 x^{5} + 25 x^{4} - 10 x^{3} - 10 x^{2} - 2$ $-\,2^{12}\cdot 3^{8}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $7855.57614668$
10.4.311040000000000.2 $x^{10} - 10 x^{8} - 10 x^{7} + 15 x^{6} + 40 x^{5} - 50 x^{3} - 30 x^{2} + 20 x + 22$ $-\,2^{17}\cdot 3^{5}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $10086.7344356$
10.0.983040000000000.4 $x^{10} - 10 x^{8} + 35 x^{6} - 4 x^{5} - 50 x^{4} + 20 x^{3} + 75 x^{2} + 60 x + 36$ $-\,2^{25}\cdot 3\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $11645.6862409$
10.0.983040000000000.5 $x^{10} - 10 x^{8} + 45 x^{6} - 12 x^{5} + 50 x^{4} + 140 x^{3} + 275 x^{2} + 100 x + 68$ $-\,2^{25}\cdot 3\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $9413.72108808$
10.2.1474560000000000.8 $x^{10} - 20 x^{7} - 20 x^{6} - 12 x^{5} - 200 x^{4} - 260 x^{3} - 105 x^{2} - 60 x + 28$ $2^{24}\cdot 3^{2}\cdot 5^{10}$ $A_5^2 : C_4$ (as 10T42) trivial $39293.0255917$
10.2.3317760000000000.11 $x^{10} - 20 x^{7} + 72 x^{5} + 50 x^{4} - 240 x^{2} + 144$ $2^{22}\cdot 3^{4}\cdot 5^{10}$ $A_5^2 : C_4$ (as 10T42) trivial $29426.6325508$
10.4.4199040000000000.6 $x^{10} - 10 x^{8} - 20 x^{7} + 25 x^{6} + 92 x^{5} + 100 x^{4} + 40 x^{3} + 80 x^{2} - 32$ $-\,2^{16}\cdot 3^{8}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $56679.6458644$
10.0.4976640000000000.4 $x^{10} + 10 x^{8} + 25 x^{6} - 4 x^{5} - 20 x^{3} + 36$ $-\,2^{21}\cdot 3^{5}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $56527.7350492$
10.4.7464960000000000.17 $x^{10} - 40 x^{6} - 32 x^{5} + 100 x^{2} + 160 x + 64$ $-\,2^{20}\cdot 3^{6}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $66925.2418894$
10.0.7464960000000000.31 $x^{10} - 30 x^{8} - 40 x^{7} + 325 x^{6} + 1240 x^{5} + 1750 x^{4} + 880 x^{3} - 205 x^{2} + 80 x + 448$ $-\,2^{20}\cdot 3^{6}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $72745.1139123$
10.0.7464960000000000.41 $x^{10} - 10 x^{8} - 10 x^{7} + 25 x^{6} + 34 x^{5} + 225 x^{4} + 80 x^{3} - 720 x^{2} + 864$ $-\,2^{20}\cdot 3^{6}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $30542.2571605$
10.6.7464960000000000.5 $x^{10} + 10 x^{8} - 20 x^{7} - 25 x^{6} + 100 x^{5} - 100 x^{4} - 40 x^{3} + 80 x^{2} - 8$ $2^{20}\cdot 3^{6}\cdot 5^{10}$ $A_5^2 : C_4$ (as 10T42) trivial $90254.350184$
10.0.8847360000000000.11 $x^{10} + 10 x^{8} + 95 x^{6} - 60 x^{5} + 350 x^{4} - 300 x^{3} + 1275 x^{2} - 1980 x + 972$ $-\,2^{25}\cdot 3^{3}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $97969.7833754$
10.4.9447840000000000.20 $x^{10} - 20 x^{7} - 60 x^{6} + 60 x^{5} + 25 x^{4} + 300 x^{3} + 240 x^{2} - 1320 x + 708$ $-\,2^{14}\cdot 3^{10}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $156976.912841$
10.0.11197440000000000.9 $x^{10} - 10 x^{8} - 10 x^{7} + 75 x^{6} - 134 x^{5} + 225 x^{4} - 120 x^{3} + 72$ $-\,2^{19}\cdot 3^{7}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $47430.7701773$
10.0.11197440000000000.28 $x^{10} - 10 x^{7} + 72 x^{5} + 75 x^{4} - 360 x^{2} + 1296$ $-\,2^{19}\cdot 3^{7}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $196004.939648$
10.4.16796160000000000.26 $x^{10} + 10 x^{8} - 40 x^{7} + 10 x^{6} + 80 x^{5} - 50 x^{4} - 160 x^{3} + 145 x^{2} + 120 x - 92$ $-\,2^{18}\cdot 3^{8}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $297527.488449$
10.4.16796160000000000.30 $x^{10} + 10 x^{8} - 20 x^{7} - 20 x^{6} - 128 x^{5} - 200 x^{4} - 260 x^{3} - 170 x^{2} + 120 x + 88$ $-\,2^{18}\cdot 3^{8}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $142530.67744$
10.0.19906560000000000.3 $x^{10} - 20 x^{8} - 40 x^{7} + 80 x^{6} + 408 x^{5} + 800 x^{4} + 720 x^{3} + 140 x^{2} - 80 x + 16$ $-\,2^{23}\cdot 3^{5}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $91736.2883685$
10.6.23592960000000000.2 $x^{10} - 20 x^{8} + 130 x^{6} - 40 x^{5} - 500 x^{4} - 400 x^{3} - 175 x^{2} + 200 x + 200$ $2^{28}\cdot 3^{2}\cdot 5^{10}$ $A_5^2 : C_4$ (as 10T42) trivial $160719.896018$
10.4.25194240000000000.2 $x^{10} - 30 x^{7} - 45 x^{6} + 102 x^{5} + 120 x^{3} + 450 x^{2} - 300 x - 12$ $-\,2^{17}\cdot 3^{9}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $220525.002214$
10.4.25194240000000000.8 $x^{10} - 10 x^{7} - 12 x^{5} - 50 x^{4} + 24$ $-\,2^{17}\cdot 3^{9}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $135651.762067$
10.4.25194240000000000.25 $x^{10} - 10 x^{7} - 45 x^{6} - 120 x^{5} - 200 x^{4} - 390 x^{3} - 90 x^{2} + 360 x + 198$ $-\,2^{17}\cdot 3^{9}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $129119.237869$
10.4.25194240000000000.30 $x^{10} - 30 x^{7} - 450 x^{4} + 1080 x^{2} - 432$ $-\,2^{17}\cdot 3^{9}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $117043.702824$
10.0.29859840000000000.37 $x^{10} - 10 x^{8} + 75 x^{6} - 140 x^{5} - 400 x^{4} + 420 x^{3} + 2760 x^{2} + 2880 x + 2052$ $-\,2^{22}\cdot 3^{6}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $81407.5797872$
10.2.41943040000000000.4 $x^{10} + 10 x^{6} - 8 x^{5} - 25 x^{2} + 40 x - 16$ $2^{32}\cdot 5^{10}$ $A_5^2 : C_4$ (as 10T42) trivial $65742.1939575$
10.0.44789760000000000.5 $x^{10} + 10 x^{8} - 20 x^{7} + 75 x^{6} - 296 x^{5} + 300 x^{4} - 60 x^{3} + 120 x^{2} + 36$ $-\,2^{21}\cdot 3^{7}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $203413.539087$
10.0.44789760000000000.8 $x^{10} + 10 x^{8} + 75 x^{6} + 300 x^{4} - 120 x^{3} + 450 x^{2} - 360 x + 72$ $-\,2^{21}\cdot 3^{7}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $202361.803679$
10.0.47829690000000000.12 $x^{10} + 15 x^{8} + 120 x^{6} - 162 x^{5} + 975 x^{4} - 1620 x^{3} + 2745 x^{2} - 1890 x + 468$ $-\,2^{10}\cdot 3^{14}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $281951.46744$
10.4.56687040000000000.3 $x^{10} + 10 x^{8} - 30 x^{7} + 25 x^{6} - 108 x^{5} + 225 x^{4} + 210 x^{3} - 630 x^{2} + 9$ $-\,2^{15}\cdot 3^{11}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $484182.494561$
10.4.56687040000000000.20 $x^{10} - 30 x^{7} + 108 x^{5} - 75 x^{4} + 180 x^{2} + 216$ $-\,2^{15}\cdot 3^{11}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $552437.894524$
10.0.67184640000000000.51 $x^{10} - 10 x^{7} + 24 x^{5} + 75 x^{4} + 216$ $-\,2^{20}\cdot 3^{8}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $322609.438413$
10.4.67184640000000000.63 $x^{10} - 10 x^{8} - 20 x^{7} - 95 x^{6} - 100 x^{5} + 700 x^{4} + 2200 x^{3} + 2900 x^{2} + 1920 x + 592$ $-\,2^{20}\cdot 3^{8}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $358594.702651$
10.0.671...000.100 $x^{10} - 10 x^{7} + 50 x^{6} - 144 x^{5} + 75 x^{4} - 500 x^{3} + 720 x^{2} + 1734$ $-\,2^{20}\cdot 3^{8}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $363906.805012$
10.0.671...000.105 $x^{10} - 20 x^{8} + 200 x^{6} - 268 x^{5} - 150 x^{4} + 600 x^{3} - 1185 x^{2} + 180 x + 2178$ $-\,2^{20}\cdot 3^{8}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $795335.468336$
10.2.67184640000000000.36 $x^{10} - 60 x^{7} - 150 x^{6} - 192 x^{5} - 350 x^{4} - 1500 x^{3} - 2715 x^{2} - 2160 x - 306$ $2^{20}\cdot 3^{8}\cdot 5^{10}$ $A_5^2 : C_4$ (as 10T42) trivial $180979.486581$
10.2.68122631259765625.3 $x^{10} - 20 x^{8} - 40 x^{7} + 70 x^{6} + 358 x^{5} + 275 x^{4} - 1530 x^{3} - 4120 x^{2} - 3450 x - 647$ $5^{10}\cdot 17^{8}$ $C_5^2 : C_8$ (as 10T18) trivial $24761.7311396$
10.0.75295360000000000.1 $x^{10} - 10 x^{6} - 8 x^{5} + 200 x^{2} + 320 x + 128$ $-\,2^{16}\cdot 5^{10}\cdot 7^{6}$ $S_5^2 \wr C_2$ (as 10T43) trivial $321223.520068$
10.0.79626240000000000.23 $x^{10} - 10 x^{8} - 20 x^{7} + 115 x^{6} - 92 x^{5} + 40 x^{3} - 190 x^{2} - 120 x + 408$ $-\,2^{25}\cdot 3^{5}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $307566.129909$
10.0.79626240000000000.49 $x^{10} - 40 x^{7} - 60 x^{6} - 96 x^{5} + 400 x^{4} + 1200 x^{3} + 2820 x^{2} + 2880 x + 2592$ $-\,2^{25}\cdot 3^{5}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $1129937.66132$
10.4.85030560000000000.13 $x^{10} - 10 x^{8} + 25 x^{6} - 18 x^{5} + 90 x^{3} + 54$ $-\,2^{14}\cdot 3^{12}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $226112.105776$
10.4.85030560000000000.16 $x^{10} - 10 x^{8} - 10 x^{7} + 10 x^{6} - 38 x^{5} + 100 x^{4} + 530 x^{3} + 605 x^{2} - 210 x - 626$ $-\,2^{14}\cdot 3^{12}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $883473.264043$
10.4.85030560000000000.17 $x^{10} - 40 x^{7} + 72 x^{5} + 100 x^{4} - 432$ $-\,2^{14}\cdot 3^{12}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $411685.398464$
10.0.100...000.92 $x^{10} + 50 x^{6} - 24 x^{5} + 240 x^{3} + 432$ $-\,2^{19}\cdot 3^{9}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $419199.388707$
10.0.100...000.122 $x^{10} - 30 x^{7} + 675 x^{4} - 1620 x^{2} + 1458$ $-\,2^{19}\cdot 3^{9}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $450721.0404$
10.0.100...000.128 $x^{10} - 10 x^{8} + 75 x^{6} - 48 x^{5} - 240 x^{3} + 1728$ $-\,2^{19}\cdot 3^{9}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $413704.589768$
10.0.100...000.159 $x^{10} - 10 x^{8} - 10 x^{7} + 75 x^{6} + 10 x^{5} + 225 x^{4} - 480 x^{3} - 1440 x^{2} + 6912$ $-\,2^{19}\cdot 3^{9}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $185764.505063$
10.0.100...000.160 $x^{10} - 20 x^{8} + 150 x^{6} - 120 x^{5} + 800 x^{4} - 960 x^{3} - 280 x^{2} + 6240 x + 7008$ $-\,2^{19}\cdot 3^{9}\cdot 5^{10}$ $S_5^2 \wr C_2$ (as 10T43) trivial $935786.936586$
10.0.120022560000000000.1 $x^{10} + 15 x^{8} + 90 x^{6} - 48 x^{5} + 270 x^{4} + 405 x^{2} - 80 x + 243$ $-\,2^{14}\cdot 3^{7}\cdot 5^{10}\cdot 7^{3}$ $S_{10}$ (as 10T45) trivial $206565.034465$
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