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Label Polynomial Discriminant Galois group Class group Regulator
10.2.2250000000000.1 $x^{10} - 5 x^{8} - 10 x^{7} - 10 x^{6} + 6 x^{5} + 25 x^{4} + 30 x^{3} + 25 x^{2} + 10 x + 4$ $2^{10}\cdot 3^{2}\cdot 5^{12}$ $A_5^2 : C_4$ (as 10T42) trivial $277.393798734$
10.2.16000000000000.1 $x^{10} - 5 x^{9} + 5 x^{8} + 25 x^{6} - 53 x^{5} + 55 x^{4} - 110 x^{3} + 95 x^{2} - 25 x - 19$ $2^{16}\cdot 5^{12}$ $(C_5^2 : C_8):C_2$ (as 10T28) trivial $725.403697336$
10.6.16000000000000.1 $x^{10} - 5 x^{9} + 5 x^{8} + 5 x^{6} - x^{5} + 55 x^{4} - 50 x^{3} + 5 x^{2} + 5 x - 1$ $2^{16}\cdot 5^{12}$ $A_5^2 : C_4$ (as 10T42) trivial $1439.52072902$
10.6.25628906250000.1 $x^{10} - 10 x^{8} - 15 x^{7} - 10 x^{6} - 7 x^{5} - 5 x^{4} + 35 x^{3} - 5 x^{2} - 5 x + 1$ $2^{4}\cdot 3^{8}\cdot 5^{12}$ $A_5^2 : C_4$ (as 10T42) trivial $2089.92661385$
10.6.25628906250000.2 $x^{10} - 10 x^{8} - 5 x^{7} + 25 x^{6} - x^{5} - 35 x^{4} + 115 x^{3} + 290 x^{2} + 210 x + 49$ $2^{4}\cdot 3^{8}\cdot 5^{12}$ $A_5^2 : C_4$ (as 10T42) trivial $1660.17397174$
10.4.45562500000000.1 $x^{10} + 10 x^{8} - 10 x^{7} + 20 x^{6} - 46 x^{5} + 50 x^{4} + 130 x^{3} - 85 x^{2} - 90 x + 4$ $-\,2^{8}\cdot 3^{6}\cdot 5^{12}$ $S_5^2 \wr C_2$ (as 10T43) trivial $2282.15038065$
10.4.45562500000000.2 $x^{10} - 5 x^{8} - 10 x^{7} + 15 x^{6} + 2 x^{5} + 5 x^{4} - 30 x^{3} + 35 x^{2} - 9$ $-\,2^{8}\cdot 3^{6}\cdot 5^{12}$ $S_5^2 \wr C_2$ (as 10T43) trivial $1677.3586266$
10.4.230660156250000.1 $x^{10} + 5 x^{8} - 10 x^{7} - 5 x^{6} - 53 x^{5} - 35 x^{4} + 125 x^{3} + 185 x^{2} - 15 x - 59$ $-\,2^{4}\cdot 3^{10}\cdot 5^{12}$ $S_5^2 \wr C_2$ (as 10T43) trivial $3685.9335142$
10.0.256000000000000.5 $x^{10} + 5 x^{8} + 15 x^{6} - 4 x^{5} + 15 x^{4} + 5 x^{2} + 9$ $-\,2^{20}\cdot 5^{12}$ $S_5^2 \wr C_2$ (as 10T43) $[2]$ $4281.79575302$
10.2.256000000000000.5 $x^{10} - 5 x^{9} + 25 x^{8} - 60 x^{7} + 120 x^{6} - 116 x^{5} + 20 x^{4} + 80 x^{3} - 160 x^{2} + 80 x - 16$ $2^{20}\cdot 5^{12}$ $A_5^2 : C_4$ (as 10T42) trivial $2615.79908463$
10.2.256000000000000.10 $x^{10} - 5 x^{9} + 15 x^{8} - 10 x^{7} - 85 x^{6} + 331 x^{5} - 645 x^{4} + 650 x^{3} - 115 x^{2} - 315 x + 179$ $2^{20}\cdot 5^{12}$ $A_5^2 : C_4$ (as 10T42) trivial $2534.34927274$
10.2.410062500000000.2 $x^{10} + 5 x^{8} + 25 x^{6} - 12 x^{5} - 5 x^{4} + 120 x^{3} - 70 x^{2} + 60 x - 44$ $2^{8}\cdot 3^{8}\cdot 5^{12}$ $A_5^2 : C_4$ (as 10T42) trivial $5990.67444759$
10.2.410062500000000.3 $x^{10} - 10 x^{8} + 25 x^{6} - 6 x^{5} - 5 x^{4} + 60 x^{3} + 50 x^{2} + 30 x + 19$ $2^{8}\cdot 3^{8}\cdot 5^{12}$ $A_5^2 : C_4$ (as 10T42) trivial $4063.14018583$
10.2.576000000000000.8 $x^{10} - 10 x^{8} + 40 x^{6} - 100 x^{4} - 80 x^{3} + 100 x^{2} - 320$ $2^{18}\cdot 3^{2}\cdot 5^{12}$ $A_5^2 : C_4$ (as 10T42) trivial $4856.88200343$
10.4.729000000000000.1 $x^{10} + 5 x^{8} - 25 x^{6} - 42 x^{5} - 50 x^{4} - 60 x^{3} + 140 x^{2} + 360 x + 176$ $-\,2^{12}\cdot 3^{6}\cdot 5^{12}$ $S_5^2 \wr C_2$ (as 10T43) trivial $10450.3958662$
10.4.729000000000000.2 $x^{10} - 5 x^{9} + 15 x^{8} - 10 x^{7} - 35 x^{6} + 201 x^{5} - 195 x^{4} - 150 x^{3} + 1035 x^{2} + 135 x - 711$ $-\,2^{12}\cdot 3^{6}\cdot 5^{12}$ $S_5^2 \wr C_2$ (as 10T43) trivial $10185.7958438$
10.2.922640625000000.1 $x^{10} + 15 x^{8} - 10 x^{7} + 75 x^{6} - 111 x^{5} + 125 x^{4} - 180 x^{3} - 180 x^{2} + 180 x - 36$ $2^{6}\cdot 3^{10}\cdot 5^{12}$ $A_5^2 : C_4$ (as 10T42) trivial $6104.21215573$
10.4.1024000000000000.3 $x^{10} + 5 x^{8} - 20 x^{7} + 75 x^{6} - 44 x^{5} - 115 x^{4} + 100 x^{3} + 15 x^{2} - 40 x + 19$ $-\,2^{22}\cdot 5^{12}$ $S_5^2 \wr C_2$ (as 10T43) trivial $8101.60735948$
10.2.1296000000000000.1 $x^{10} + 5 x^{8} - 45 x^{6} - 16 x^{5} - 165 x^{4} + 25 x^{2} - 1$ $2^{16}\cdot 3^{4}\cdot 5^{12}$ $A_5^2 : C_4$ (as 10T42) trivial $6045.56920145$
10.6.1296000000000000.1 $x^{10} - 10 x^{8} - 5 x^{6} - 64 x^{5} - 100 x^{3} - 105 x^{2} + 120 x + 64$ $2^{16}\cdot 3^{4}\cdot 5^{12}$ $A_5^2 : C_4$ (as 10T42) trivial $15975.978276$
10.2.1296000000000000.5 $x^{10} + 10 x^{8} - 20 x^{7} + 15 x^{6} - 192 x^{5} + 50 x^{4} - 480 x^{3} + 405 x^{2} + 100 x + 16$ $2^{16}\cdot 3^{4}\cdot 5^{12}$ $A_5^2 : C_4$ (as 10T42) trivial $9951.05464572$
10.2.1296000000000000.6 $x^{10} + 15 x^{8} - 20 x^{7} + 120 x^{6} - 148 x^{5} + 540 x^{4} - 560 x^{3} + 540 x^{2} - 200 x - 124$ $2^{16}\cdot 3^{4}\cdot 5^{12}$ $(C_5^2 : C_8):C_2$ (as 10T28) trivial $7339.08202734$
10.4.1640250000000000.4 $x^{10} + 5 x^{8} - 10 x^{7} - 55 x^{6} - 136 x^{5} - 345 x^{4} - 280 x^{3} - 305 x^{2} - 10 x + 19$ $-\,2^{10}\cdot 3^{8}\cdot 5^{12}$ $S_5^2 \wr C_2$ (as 10T43) trivial $17327.6483847$
10.4.1640250000000000.9 $x^{10} - 5 x^{9} + 5 x^{8} - 10 x^{7} - 5 x^{6} + 243 x^{5} - 705 x^{4} + 2040 x^{3} - 5040 x^{2} + 5760 x - 2304$ $-\,2^{10}\cdot 3^{8}\cdot 5^{12}$ $S_5^2 \wr C_2$ (as 10T43) trivial $15145.124628$
10.6.2075941406250000.1 $x^{10} - 10 x^{8} - 10 x^{7} + 25 x^{6} + 4 x^{5} - 115 x^{4} + 170 x^{3} + 730 x^{2} + 540 x + 89$ $2^{4}\cdot 3^{12}\cdot 5^{12}$ $A_5^2 : C_4$ (as 10T42) trivial $15921.2978384$
10.4.2304000000000000.5 $x^{10} - 5 x^{9} - 5 x^{8} + 50 x^{7} - 5 x^{6} - 145 x^{5} - 45 x^{4} + 190 x^{3} + 175 x^{2} - 25 x - 55$ $-\,2^{20}\cdot 3^{2}\cdot 5^{12}$ $S_5^2 \wr C_2$ (as 10T43) trivial $12790.700327$
10.4.2304000000000000.9 $x^{10} - 5 x^{9} + 5 x^{8} + 10 x^{6} + 2 x^{5} + 90 x^{4} - 200 x^{3} - 735 x^{2} + 535 x + 781$ $-\,2^{20}\cdot 3^{2}\cdot 5^{12}$ $S_5^2 \wr C_2$ (as 10T43) trivial $11845.3341815$
10.0.2916000000000000.11 $x^{10} + 10 x^{8} - 10 x^{7} + 45 x^{6} - 58 x^{5} + 150 x^{4} - 120 x^{3} + 300 x^{2} - 120 x + 216$ $-\,2^{14}\cdot 3^{6}\cdot 5^{12}$ $S_5^2 \wr C_2$ (as 10T43) $[2]$ $23180.2711201$
10.6.3157035156250000.1 $x^{10} - 5 x^{9} + 30 x^{7} - 30 x^{6} - 26 x^{5} + 20 x^{4} + 5 x^{3} + 45 x^{2} - 20 x - 11$ $2^{4}\cdot 5^{12}\cdot 29^{2}\cdot 31^{2}$ $A_5^2 : C_4$ (as 10T42) trivial $26911.586886500438$
10.4.3690562500000000.5 $x^{10} - 5 x^{8} - 10 x^{7} - 30 x^{6} + 32 x^{5} + 140 x^{4} + 120 x^{3} + 200 x^{2} - 144$ $-\,2^{8}\cdot 3^{10}\cdot 5^{12}$ $S_5^2 \wr C_2$ (as 10T43) trivial $16531.9415206$
10.4.3690562500000000.6 $x^{10} - 5 x^{9} + 5 x^{8} + 10 x^{7} - 30 x^{6} - 2 x^{5} + 135 x^{4} - 215 x^{3} - 260 x^{2} + 415 x - 109$ $-\,2^{8}\cdot 3^{10}\cdot 5^{12}$ $S_5^2 \wr C_2$ (as 10T43) trivial $19015.8120449$
10.4.3690562500000000.7 $x^{10} - 10 x^{8} - 10 x^{7} + 25 x^{6} + 124 x^{5} - 65 x^{4} - 280 x^{3} + 80 x^{2} + 90 x - 71$ $-\,2^{8}\cdot 3^{10}\cdot 5^{12}$ $S_5^2 \wr C_2$ (as 10T43) trivial $21174.4626058$
10.4.3690562500000000.10 $x^{10} + 5 x^{8} + 10 x^{6} - 228 x^{5} + 90 x^{4} + 600 x^{3} - 1755 x^{2} + 2700 x - 1359$ $-\,2^{8}\cdot 3^{10}\cdot 5^{12}$ $S_5^2 \wr C_2$ (as 10T43) trivial $18035.1495626$
10.4.5184000000000000.1 $x^{10} - 5 x^{8} - 75 x^{6} - 44 x^{5} + 125 x^{4} + 60 x^{3} - 75 x^{2} + 9$ $-\,2^{18}\cdot 3^{4}\cdot 5^{12}$ $S_5^2 \wr C_2$ (as 10T43) trivial $26865.6608165$
10.4.5184000000000000.2 $x^{10} - 15 x^{8} - 20 x^{7} + 40 x^{6} + 384 x^{5} - 190 x^{4} - 1040 x^{3} + 360 x^{2} + 720 x - 76$ $-\,2^{18}\cdot 3^{4}\cdot 5^{12}$ $S_5^2 \wr C_2$ (as 10T43) trivial $26511.3297768$
10.0.5184000000000000.3 $x^{10} + 15 x^{8} - 20 x^{7} + 85 x^{6} - 72 x^{5} + 5 x^{4} + 200 x^{3} - 105 x^{2} - 100 x + 61$ $-\,2^{18}\cdot 3^{4}\cdot 5^{12}$ $S_5^2 \wr C_2$ (as 10T43) $[2]$ $23234.8572432$
10.0.5184000000000000.4 $x^{10} + 10 x^{8} - 20 x^{7} + 50 x^{6} - 144 x^{5} + 440 x^{4} - 480 x^{3} + 440 x^{2} - 160 x + 64$ $-\,2^{18}\cdot 3^{4}\cdot 5^{12}$ $S_5^2 \wr C_2$ (as 10T43) $[2]$ $68466.4292853$
10.0.6144000000000000.1 $x^{10} - 10 x^{6} - 88 x^{5} + 300 x^{4} + 225 x^{2} + 40 x + 36$ $-\,2^{23}\cdot 3\cdot 5^{12}$ $S_5^2 \wr C_2$ (as 10T43) $[2]$ $36114.2181792$
10.6.6561000000000000.1 $x^{10} - 5 x^{9} + 5 x^{8} - 25 x^{6} + 233 x^{5} - 435 x^{4} + 110 x^{3} + 95 x^{2} - 25 x + 1$ $2^{12}\cdot 3^{8}\cdot 5^{12}$ $A_5^2 : C_4$ (as 10T42) trivial $37387.2248898$
10.6.6561000000000000.4 $x^{10} - 30 x^{7} - 45 x^{6} + 12 x^{5} + 100 x^{4} + 300 x^{3} + 45 x^{2} - 270 x + 36$ $2^{12}\cdot 3^{8}\cdot 5^{12}$ $A_5^2 : C_4$ (as 10T42) trivial $40342.748639$
10.6.6561000000000000.7 $x^{10} - 5 x^{9} + 5 x^{8} + 20 x^{6} - 10 x^{5} - 95 x^{4} + 165 x^{3} - 200 x^{2} + 175 x - 55$ $2^{12}\cdot 3^{8}\cdot 5^{12}$ $A_5^2 : C_4$ (as 10T42) trivial $35800.2331678$
10.2.6561000000000000.18 $x^{10} - 10 x^{7} - 65 x^{6} - 95 x^{4} - 370 x^{3} - 300 x + 55$ $2^{12}\cdot 3^{8}\cdot 5^{12}$ $A_5^2 : C_4$ (as 10T42) trivial $24857.892168$
10.4.11664000000000000.1 $x^{10} - 25 x^{8} - 20 x^{7} + 185 x^{6} + 184 x^{5} - 525 x^{4} - 1100 x^{3} - 1265 x^{2} - 380 x - 11$ $-\,2^{16}\cdot 3^{6}\cdot 5^{12}$ $S_5^2 \wr C_2$ (as 10T43) trivial $45226.8147659$
10.2.14762250000000000.6 $x^{10} + 20 x^{8} - 10 x^{7} + 130 x^{6} - 140 x^{5} + 295 x^{4} - 520 x^{3} + 200 x^{2} - 20$ $2^{10}\cdot 3^{10}\cdot 5^{12}$ $A_5^2 : C_4$ (as 10T42) trivial $38224.7574432$
10.2.14762250000000000.20 $x^{10} - 5 x^{9} + 20 x^{8} - 25 x^{7} + 25 x^{6} + 78 x^{5} - 275 x^{4} + 985 x^{3} + 1490 x^{2} - 625 x - 449$ $2^{10}\cdot 3^{10}\cdot 5^{12}$ $A_5^2 : C_4$ (as 10T42) trivial $44170.5306745$
10.0.17496000000000000.9 $x^{10} + 15 x^{8} - 20 x^{7} + 60 x^{6} - 72 x^{5} + 350 x^{4} - 240 x^{3} + 120 x^{2} - 160 x + 96$ $-\,2^{15}\cdot 3^{7}\cdot 5^{12}$ $S_5^2 \wr C_2$ (as 10T43) $[2]$ $95239.2044588$
10.0.17496000000000000.13 $x^{10} - 10 x^{8} - 10 x^{7} + 70 x^{6} + 106 x^{5} - 225 x^{4} - 370 x^{3} + 285 x^{2} + 630 x + 249$ $-\,2^{15}\cdot 3^{7}\cdot 5^{12}$ $S_5^2 \wr C_2$ (as 10T43) $[2]$ $25797.5709203$
10.0.17496000000000000.19 $x^{10} + 5 x^{8} + 15 x^{6} - 12 x^{5} + 45 x^{4} + 180 x^{3} + 486$ $-\,2^{15}\cdot 3^{7}\cdot 5^{12}$ $S_5^2 \wr C_2$ (as 10T43) $[2]$ $183259.277733$
10.0.20736000000000000.7 $x^{10} - 10 x^{8} - 20 x^{7} + 100 x^{6} - 84 x^{5} + 90 x^{4} - 240 x^{3} + 465 x^{2} - 360 x + 144$ $-\,2^{20}\cdot 3^{4}\cdot 5^{12}$ $S_5^2 \wr C_2$ (as 10T43) $[2]$ $56883.4666832$
10.0.20736000000000000.11 $x^{10} - 40 x^{7} + 40 x^{6} + 200 x^{4} - 240 x^{3} + 600 x^{2} - 800 x + 320$ $-\,2^{20}\cdot 3^{4}\cdot 5^{12}$ $S_5^2 \wr C_2$ (as 10T43) $[2]$ $72869.8173421$
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