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Label Polynomial Discriminant Galois group Class group Regulator
6.4.570152223.1 $x^{6} - 2 x^{5} - 8 x^{4} + 22 x^{3} - 46 x^{2} + 48 x - 11$ $-\,3^{3}\cdot 59\cdot 71^{3}$ $C_3^2:D_4$ (as 6T13) trivial $310.970044396$
6.2.733001728.4 $x^{6} - 2 x^{5} - 3 x^{4} + 36 x^{3} - 28 x^{2} - 64 x - 28$ $2^{11}\cdot 71^{3}$ $C_3^2:D_4$ (as 6T13) trivial $720.471457317$
6.4.1259846720.1 $x^{6} - 2 x^{5} + x^{4} + 34 x^{3} - 34 x^{2} + 5$ $-\,2^{6}\cdot 5\cdot 11\cdot 71^{3}$ $C_3^2:D_4$ (as 6T13) trivial $414.252505185$
6.2.1959920636.1 $x^{6} - 6 x^{4} - 21 x^{3} + 9 x^{2} - 8 x - 14$ $2^{2}\cdot 37^{2}\cdot 71^{3}$ $S_6$ (as 6T16) trivial $612.722561078$
6.2.2174309325.1 $x^{6} - 3 x^{5} + 2 x^{4} - 14 x^{3} + 36 x^{2} - 57 x + 12$ $3^{5}\cdot 5^{2}\cdot 71^{3}$ $S_6$ (as 6T16) trivial $950.153431202$
6.4.3556203696.1 $x^{6} - x^{5} - 26 x^{4} + 55 x^{3} + 148 x^{2} - 513 x + 361$ $-\,2^{4}\cdot 3^{3}\cdot 23\cdot 71^{3}$ $C_3^2:D_4$ (as 6T13) trivial $485.586898203$
6.2.3865438800.2 $x^{6} - 2 x^{5} - 13 x^{4} + 36 x^{3} + 27 x^{2} - 12 x - 21$ $2^{4}\cdot 3^{3}\cdot 5^{2}\cdot 71^{3}$ $\PGL(2,5)$ (as 6T14) trivial $1809.79792022$
6.4.4008603200.1 $x^{6} - 22 x^{4} - 34 x^{3} + 50 x^{2} + 90 x + 5$ $-\,2^{6}\cdot 5^{2}\cdot 7\cdot 71^{3}$ $C_3^2:D_4$ (as 6T13) trivial $2234.07755067$
6.2.4261646277.2 $x^{6} - x^{5} - 10 x^{4} + x^{3} + 25 x^{2} + 40 x - 11$ $3^{5}\cdot 7^{2}\cdot 71^{3}$ $S_6$ (as 6T16) trivial $844.641314492$
6.4.4435591023.2 $x^{6} - 15 x^{4} - 17 x^{3} + 3 x^{2} + 21 x + 19$ $-\,3^{6}\cdot 17\cdot 71^{3}$ $C_3^2:D_4$ (as 6T13) trivial $865.4820841$
6.2.5112042813.1 $x^{6} - x^{5} - 160 x^{4} + 105 x^{3} + 8481 x^{2} - 3128 x - 148823$ $3^{3}\cdot 23^{2}\cdot 71^{3}$ $D_{6}$ (as 6T3) $[7]$ $47.777738655$
6.2.5566231872.2 $x^{6} + 9 x^{4} - 16 x^{3} - 33 x^{2} - 72 x + 135$ $2^{6}\cdot 3^{5}\cdot 71^{3}$ $S_6$ (as 6T16) trivial $1437.36383454$
6.2.6597015552.1 $x^{6} - 12 x^{4} - 56 x^{3} + 36 x^{2} + 336 x - 352$ $2^{11}\cdot 3^{2}\cdot 71^{3}$ $C_3^2:D_4$ (as 6T13) trivial $1890.63263646$
6.2.7576260048.4 $x^{6} - 2 x^{5} + 22 x^{4} - 100 x^{3} + 136 x^{2} - 84 x + 16$ $2^{4}\cdot 3^{3}\cdot 7^{2}\cdot 71^{3}$ $\PGL(2,5)$ (as 6T14) $[4]$ $375.431012388$
6.2.8796020736.1 $x^{6} - 6 x^{4} - 52 x^{3} + 9 x^{2} + 156 x + 108$ $2^{13}\cdot 3\cdot 71^{3}$ $C_3^2:D_4$ (as 6T13) $[3]$ $1081.05262325$
6.2.8813200464.1 $x^{6} - 2 x^{5} - x^{4} + 64 x^{3} - 61 x^{2} - 62 x + 109$ $2^{4}\cdot 3^{4}\cdot 19\cdot 71^{3}$ $C_3^2:D_4$ (as 6T13) trivial $988.317073991$
6.2.9286716717.2 $x^{6} - x^{5} - 160 x^{4} + 109 x^{3} + 8479 x^{2} - 2490 x - 148929$ $3^{3}\cdot 31^{2}\cdot 71^{3}$ $D_{6}$ (as 6T3) trivial $529.908193056$
6.2.9286716717.3 $x^{6} - x^{5} - 8 x^{4} + 81 x^{3} + 135 x^{2} + 252 x - 477$ $3^{3}\cdot 31^{2}\cdot 71^{3}$ $S_3^2$ (as 6T9) trivial $596.65472949$
6.2.11086651136.1 $x^{6} - 2 x^{5} + 74 x^{4} - 74 x^{3} - 140 x^{2} - 4900 x - 85750$ $2^{8}\cdot 11^{2}\cdot 71^{3}$ $D_{6}$ (as 6T3) trivial $833.718609428$
6.2.12117434816.1 $x^{6} + 71 x^{4} - 357911$ $2^{6}\cdot 23^{2}\cdot 71^{3}$ $S_4\times C_2$ (as 6T11) trivial $288.82974823$
6.2.12117434816.2 $x^{6} - 2 x^{5} - 212 x^{4} + 286 x^{3} + 14979 x^{2} - 9656 x - 353011$ $2^{6}\cdot 23^{2}\cdot 71^{3}$ $D_{6}$ (as 6T3) trivial $820.808501584$
6.0.12862247607.1 $x^{6} - 3 x^{5} + 13 x^{4} + 3 x^{3} - 12 x^{2} + 115 x + 125$ $-\,3^{3}\cdot 11^{3}\cdot 71^{3}$ $\PGL(2,5)$ (as 6T14) $[2]$ $575.135382738$
6.6.13229464293.2 $x^{6} - x^{5} - 30 x^{4} + 54 x^{3} + 206 x^{2} - 578 x + 367$ $3^{3}\cdot 37^{2}\cdot 71^{3}$ $S_3\times C_3$ (as 6T5) trivial $675.66728115$
6.2.16244506557.3 $x^{6} - 2 x^{5} + 30 x^{4} - 78 x^{3} + 206 x^{2} - 675 x + 263$ $3^{3}\cdot 41^{2}\cdot 71^{3}$ $\PGL(2,5)$ (as 6T14) trivial $1122.66831737$
6.2.16698695616.4 $x^{6} - 15 x^{4} - 70 x^{3} + 216 x^{2} - 114 x - 53$ $2^{6}\cdot 3^{6}\cdot 71^{3}$ $S_6$ (as 6T16) trivial $1284.48250963$
6.4.16859039744.1 $x^{6} - 4 x^{4} - 24 x^{3} + 4 x^{2} + 48 x + 2$ $-\,2^{11}\cdot 23\cdot 71^{3}$ $C_3^2:D_4$ (as 6T13) $[3]$ $1398.23326014$
6.2.18708723792.1 $x^{6} - x^{5} - 158 x^{4} + 103 x^{3} + 8482 x^{2} - 3237 x - 154493$ $2^{4}\cdot 3^{3}\cdot 11^{2}\cdot 71^{3}$ $D_{6}$ (as 6T3) trivial $847.281217164$
6.2.22012958144.1 $x^{6} - 211 x^{4} - 2 x^{3} + 15124 x^{2} - 428 x - 368063$ $2^{6}\cdot 31^{2}\cdot 71^{3}$ $D_{6}$ (as 6T3) trivial $798.109878497$
6.2.29686569984.5 $x^{6} - 49 x^{4} - 112 x^{3} + 192 x^{2} - 96 x + 12$ $2^{10}\cdot 3^{4}\cdot 71^{3}$ $S_6$ (as 6T16) trivial $2831.11084965$
6.2.30198740625.2 $x^{6} - x^{5} - 20 x^{4} + 25 x^{3} + 145 x^{2} - 43 x - 62$ $3^{3}\cdot 5^{5}\cdot 71^{3}$ $\PGL(2,5)$ (as 6T14) trivial $2866.40781879$
6.2.30305040192.7 $x^{6} - 2 x^{5} - 13 x^{4} - 30 x^{3} + 93 x^{2} + 24 x - 84$ $2^{6}\cdot 3^{3}\cdot 7^{2}\cdot 71^{3}$ $\PGL(2,5)$ (as 6T14) trivial $2970.19462486$
6.6.30969323008.1 $x^{6} - 2 x^{5} - 43 x^{4} - 14 x^{3} + 400 x^{2} + 424 x - 437$ $2^{9}\cdot 13^{2}\cdot 71^{3}$ $S_3\times C_3$ (as 6T5) $[3]$ $1042.91029215$
6.2.30969323008.1 $x^{6} - 2 x^{5} + 37 x^{4} - 250 x^{3} + 3165 x^{2} - 6408 x - 39742$ $2^{9}\cdot 13^{2}\cdot 71^{3}$ $D_{6}$ (as 6T3) $[3]$ $608.935893862$
6.6.30969323008.2 $x^{6} - 26 x^{4} - 10 x^{3} + 169 x^{2} + 130 x - 117$ $2^{9}\cdot 13^{2}\cdot 71^{3}$ $S_3\times C_3$ (as 6T5) $[3]$ $2274.97576604$
6.6.30969323008.3 $x^{6} - 2 x^{5} - 43 x^{4} + 114 x^{3} + 272 x^{2} - 972 x + 657$ $2^{9}\cdot 13^{2}\cdot 71^{3}$ $S_3\times C_3$ (as 6T5) $[3]$ $1673.49060566$
6.4.31427449088.1 $x^{6} - 2 x^{5} - 13 x^{4} + 36 x^{3} - 257 x^{2} + 982 x - 1015$ $-\,2^{8}\cdot 7^{3}\cdot 71^{3}$ $C_3^2:D_4$ (as 6T13) $[3]$ $2128.65188004$
6.2.33076702976.2 $x^{6} + 17 x^{4} - 2 x^{3} - 265 x^{2} + 338 x - 3407$ $2^{8}\cdot 19^{2}\cdot 71^{3}$ $\PGL(2,5)$ (as 6T14) $[4]$ $1111.45260639$
6.2.35917084672.6 $x^{6} - 2 x^{5} + 11 x^{4} - 84 x^{3} + 99 x^{2} - 370 x + 233$ $2^{11}\cdot 7^{2}\cdot 71^{3}$ $C_3^2:D_4$ (as 6T13) $[3]$ $1735.74734243$
6.2.39278584784.3 $x^{6} - x^{5} - 20 x^{4} + 37 x^{3} + 68 x^{2} - 129 x + 81$ $2^{4}\cdot 19^{3}\cdot 71^{3}$ $\PGL(2,5)$ (as 6T14) trivial $2718.15060228$
6.2.39278584784.4 $x^{6} - x^{5} + 13 x^{4} - 31 x^{3} + 23 x^{2} - 147 x + 214$ $2^{4}\cdot 19^{3}\cdot 71^{3}$ $\PGL(2,5)$ (as 6T14) trivial $7464.22266721$
6.2.40828697325.2 $x^{6} - x^{5} + 3 x^{4} - 30 x^{3} - 67 x^{2} - 56 x + 1$ $3^{3}\cdot 5^{2}\cdot 13^{2}\cdot 71^{3}$ $\PGL(2,5)$ (as 6T14) $[4]$ $264.430649972$
6.4.42278236875.1 $x^{6} - 2 x^{5} - x^{4} - 31 x^{3} + 34 x^{2} + 33 x + 6$ $-\,3^{3}\cdot 5^{4}\cdot 7\cdot 71^{3}$ $C_3^2:D_4$ (as 6T13) $[2]$ $4590.78581543$
6.2.44346604544.1 $x^{6} + 71 x^{4} + 5041 x^{2} - 357911$ $2^{10}\cdot 11^{2}\cdot 71^{3}$ $S_4\times C_2$ (as 6T11) trivial $1517.11203654$
6.2.44529854976.1 $x^{6} - 2 x^{5} - 5 x^{4} - 32 x^{3} - 24 x^{2} - 312 x - 420$ $2^{9}\cdot 3^{5}\cdot 71^{3}$ $S_6$ (as 6T16) trivial $18517.2231548$
6.2.45812608000.4 $x^{6} - 9 x^{4} - 132 x^{3} + 464 x^{2} - 116 x - 614$ $2^{10}\cdot 5^{3}\cdot 71^{3}$ $C_3^2:D_4$ (as 6T13) trivial $8349.61544307$
6.2.45812608000.5 $x^{6} - 14 x^{4} - 24 x^{3} - 164 x^{2} - 400 x - 424$ $2^{10}\cdot 5^{3}\cdot 71^{3}$ $S_6$ (as 6T16) trivial $1772.50271398$
6.4.46179108864.2 $x^{6} - 2 x^{5} + 11 x^{4} - 16 x^{3} - 111 x^{2} - 30 x + 9$ $-\,2^{11}\cdot 3^{2}\cdot 7\cdot 71^{3}$ $C_3^2:D_4$ (as 6T13) $[9]$ $1490.06942413$
6.0.50325149888.1 $x^{6} - 13 x^{4} - 4 x^{3} + 273 x^{2} + 26 x + 4$ $-\,2^{6}\cdot 13^{3}\cdot 71^{3}$ $S_3^2$ (as 6T9) $[30]$ $130.180246022$
6.0.50325149888.5 $x^{6} - x^{5} + 56 x^{4} - 179 x^{3} - 56 x^{2} - 9217 x + 76193$ $-\,2^{6}\cdot 13^{3}\cdot 71^{3}$ $D_{6}$ (as 6T3) $[30]$ $35.8874405812$
6.6.55816936272.1 $x^{6} - 2 x^{5} - 49 x^{4} + 72 x^{3} + 603 x^{2} - 550 x - 731$ $2^{4}\cdot 3^{3}\cdot 19^{2}\cdot 71^{3}$ $S_3\times C_3$ (as 6T5) trivial $3124.31041016$
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