Learn more

Refine search


Results (1-50 of 412 matches)

Next   displayed columns for results
Label Polynomial Discriminant Galois group Class group Regulator
8.0.42180533641.1 $x^{8} - x^{7} + x^{6} + 5 x^{5} - x^{4} + 10 x^{3} + 4 x^{2} - 8 x + 16$ $59^{6}$ $S_4$ (as 8T14) $[3]$ $86.9905915914$
8.0.1898124013845.1 $x^{8} + 3 x^{6} - 4 x^{4} - 61 x^{2} + 125$ $3^{2}\cdot 5\cdot 59^{6}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3, 3]$ $159.559643767$
8.0.3416623224921.1 $x^{8} - 3 x^{7} - 18 x^{6} + 63 x^{5} + 551 x^{4} + 1638 x^{3} + 2700 x^{2} + 2496 x + 1024$ $3^{4}\cdot 59^{6}$ $D_4$ (as 8T4) $[3, 3, 3]$ $204.100407396$
8.0.3416623224921.2 $x^{8} - x^{7} + 8 x^{6} - 15 x^{5} + 57 x^{4} - 71 x^{3} + 142 x^{2} + 33 x + 9$ $3^{4}\cdot 59^{6}$ $S_4\times C_2$ (as 8T24) $[4]$ $1227.45406537$
8.0.10798216612096.1 $x^{8} + 15 x^{6} + 18 x^{4} - 14 x^{2} + 9$ $2^{8}\cdot 59^{6}$ $C_2^3:S_4$ (as 8T39) $[2]$ $798.677382978$
8.0.10798216612096.2 $x^{8} + 3 x^{6} - 4 x^{4} + 116 x^{2} + 361$ $2^{8}\cdot 59^{6}$ $C_2^3:S_4$ (as 8T39) $[2]$ $1515.05226277$
8.0.10798216612096.3 $x^{8} + 15 x^{6} + 77 x^{4} + 163 x^{2} + 9$ $2^{8}\cdot 59^{6}$ $S_4\times C_2$ (as 8T24) $[2]$ $1780.82125836$
8.0.18221990532912.1 $x^{8} - 11 x^{6} + 38 x^{4} + 9 x^{2} + 27$ $2^{4}\cdot 3^{3}\cdot 59^{6}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3, 3]$ $417.197127687$
8.0.18601615335681.1 $x^{8} - 2 x^{7} + 6 x^{6} - 81 x^{5} + 212 x^{4} - 246 x^{3} + 1820 x^{2} - 4311 x + 3321$ $3^{2}\cdot 7^{2}\cdot 59^{6}$ $C_2^2 \wr C_2$ (as 8T18) $[3, 3]$ $480.312530262$
8.0.26362833525625.2 $x^{8} - x^{7} + 18 x^{6} + 7 x^{5} + 113 x^{4} + 265 x^{3} + 386 x^{2} + 887 x + 1079$ $5^{4}\cdot 59^{6}$ $S_4\times C_2$ (as 8T24) $[8]$ $481.667783378$
8.0.26362833525625.3 $x^{8} - x^{7} + 11 x^{6} + 27 x^{5} - 27 x^{4} - 85 x^{3} + 267 x^{2} - 246 x + 104$ $5^{4}\cdot 59^{6}$ $\PSL(2,7)$ (as 8T37) $[2, 6]$ $1466.3693318$
8.2.27332985799368.1 $x^{8} - 6 x^{6} - 16 x^{4} + 75 x^{2} - 242$ $-\,2^{3}\cdot 3^{4}\cdot 59^{6}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3]$ $4809.41723463$
8.2.37582855474131.1 $x^{8} + 4 x^{6} - 112 x^{4} + 1007 x^{2} - 176$ $-\,3^{4}\cdot 11\cdot 59^{6}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3]$ $1846.96603384$
8.0.47453100346125.2 $x^{8} - x^{7} + 7 x^{6} - 88 x^{5} + 352 x^{4} - 780 x^{3} + 1251 x^{2} - 891 x + 729$ $3^{2}\cdot 5^{3}\cdot 59^{6}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3, 6]$ $893.944303353$
8.0.85415580623025.1 $x^{8} - x^{7} - 11 x^{6} + 73 x^{5} - 36 x^{4} - 604 x^{3} + 2821 x^{2} - 4778 x + 2656$ $3^{4}\cdot 5^{2}\cdot 59^{6}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[12]$ $1026.12756942$
8.0.85415580623025.2 $x^{8} - x^{7} + 8 x^{6} - 15 x^{5} - 61 x^{4} + 165 x^{3} + 968 x^{2} + 1331 x + 14641$ $3^{4}\cdot 5^{2}\cdot 59^{6}$ $D_4\times C_2$ (as 8T9) $[12]$ $3820.07011813$
8.0.85415580623025.3 $x^{8} - x^{7} - 36 x^{6} + 18 x^{5} + 265 x^{4} - 396 x^{3} + 984 x^{2} + 10648 x + 19024$ $3^{4}\cdot 5^{2}\cdot 59^{6}$ $C_2^2 \wr C_2$ (as 8T18) $[3, 12]$ $282.402443479$
8.0.85415580623025.4 $x^{8} - 3 x^{7} - 15 x^{6} + 12 x^{5} + 185 x^{4} + 498 x^{3} + 672 x^{2} + 480 x + 145$ $3^{4}\cdot 5^{2}\cdot 59^{6}$ $C_2^2 \wr C_2$ (as 8T18) $[6, 6]$ $170.737196943$
8.2.86385732896768.2 $x^{8} + 3 x^{6} + 55 x^{4} + 293 x^{2} - 288$ $-\,2^{11}\cdot 59^{6}$ $C_2 \wr S_4$ (as 8T44) trivial $198074.543071$
8.2.86385732896768.3 $x^{8} + 17 x^{6} + 160 x^{4} - 176 x^{2} - 128$ $-\,2^{11}\cdot 59^{6}$ $C_2 \wr S_4$ (as 8T44) trivial $75152.7190367$
8.0.97183949508864.2 $x^{8} + 4 x^{6} + 65 x^{4} + 4 x^{2} + 1$ $2^{8}\cdot 3^{2}\cdot 59^{6}$ $C_2^2 \wr C_2$ (as 8T18) $[3, 3]$ $3164.45578572$
8.0.97183949508864.3 $x^{8} + 15 x^{6} + 313 x^{4} + 4824 x^{2} + 32400$ $2^{8}\cdot 3^{2}\cdot 59^{6}$ $D_4\times C_2$ (as 8T9) $[3, 3, 3]$ $1388.0339689$
8.0.101275461272041.1 $x^{8} - 13 x^{6} + 410 x^{4} + 1688 x^{2} + 841$ $7^{4}\cdot 59^{6}$ $D_4$ (as 8T4) $[3]$ $1922.17520523$
8.0.101275461272041.2 $x^{8} + 7 x^{6} - 48 x^{4} + 239 x^{2} + 2601$ $7^{4}\cdot 59^{6}$ $S_4$ (as 8T14) $[3]$ $15678.1085575$
8.0.101275461272041.3 $x^{8} - 2 x^{7} - 6 x^{6} - 4 x^{5} + 69 x^{4} + 96 x^{3} + 25 x^{2} + 213 x + 491$ $7^{4}\cdot 59^{6}$ $S_4\times C_2$ (as 8T24) $[4]$ $1055.0119083$
8.0.167414538021129.1 $x^{8} - 37 x^{6} + 742 x^{4} - 2196 x^{2} + 2025$ $3^{4}\cdot 7^{2}\cdot 59^{6}$ $C_2^2 \wr C_2$ (as 8T18) $[3, 6]$ $574.089618696$
8.0.167414538021129.3 $x^{8} - 2 x^{7} + 32 x^{6} - 2 x^{5} + 617 x^{4} + 88 x^{3} + 7141 x^{2} + 6525 x + 50625$ $3^{4}\cdot 7^{2}\cdot 59^{6}$ $D_4\times C_2$ (as 8T9) $[6]$ $6558.73425382$
8.0.172771465793536.2 $x^{8} + 15 x^{6} - 41 x^{4} - 663 x^{2} + 3136$ $2^{12}\cdot 59^{6}$ $S_4\times C_2$ (as 8T24) $[2]$ $45981.8604823$
8.4.172771465793536.2 $x^{8} - 2 x^{7} - 21 x^{6} + 48 x^{5} + 79 x^{4} - 152 x^{3} - 9 x^{2} + 146 x - 113$ $2^{12}\cdot 59^{6}$ $S_4\times C_2$ (as 8T24) trivial $14491.4516845$
8.0.172771465793536.3 $x^{8} - 2 x^{7} + 33 x^{6} - 92 x^{5} + 228 x^{4} - 872 x^{3} + 1380 x^{2} - 1136 x + 3824$ $2^{12}\cdot 59^{6}$ $S_4$ (as 8T14) $[6]$ $23185.1673353$
8.4.172771465793536.3 $x^{8} - 2 x^{7} - 21 x^{6} + 48 x^{5} - 39 x^{4} - 34 x^{3} - 599 x^{2} - 444 x + 4194$ $2^{12}\cdot 59^{6}$ $S_4\times C_2$ (as 8T24) trivial $86444.3285013$
8.4.172771465793536.4 $x^{8} - 8 x^{6} + 24 x^{4} - 504 x^{2} + 16$ $2^{12}\cdot 59^{6}$ $S_4\times C_2$ (as 8T24) trivial $36075.365695$
8.4.172771465793536.5 $x^{8} - 4 x^{7} - 16 x^{6} + 62 x^{5} + 28 x^{4} - 164 x^{3} - 71 x^{2} + 164 x + 78$ $2^{12}\cdot 59^{6}$ $S_4\times C_2$ (as 8T24) trivial $126672.964995$
8.0.172771465793536.6 $x^{8} - 4 x^{7} + 24 x^{6} - 58 x^{5} + 147 x^{4} - 202 x^{3} + 250 x^{2} - 158 x + 45$ $2^{12}\cdot 59^{6}$ $S_4$ (as 8T14) $[2, 6]$ $1779.13823898$
8.4.172771465793536.6 $x^{8} - 4 x^{7} - 17 x^{6} + 6 x^{5} - 54 x^{4} - 64 x^{3} - 20 x^{2} + 152 x + 248$ $2^{12}\cdot 59^{6}$ $V_4^2:(S_3\times C_2)$ (as 8T41) trivial $141317.626539$
8.0.172771465793536.7 $x^{8} - 4 x^{7} + 14 x^{6} - 28 x^{5} + 49 x^{4} - 56 x^{3} + 292 x^{2} - 268 x + 75$ $2^{12}\cdot 59^{6}$ $S_4$ (as 8T14) $[2, 6]$ $2317.44803847$
8.0.172771465793536.8 $x^{8} + 60 x^{6} + 642 x^{4} + 284 x^{2} + 121$ $2^{12}\cdot 59^{6}$ $S_4\times C_2$ (as 8T24) $[8]$ $5229.82097275$
8.4.172771465793536.8 $x^{8} - 18 x^{6} + 33 x^{4} + 196 x^{2} + 576$ $2^{12}\cdot 59^{6}$ $S_4\times C_2$ (as 8T24) trivial $128343.849506$
8.0.172771465793536.10 $x^{8} - 4 x^{7} + 8 x^{6} - 10 x^{5} - 21 x^{4} + 54 x^{3} + 2 x^{2} - 30 x + 225$ $2^{12}\cdot 59^{6}$ $D_4$ (as 8T4) $[3]$ $25481.331632$
8.0.172771465793536.11 $x^{8} - 2 x^{7} + 12 x^{6} + 28 x^{5} + 147 x^{4} + 280 x^{3} + 492 x^{2} + 478 x + 265$ $2^{12}\cdot 59^{6}$ $V_4^2:S_3$ (as 8T34) $[2, 6]$ $2191.89993134$
8.4.218663886394944.1 $x^{8} - 4 x^{7} + 34 x^{6} - 88 x^{5} - 270 x^{4} + 682 x^{3} - 1343 x^{2} + 988 x + 2578$ $2^{6}\cdot 3^{4}\cdot 59^{6}$ $C_2^2 \wr C_2$ (as 8T18) $[3]$ $35269.0616549$
8.0.218663886394944.1 $x^{8} - 13 x^{6} + 115 x^{4} - 318 x^{2} + 900$ $2^{6}\cdot 3^{4}\cdot 59^{6}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 12]$ $513.420364477$
8.0.218663886394944.2 $x^{8} + 45 x^{6} + 575 x^{4} + 1923 x^{2} + 1024$ $2^{6}\cdot 3^{4}\cdot 59^{6}$ $D_4\times C_2$ (as 8T9) $[12]$ $5555.44334107$
8.4.218663886394944.3 $x^{8} + 7 x^{6} + 11 x^{4} - 115 x^{2} + 64$ $2^{6}\cdot 3^{4}\cdot 59^{6}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3]$ $43086.6812617$
8.0.218663886394944.5 $x^{8} - 3 x^{7} + 7 x^{6} - 8 x^{5} + 200 x^{4} - 22 x^{3} + 123 x^{2} + 287 x + 499$ $2^{6}\cdot 3^{4}\cdot 59^{6}$ $C_2^2 \wr C_2$ (as 8T18) $[12]$ $1191.98886724$
8.0.269955415302400.2 $x^{8} - 4 x^{7} + 8 x^{6} - 10 x^{5} + 97 x^{4} + 54 x^{3} - 352 x^{2} + 206 x + 5417$ $2^{8}\cdot 5^{2}\cdot 59^{6}$ $Q_8:C_2$ (as 8T11) $[3]$ $4179.76173166$
8.0.269955415302400.4 $x^{8} - 58 x^{6} + 819 x^{4} + 1582 x^{2} + 121$ $2^{8}\cdot 5^{2}\cdot 59^{6}$ $D_4\times C_2$ (as 8T9) $[3]$ $11938.3032327$
8.2.345542931587072.1 $x^{8} + 3 x^{6} - 122 x^{4} + 352 x^{2} - 288$ $-\,2^{13}\cdot 59^{6}$ $C_2 \wr S_4$ (as 8T44) trivial $111777.903729$
8.2.345542931587072.2 $x^{8} - 11 x^{6} - 80 x^{4} + 68 x^{2} - 32$ $-\,2^{13}\cdot 59^{6}$ $C_2 \wr S_4$ (as 8T44) trivial $158996.907719$
8.0.388735798035456.1 $x^{8} + 7 x^{6} + 11 x^{4} - 56 x^{2} + 64$ $2^{10}\cdot 3^{2}\cdot 59^{6}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3, 3]$ $4972.95418979$
Next   displayed columns for results