Learn more

Refine search


Results (1-50 of 425 matches)

Next   displayed columns for results
Label Polynomial Discriminant Galois group Class group Regulator
8.0.10376122997601.1 $x^{8} - 3 x^{7} + 13 x^{6} - 30 x^{5} + 118 x^{4} - 1470 x^{3} + 8493 x^{2} - 18963 x + 16641$ $3^{4}\cdot 71^{6}$ $D_4$ (as 8T4) $[3, 21]$ $665.919273393$
8.0.13834830663468.2 $x^{8} - 14 x^{6} + 38 x^{4} + 77 x^{2} + 48$ $2^{2}\cdot 3^{3}\cdot 71^{6}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[21]$ $2789.86979626$
8.0.18446440884624.1 $x^{8} + 2 x^{6} - 34 x^{4} - 35 x^{2} + 324$ $2^{4}\cdot 3^{2}\cdot 71^{6}$ $C_2^2 \wr C_2$ (as 8T18) $[21]$ $1024.5637227$
8.0.28822563882225.1 $x^{8} - 2 x^{7} + 9 x^{6} + 77 x^{5} + 100 x^{4} + 881 x^{3} + 4914 x^{2} + 9916 x + 8152$ $3^{2}\cdot 5^{2}\cdot 71^{6}$ $C_2^2 \wr C_2$ (as 8T18) $[21]$ $4688.50890616$
8.0.28822563882225.2 $x^{8} - 3 x^{7} + 28 x^{6} - 117 x^{5} + 32 x^{4} + 23 x^{3} + 291 x^{2} + 666 x + 324$ $3^{2}\cdot 5^{2}\cdot 71^{6}$ $C_2^2 \wr C_2$ (as 8T18) $[21]$ $1603.11797288$
8.4.32793672683776.1 $x^{8} + 3 x^{6} - 112 x^{4} + 299 x^{2} + 25$ $2^{8}\cdot 71^{6}$ $C_2^3:S_4$ (as 8T39) trivial $47240.8489934$
8.0.32793672683776.1 $x^{8} - 35 x^{6} + 486 x^{4} - 2835 x^{2} + 6561$ $2^{8}\cdot 71^{6}$ $C_2^2 \wr C_2$ (as 8T18) $[35]$ $245.394149723$
8.0.32793672683776.2 $x^{8} - 4 x^{7} + 8 x^{6} - 10 x^{5} - 27 x^{4} + 66 x^{3} + 2 x^{2} - 36 x + 324$ $2^{8}\cdot 71^{6}$ $D_4$ (as 8T4) $[7]$ $1397.72319862$
8.4.32793672683776.2 $x^{8} - 11 x^{6} + x^{4} + 152 x^{2} + 144$ $2^{8}\cdot 71^{6}$ $C_2^3:S_4$ (as 8T39) trivial $52584.0884216$
8.0.51240113568400.1 $x^{8} + 37 x^{6} + 469 x^{4} + 2620 x^{2} + 8100$ $2^{4}\cdot 5^{2}\cdot 71^{6}$ $C_2^2 \wr C_2$ (as 8T18) $[7]$ $912.847254977$
8.0.51240113568400.2 $x^{8} - 4 x^{7} - 27 x^{6} + 24 x^{5} + 479 x^{4} + 370 x^{3} - 2490 x^{2} - 4104 x + 11664$ $2^{4}\cdot 5^{2}\cdot 71^{6}$ $C_2^2 \wr C_2$ (as 8T18) $[7]$ $9597.25820038$
8.0.51880614988005.2 $x^{8} - 4 x^{7} + 11 x^{6} - 19 x^{5} + 478 x^{4} - 929 x^{3} + 847 x^{2} - 385 x + 107$ $3^{4}\cdot 5\cdot 71^{6}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[21]$ $588.174586333$
8.0.73785763538496.1 $x^{8} - x^{7} + 26 x^{6} - 57 x^{5} - 55 x^{4} + 316 x^{3} - 238 x^{2} - 700 x + 1032$ $2^{6}\cdot 3^{2}\cdot 71^{6}$ $C_2^2 \wr C_2$ (as 8T18) $[21]$ $3939.24905946$
8.0.73785763538496.2 $x^{8} - 47 x^{6} + 642 x^{4} - 1692 x^{2} + 1296$ $2^{6}\cdot 3^{2}\cdot 71^{6}$ $C_2^2 \wr C_2$ (as 8T18) $[105]$ $661.406338588$
8.0.73785763538496.3 $x^{8} - 3 x^{7} - 6 x^{6} - 5 x^{5} + 397 x^{4} - 26 x^{3} - 202 x^{2} - 8676 x + 19980$ $2^{6}\cdot 3^{2}\cdot 71^{6}$ $C_2^2 \wr C_2$ (as 8T18) $[21]$ $1614.58542257$
8.0.131174690735104.1 $x^{8} - 4 x^{7} - 4 x^{6} + 26 x^{5} + 44 x^{4} - 136 x^{3} + 117 x^{2} - 44 x + 8$ $2^{10}\cdot 71^{6}$ $C_2^3:S_4$ (as 8T39) $[6]$ $9985.78130512$
8.0.131174690735104.2 $x^{8} - 4 x^{7} + 10 x^{6} - 16 x^{5} + 90 x^{4} - 158 x^{3} + 507 x^{2} - 430 x + 782$ $2^{10}\cdot 71^{6}$ $C_2^3:S_4$ (as 8T39) $[6]$ $8971.09374482$
8.0.131174690735104.5 $x^{8} - 4 x^{7} + 43 x^{6} - 44 x^{5} + 439 x^{4} + 374 x^{3} + 1882 x^{2} + 3060 x + 8100$ $2^{10}\cdot 71^{6}$ $C_2^2 \wr C_2$ (as 8T18) $[7]$ $5624.21299442$
8.0.166017967961616.1 $x^{8} + 30 x^{6} + 373 x^{4} + 2220 x^{2} + 4624$ $2^{4}\cdot 3^{4}\cdot 71^{6}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[60]$ $364.013701198$
8.0.166017967961616.2 $x^{8} - 71 x^{4} + 5041$ $2^{4}\cdot 3^{4}\cdot 71^{6}$ $D_4\times C_2$ (as 8T9) $[28]$ $2713.07320706$
8.0.166017967961616.3 $x^{8} + 2 x^{6} + 250 x^{4} - 177 x^{2} + 324$ $2^{4}\cdot 3^{4}\cdot 71^{6}$ $C_2^2 \wr C_2$ (as 8T18) $[84]$ $4101.44057706$
8.0.221357290615488.2 $x^{8} - 3 x^{7} + 21 x^{6} - 48 x^{5} + 18 x^{4} + 108 x^{3} - 49 x^{2} + 357 x + 747$ $2^{6}\cdot 3^{3}\cdot 71^{6}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[42]$ $2448.72386669$
8.0.221357290615488.3 $x^{8} - 11 x^{6} + x^{4} - 132 x^{2} + 2700$ $2^{6}\cdot 3^{3}\cdot 71^{6}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[21]$ $6382.05590151$
8.0.259403074940025.3 $x^{8} - x^{7} - 26 x^{6} - 231 x^{5} + 651 x^{4} + 3114 x^{3} + 5544 x^{2} + 18360 x + 32400$ $3^{4}\cdot 5^{2}\cdot 71^{6}$ $D_4\times C_2$ (as 8T9) $[14]$ $10525.9475375$
8.0.295143054153984.1 $x^{8} - 3 x^{7} + 22 x^{6} - 68 x^{5} + 213 x^{4} - 503 x^{3} + 3638 x^{2} + 4284 x + 3992$ $2^{8}\cdot 3^{2}\cdot 71^{6}$ $C_2^2 \wr C_2$ (as 8T18) $[70]$ $2626.22129918$
8.0.295143054153984.5 $x^{8} - 2 x^{7} + 27 x^{6} + 50 x^{5} - 72 x^{4} + 88 x^{3} + 6328 x^{2} + 12048 x + 21024$ $2^{8}\cdot 3^{2}\cdot 71^{6}$ $C_2^2 \wr C_2$ (as 8T18) $[14]$ $2214.51006207$
8.0.295143054153984.6 $x^{8} + 30 x^{6} - 53 x^{4} + 90 x^{2} + 9$ $2^{8}\cdot 3^{2}\cdot 71^{6}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[10]$ $1514.69808227$
8.0.295143054153984.7 $x^{8} + 72 x^{6} + 1944 x^{4} + 23257 x^{2} + 104976$ $2^{8}\cdot 3^{2}\cdot 71^{6}$ $D_4\times C_2$ (as 8T9) $[3, 42]$ $1249.96786527$
8.0.295143054153984.8 $x^{8} - 22 x^{6} - 67 x^{4} + 5192 x^{2} + 36100$ $2^{8}\cdot 3^{2}\cdot 71^{6}$ $C_2^2 \wr C_2$ (as 8T18) $[42]$ $932.522088888$
8.0.393524072205312.3 $x^{8} - 14 x^{6} + 109 x^{4} + 148 x^{2} + 48$ $2^{10}\cdot 3\cdot 71^{6}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[7]$ $4373.06683276$
8.0.442714581230976.2 $x^{8} - 13 x^{6} + 19 x^{4} + 444 x^{2} + 864$ $2^{7}\cdot 3^{3}\cdot 71^{6}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[21]$ $4659.12781911$
8.0.442714581230976.4 $x^{8} - 7 x^{6} + 45 x^{4} + 54 x^{2} + 216$ $2^{7}\cdot 3^{3}\cdot 71^{6}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[21]$ $28226.4934703$
8.4.498053903884848.1 $x^{8} - 3 x^{7} - 26 x^{6} + 182 x^{5} - 349 x^{4} - 134 x^{3} + 1152 x^{2} - 785 x - 989$ $2^{4}\cdot 3^{5}\cdot 71^{6}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3]$ $20825.5219384$
8.0.498053903884848.2 $x^{8} - 3 x^{7} + 51 x^{6} - 151 x^{5} + 1029 x^{4} - 2337 x^{3} + 8590 x^{2} - 11580 x + 22608$ $2^{4}\cdot 3^{5}\cdot 71^{6}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[42]$ $4986.39341877$
8.4.498053903884848.2 $x^{8} - 31 x^{6} + 316 x^{4} - 1893 x^{2} + 4107$ $2^{4}\cdot 3^{5}\cdot 71^{6}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3]$ $18286.9749503$
8.4.524698762940416.1 $x^{8} + 6 x^{6} - 448 x^{4} + 2392 x^{2} + 400$ $2^{12}\cdot 71^{6}$ $C_2^3:S_4$ (as 8T39) trivial $41661.5474232$
8.8.524698762940416.1 $x^{8} - 44 x^{6} + 513 x^{4} - 2058 x^{2} + 2500$ $2^{12}\cdot 71^{6}$ $S_4$ (as 8T14) $[3]$ $78545.4613848$
8.4.524698762940416.2 $x^{8} - 22 x^{6} + 4 x^{4} + 1216 x^{2} + 2304$ $2^{12}\cdot 71^{6}$ $C_2^3:S_4$ (as 8T39) trivial $71127.3323$
8.8.524698762940416.2 $x^{8} - 39 x^{6} + 384 x^{4} - 295 x^{2} + 49$ $2^{12}\cdot 71^{6}$ $S_4\times C_2$ (as 8T24) trivial $308427.352266$
8.0.524698762940416.3 $x^{8} - 4 x^{7} - 62 x^{6} + 200 x^{5} + 963 x^{4} - 2264 x^{3} + 3382 x^{2} - 2216 x + 664$ $2^{12}\cdot 71^{6}$ $D_4$ (as 8T4) $[5, 105]$ $280.361079044$
8.0.524698762940416.4 $x^{8} - 2 x^{7} + 2 x^{6} - 90 x^{5} + 2754 x^{4} - 810 x^{3} + 162 x^{2} - 1458 x + 6561$ $2^{12}\cdot 71^{6}$ $D_4\times C_2$ (as 8T9) $[70]$ $5025.96383193$
8.0.524698762940416.6 $x^{8} - 4 x^{7} - 28 x^{6} + 98 x^{5} + 368 x^{4} - 52 x^{3} + 1811 x^{2} + 9308 x + 10798$ $2^{12}\cdot 71^{6}$ $C_2^2 \wr C_2$ (as 8T18) $[35]$ $3138.99389013$
8.0.524698762940416.7 $x^{8} - 4 x^{7} + 25 x^{6} + 10 x^{5} + 1285 x^{4} + 4840 x^{3} + 18567 x^{2} + 25970 x + 25082$ $2^{12}\cdot 71^{6}$ $S_4\times C_2$ (as 8T24) $[2, 12]$ $6041.05635519$
8.0.524698762940416.8 $x^{8} - 2 x^{7} + 2 x^{6} + 52 x^{5} + 269 x^{4} + 326 x^{3} + 162 x^{2} - 180 x + 100$ $2^{12}\cdot 71^{6}$ $S_4\times C_2$ (as 8T24) $[4, 8]$ $2444.99615299$
8.0.524698762940416.9 $x^{8} + 36 x^{6} + 273 x^{4} + 502 x^{2} + 100$ $2^{12}\cdot 71^{6}$ $S_4\times C_2$ (as 8T24) $[12]$ $2444.99615299$
8.0.524698762940416.10 $x^{8} + 2 x^{6} + 37 x^{4} - 248 x^{2} + 324$ $2^{12}\cdot 71^{6}$ $S_4\times C_2$ (as 8T24) $[2, 2, 6]$ $4678.02827566$
8.0.590286108307968.1 $x^{8} + 19 x^{6} + 162 x^{4} + 584 x^{2} + 800$ $2^{9}\cdot 3^{2}\cdot 71^{6}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[21]$ $13494.080213$
8.0.590286108307968.2 $x^{8} - 3 x^{7} + 12 x^{6} + 61 x^{5} - 159 x^{4} + 116 x^{3} + 740 x^{2} - 836 x + 1444$ $2^{9}\cdot 3^{2}\cdot 71^{6}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[21]$ $4789.2257622$
8.0.590286108307968.3 $x^{8} + 3 x^{6} + 101 x^{4} + 654 x^{2} + 1800$ $2^{9}\cdot 3^{2}\cdot 71^{6}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[21]$ $6882.8617049$
8.0.590286108307968.4 $x^{8} - 3 x^{7} + 13 x^{6} + 41 x^{5} - 24 x^{4} + 92 x^{3} + 3168 x^{2} - 7248 x + 17280$ $2^{9}\cdot 3^{2}\cdot 71^{6}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[21]$ $26205.0365017$
Next   displayed columns for results