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Label Polynomial Discriminant Galois group Class group Regulator
6.0.81850580.1 $x^{6} - x^{5} - 5 x^{4} + x^{3} + 24 x^{2} - 4 x + 8$ $-\,2^{2}\cdot 5\cdot 7^{2}\cdot 17^{4}$ $S_6$ (as 6T16) trivial $144.113952485$
6.2.86861840.1 $x^{6} - 2 x^{5} - 6 x^{4} + 12 x^{3} + 9 x^{2} - 30 x + 20$ $2^{4}\cdot 5\cdot 13\cdot 17^{4}$ $S_6$ (as 6T16) trivial $97.2798894548$
6.2.197777728.1 $x^{6} + 8 x^{4} - 34 x^{3} - 7 x^{2} + 34 x + 24$ $2^{6}\cdot 17^{4}\cdot 37$ $S_6$ (as 6T16) trivial $536.418718171$
6.4.198362375.1 $x^{6} - 3 x^{5} - 8 x^{4} + 4 x^{3} + 52 x^{2} + 39 x - 9$ $-\,5^{3}\cdot 17^{4}\cdot 19$ $C_3^2:D_4$ (as 6T13) trivial $104.07176812$
6.2.225506700.2 $x^{6} - 2 x^{5} - 5 x^{4} + 22 x^{3} - 65 x^{2} + 70 x - 30$ $2^{2}\cdot 3^{3}\cdot 5^{2}\cdot 17^{4}$ $S_6$ (as 6T16) trivial $327.633551609$
6.2.256576512.3 $x^{6} - 2 x^{5} - 3 x^{4} + 8 x^{3} + 10 x^{2} + 8 x + 2$ $2^{10}\cdot 3\cdot 17^{4}$ $S_6$ (as 6T16) trivial $304.52190434$
6.2.297668844.1 $x^{6} - 3 x^{5} - 8 x^{4} + 21 x^{3} + 18 x^{2} - 12 x - 9$ $2^{2}\cdot 3^{4}\cdot 11\cdot 17^{4}$ $S_6$ (as 6T16) trivial $555.770968979$
6.2.299339264.1 $x^{6} - x^{5} - 3 x^{4} + 28 x^{3} - 59 x^{2} + 59 x - 27$ $2^{9}\cdot 7\cdot 17^{4}$ $S_6$ (as 6T16) trivial $315.608055461$
6.2.331411328.1 $x^{6} - 9 x^{4} + 10 x^{2} - 34 x + 58$ $2^{7}\cdot 17^{4}\cdot 31$ $S_6$ (as 6T16) trivial $339.09528967$
6.0.426207663.3 $x^{6} - 33 x^{4} - 51 x^{3} + 261 x^{2} + 918 x + 981$ $-\,3^{6}\cdot 7\cdot 17^{4}$ $C_3^2:D_4$ (as 6T13) $[3]$ $114.183758861$
6.0.489349539.1 $x^{6} - x^{5} - 39 x^{4} + 52 x^{3} + 432 x^{2} - 973 x + 637$ $-\,3^{3}\cdot 7\cdot 17^{4}\cdot 31$ $C_3^2:D_4$ (as 6T13) $[3]$ $136.879931737$
6.2.511566125.1 $x^{6} - x^{5} + 7 x^{4} + 10 x^{3} + 8 x^{2} + 15 x - 5$ $5^{3}\cdot 7^{2}\cdot 17^{4}$ $S_6$ (as 6T16) trivial $170.217357409$
6.2.513153024.2 $x^{6} - x^{5} + 8 x^{4} - 2 x^{3} + 11 x^{2} + 9 x - 6$ $2^{11}\cdot 3\cdot 17^{4}$ $S_6$ (as 6T16) trivial $1186.4797898$
6.2.662822656.1 $x^{6} - 2 x^{5} + 12 x^{4} - 12 x^{3} + 20 x^{2} - 32 x - 64$ $2^{8}\cdot 17^{4}\cdot 31$ $S_6$ (as 6T16) $[3]$ $432.540300006$
6.0.732896775.2 $x^{6} - x^{5} - 5 x^{4} + x^{3} + 7 x^{2} + 132 x + 229$ $-\,3^{3}\cdot 5^{2}\cdot 13\cdot 17^{4}$ $C_3^2:D_4$ (as 6T13) $[3]$ $90.3714112073$
6.0.787018383.1 $x^{6} - x^{5} + 29 x^{4} + 69 x^{3} + 177 x^{2} + 1288 x + 2116$ $-\,3^{3}\cdot 17^{4}\cdot 349$ $C_3^2:D_4$ (as 6T13) $[3]$ $97.7648686174$
6.0.814079187.2 $x^{6} - 3 x^{5} + 4 x^{4} + 14 x^{3} - 44 x^{2} + 28 x + 199$ $-\,3^{3}\cdot 17^{4}\cdot 19^{2}$ $S_3\times C_3$ (as 6T5) $[3]$ $41.8420270249$
6.0.814079187.3 $x^{6} - 3 x^{5} + 4 x^{4} + 116 x^{3} - 146 x^{2} + 28 x + 3871$ $-\,3^{3}\cdot 17^{4}\cdot 19^{2}$ $S_3\times C_3$ (as 6T5) $[3]$ $145.019638544$
6.2.845650125.2 $x^{6} - 3 x^{5} + 6 x^{4} + 27 x^{3} - 45 x^{2} + 150 x - 135$ $3^{4}\cdot 5^{3}\cdot 17^{4}$ $S_6$ (as 6T16) trivial $335.259457114$
6.2.902026800.3 $x^{6} - x^{5} + 14 x^{4} - 6 x^{3} - 42 x^{2} + 76 x - 44$ $2^{4}\cdot 3^{3}\cdot 5^{2}\cdot 17^{4}$ $S_6$ (as 6T16) trivial $910.512833922$
6.0.916726496.1 $x^{6} - x^{5} - 16 x^{4} - 20 x^{3} + 106 x^{2} + 324 x + 268$ $-\,2^{5}\cdot 7^{3}\cdot 17^{4}$ $C_3^2:D_4$ (as 6T13) $[3]$ $179.522850619$
6.0.1217736180.1 $x^{6} - 3 x^{5} + 6 x^{4} + 10 x^{3} + 57 x^{2} + 48 x + 52$ $-\,2^{2}\cdot 3^{6}\cdot 5\cdot 17^{4}$ $S_6$ (as 6T16) trivial $260.851068397$
6.2.1298918592.1 $x^{6} - 2 x^{5} - 3 x^{4} + 42 x^{3} - 58 x^{2} + 42 x - 49$ $2^{6}\cdot 3^{5}\cdot 17^{4}$ $S_6$ (as 6T16) trivial $387.253082904$
6.4.1400396607.1 $x^{6} - 2 x^{5} - 2 x^{4} - 16 x^{3} + 23 x^{2} + 50 x - 27$ $-\,3^{6}\cdot 17^{4}\cdot 23$ $S_6$ (as 6T16) trivial $962.886838549$
6.0.1403737447.1 $x^{6} - x^{5} + x^{4} + 48 x^{3} + 225 x^{2} + 188 x + 64$ $-\,7^{5}\cdot 17^{4}$ $S_3\times C_3$ (as 6T5) $[3]$ $189.349763578$
6.2.1513818125.1 $x^{6} - x^{5} - 25 x^{3} - 85 x^{2} + 744 x - 909$ $5^{4}\cdot 17^{4}\cdot 29$ $C_3^2:D_4$ (as 6T13) trivial $226.634447852$
6.2.1582221824.1 $x^{6} - 16 x^{4} + 57 x^{2} - 136 x - 294$ $2^{9}\cdot 17^{4}\cdot 37$ $S_6$ (as 6T16) trivial $905.007919462$
6.4.1618219375.1 $x^{6} - 34 x^{4} - 17 x^{3} + 289 x^{2} + 289 x - 289$ $-\,5^{4}\cdot 17^{4}\cdot 31$ $C_3^2:D_4$ (as 6T13) trivial $468.813441552$
6.0.1767972528.3 $x^{6} - 3 x^{5} + 4 x^{4} + 31 x^{3} - 44 x^{2} + 11 x + 301$ $-\,2^{4}\cdot 3^{3}\cdot 7^{2}\cdot 17^{4}$ $S_3\times C_3$ (as 6T5) $[3]$ $156.9998182$
6.0.1767972528.6 $x^{6} - 3 x^{5} + 4 x^{4} + 65 x^{3} - 248 x^{2} + 181 x + 8359$ $-\,2^{4}\cdot 3^{3}\cdot 7^{2}\cdot 17^{4}$ $S_3\times C_3$ (as 6T5) $[3]$ $164.138536212$
6.2.1804053600.1 $x^{6} - x^{5} + 8 x^{4} - 2 x^{3} + 28 x^{2} - 8 x - 176$ $2^{5}\cdot 3^{3}\cdot 5^{2}\cdot 17^{4}$ $S_6$ (as 6T16) trivial $1487.15809174$
6.0.1876215744.1 $x^{6} - 2 x^{5} - 38 x^{4} + 100 x^{3} + 536 x^{2} - 2490 x + 2881$ $-\,2^{6}\cdot 3^{3}\cdot 13\cdot 17^{4}$ $C_3^2:D_4$ (as 6T13) $[3]$ $308.694387144$
6.0.1881561088.1 $x^{6} - 2 x^{5} - 13 x^{4} + 44 x^{3} - 4 x^{2} - 240 x + 424$ $-\,2^{11}\cdot 11\cdot 17^{4}$ $S_6$ (as 6T16) $[5]$ $229.30327692$
6.0.1887491079.1 $x^{6} - 33 x^{4} - 17 x^{3} + 159 x^{2} + 306 x + 2341$ $-\,3^{6}\cdot 17^{4}\cdot 31$ $C_3^2:D_4$ (as 6T13) $[3]$ $271.773768209$
6.2.1967086592.1 $x^{6} - 2 x^{5} + 17 x^{4} + 4 x^{3} + 34 x^{2} + 8 x - 2$ $2^{10}\cdot 17^{4}\cdot 23$ $S_6$ (as 6T16) trivial $1126.77664185$
6.2.2112162569.1 $x^{6} - x^{5} + 3 x^{4} + 7 x^{3} - 20 x^{2} + 33 x - 18$ $11^{3}\cdot 17^{4}\cdot 19$ $S_6$ (as 6T16) trivial $965.423589842$
6.2.2164864320.3 $x^{6} - 2 x^{5} - 5 x^{4} - 12 x^{3} - 14 x^{2} - 32 x - 64$ $2^{6}\cdot 3^{4}\cdot 5\cdot 17^{4}$ $S_6$ (as 6T16) trivial $3829.51690007$
6.0.2205873131.2 $x^{6} - x^{5} - 16 x^{4} - 3 x^{3} + 157 x^{2} - 186 x + 64$ $-\,7^{4}\cdot 11\cdot 17^{4}$ $C_3^2:D_4$ (as 6T13) $[3]$ $861.359638678$
6.2.2309188608.4 $x^{6} - 2 x^{5} - 13 x^{4} - 24 x^{3} - 89 x^{2} - 70 x - 103$ $2^{10}\cdot 3^{3}\cdot 17^{4}$ $S_6$ (as 6T16) trivial $795.632144535$
6.0.2374585551.1 $x^{6} - 33 x^{4} - 51 x^{3} + 159 x^{2} + 918 x + 2919$ $-\,3^{7}\cdot 13\cdot 17^{4}$ $C_3^2:D_4$ (as 6T13) $[3]$ $398.45852005$
6.2.2597837184.2 $x^{6} - 2 x^{5} + 11 x^{4} - 22 x^{3} - 8 x^{2} + 38 x - 14$ $2^{7}\cdot 3^{5}\cdot 17^{4}$ $S_6$ (as 6T16) trivial $1260.61466989$
6.0.2864770300.2 $x^{6} - 3 x^{5} + 27 x^{4} - 32 x^{3} + 216 x^{2} - 22 x + 1192$ $-\,2^{2}\cdot 5^{2}\cdot 7^{3}\cdot 17^{4}$ $S_3^2$ (as 6T9) $[3]$ $242.309822162$
6.4.3030810048.1 $x^{6} - 2 x^{5} - 5 x^{4} + 22 x^{3} - 65 x^{2} + 70 x + 21$ $-\,2^{6}\cdot 3^{4}\cdot 7\cdot 17^{4}$ $S_6$ (as 6T16) trivial $2021.87028105$
6.0.3087186723.2 $x^{6} + x^{4} - 17 x^{3} - 62 x^{2} + 17 x + 403$ $-\,3^{3}\cdot 17^{4}\cdot 37^{2}$ $S_3\times C_3$ (as 6T5) $[3]$ $177.719366433$
6.0.3087186723.3 $x^{6} - 2 x^{5} + 64 x^{4} - 172 x^{3} + 1318 x^{2} - 3867 x + 3187$ $-\,3^{3}\cdot 17^{4}\cdot 37^{2}$ $S_3\times C_3$ (as 6T5) $[3]$ $94.5716842428$
6.4.3164443648.1 $x^{6} - 2 x^{5} - 2 x^{4} + 52 x^{3} - 45 x^{2} - 86 x + 24$ $-\,2^{10}\cdot 17^{4}\cdot 37$ $S_6$ (as 6T16) trivial $3676.77118704$
6.2.3207206400.2 $x^{6} - 15 x^{4} - 34 x^{3} - 10 x^{2} - 6$ $2^{9}\cdot 3\cdot 5^{2}\cdot 17^{4}$ $S_6$ (as 6T16) trivial $1723.20492387$
6.4.3233933120.1 $x^{6} - 2 x^{5} - 12 x^{4} + 54 x^{3} - 43 x^{2} - 152 x - 11$ $-\,2^{6}\cdot 5\cdot 11^{2}\cdot 17^{4}$ $S_6$ (as 6T16) trivial $1059.43720441$
6.2.3421020160.1 $x^{6} - 2 x^{5} - 17 x^{4} + 4 x^{3} + 34 x^{2} - 60 x - 70$ $2^{13}\cdot 5\cdot 17^{4}$ $S_6$ (as 6T16) trivial $2303.70569441$
6.4.3608107200.2 $x^{6} - 2 x^{5} - 3 x^{4} + 8 x^{3} - 41 x^{2} + 42 x + 19$ $-\,2^{6}\cdot 3^{3}\cdot 5^{2}\cdot 17^{4}$ $S_6$ (as 6T16) trivial $1128.02492807$
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