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Label Polynomial Discriminant Galois group Class group Regulator
6.0.121328851.1 $x^{6} - 3 x^{5} - x^{4} - 12 x^{3} + 71 x^{2} + 96 x + 163$ $-\,7^{2}\cdot 19^{5}$ $S_3\times C_3$ (as 6T5) $[3]$ $25.678740087$
6.0.158470336.1 $x^{6} - 3 x^{5} - x^{4} - 12 x^{3} + 52 x^{2} + 20 x + 68$ $-\,2^{6}\cdot 19^{5}$ $D_{6}$ (as 6T3) $[3]$ $33.1099798427$
6.2.255038197.2 $x^{6} - 3 x^{5} - x^{4} + 7 x^{3} - 5 x^{2} - 18 x - 8$ $19^{5}\cdot 103$ $S_6$ (as 6T16) $[3]$ $109.257774467$
6.0.398651939.1 $x^{6} - x^{5} + 2 x^{4} + 8 x^{3} + 18 x^{2} + 14 x + 7$ $-\,7\cdot 19^{5}\cdot 23$ $C_3^2:D_4$ (as 6T13) $[6]$ $17.441380723$
6.0.633881344.1 $x^{6} - 2 x^{5} + 8 x^{4} - 12 x^{3} + 41 x^{2} - 46 x + 68$ $-\,2^{8}\cdot 19^{5}$ $S_4\times C_2$ (as 6T11) $[6]$ $17.7437539865$
6.0.775018987.1 $x^{6} - 2 x^{5} + 8 x^{4} - 12 x^{3} + 22 x^{2} - 27 x + 11$ $-\,19^{5}\cdot 313$ $C_3^2:D_4$ (as 6T13) $[3]$ $27.0762162451$
6.0.814636571.1 $x^{6} - x^{5} + 2 x^{4} - 11 x^{3} - x^{2} + 14 x + 7$ $-\,7\cdot 19^{5}\cdot 47$ $C_3^2:D_4$ (as 6T13) $[3]$ $33.1239091084$
6.0.990439600.1 $x^{6} - x^{5} + 2 x^{4} - 49 x^{3} + 132 x^{2} - 195 x + 425$ $-\,2^{4}\cdot 5^{2}\cdot 19^{5}$ $D_{6}$ (as 6T3) $[3, 3]$ $33.5100484823$
6.0.1198431916.1 $x^{6} - 2 x^{5} + 8 x^{4} + 7 x^{3} + 22 x^{2} + 11 x + 11$ $-\,2^{2}\cdot 11^{2}\cdot 19^{5}$ $S_6$ (as 6T16) $[12]$ $18.1491876721$
6.0.1238049500.1 $x^{6} - 3 x^{5} + 18 x^{4} - 12 x^{3} + 52 x^{2} + 96 x + 144$ $-\,2^{2}\cdot 5^{3}\cdot 19^{5}$ $S_3^2$ (as 6T9) $[24]$ $43.5806451898$
6.2.1267762688.2 $x^{6} - 38 x^{3} - 38 x^{2} - 76 x + 323$ $2^{9}\cdot 19^{5}$ $D_{6}$ (as 6T3) $[3]$ $142.50146044$
6.2.1604512152.2 $x^{6} - 3 x^{5} + 18 x^{4} + 7 x^{3} - 24 x^{2} - 18 x - 8$ $2^{3}\cdot 3^{4}\cdot 19^{5}$ $S_6$ (as 6T16) $[3]$ $563.484847448$
6.0.1941261616.2 $x^{6} - 2 x^{5} - 11 x^{4} + 26 x^{3} + 41 x^{2} - 8 x + 125$ $-\,2^{4}\cdot 7^{2}\cdot 19^{5}$ $S_3\times C_3$ (as 6T5) $[3, 3]$ $47.6633763961$
6.0.1941261616.4 $x^{6} - 3 x^{5} - 20 x^{4} + 45 x^{3} + 280 x^{2} + 381 x + 163$ $-\,2^{4}\cdot 7^{2}\cdot 19^{5}$ $S_3\times C_3$ (as 6T5) $[3, 3]$ $14.3254424945$
6.0.2693995712.1 $x^{6} - x^{5} + 2 x^{4} - 11 x^{3} + 37 x^{2} + 14 x + 26$ $-\,2^{6}\cdot 17\cdot 19^{5}$ $S_4\times C_2$ (as 6T11) $[6]$ $120.778731975$
6.0.2785611375.2 $x^{6} - 2 x^{5} + 8 x^{4} + 7 x^{3} + 41 x^{2} + 49 x + 49$ $-\,3^{2}\cdot 5^{3}\cdot 19^{5}$ $C_3^2:D_4$ (as 6T13) $[3]$ $201.155012087$
6.2.2971318800.1 $x^{6} - x^{5} - 17 x^{4} - 11 x^{3} + 56 x^{2} - 24 x - 12$ $2^{4}\cdot 3\cdot 5^{2}\cdot 19^{5}$ $S_4\times C_2$ (as 6T11) $[3]$ $347.761220736$
6.4.3961758400.1 $x^{6} - 2 x^{5} - 11 x^{4} - 12 x^{3} + 79 x^{2} - 8 x - 65$ $-\,2^{6}\cdot 5^{2}\cdot 19^{5}$ $S_4\times C_2$ (as 6T11) $[3]$ $491.373929148$
6.2.4278699072.6 $x^{6} - 3 x^{5} - 20 x^{4} + 26 x^{3} + 109 x^{2} + 229 x + 106$ $2^{6}\cdot 3^{3}\cdot 19^{5}$ $D_{6}$ (as 6T3) $[3]$ $1264.61896163$
6.0.4578307051.1 $x^{6} - x^{5} + 21 x^{4} + 8 x^{3} + 37 x^{2} + 128 x + 83$ $-\,19^{5}\cdot 43^{2}$ $S_3\times C_3$ (as 6T5) $[3]$ $50.3262544452$
6.0.4952198000.1 $x^{6} - 3 x^{5} + 37 x^{4} - 69 x^{3} + 394 x^{2} - 360 x + 1170$ $-\,2^{4}\cdot 5^{3}\cdot 19^{5}$ $D_{6}$ (as 6T3) $[3, 24]$ $33.5100484823$
6.4.4952198000.1 $x^{6} - 3 x^{5} - x^{4} + 7 x^{3} - 24 x^{2} + 20 x + 68$ $-\,2^{4}\cdot 5^{3}\cdot 19^{5}$ $S_4\times C_2$ (as 6T11) $[3]$ $802.340667575$
6.2.5071050752.1 $x^{6} - 38 x^{2} - 76 x - 38$ $2^{11}\cdot 19^{5}$ $S_3^2$ (as 6T9) $[3]$ $172.468305585$
6.2.5071050752.2 $x^{6} - 19 x^{2} - 38$ $2^{11}\cdot 19^{5}$ $S_4\times C_2$ (as 6T11) $[6]$ $302.368128692$
6.0.5945113699.1 $x^{6} - x^{5} + 2 x^{4} + 122 x^{3} + 474 x^{2} + 888 x + 881$ $-\,7^{4}\cdot 19^{5}$ $C_6$ (as 6T1) $[3, 3]$ $43.4693954291$
6.0.6440333499.1 $x^{6} - x^{5} - 17 x^{4} + 8 x^{3} + 113 x^{2} + 33 x + 7$ $-\,3^{2}\cdot 17^{2}\cdot 19^{5}$ $D_{6}$ (as 6T3) $[3]$ $179.112758889$
6.0.7220304684.1 $x^{6} - 3 x^{5} + 18 x^{4} - 31 x^{3} + 90 x^{2} - 18 x + 11$ $-\,2^{2}\cdot 3^{6}\cdot 19^{5}$ $S_6$ (as 6T16) $[6]$ $115.586430031$
6.2.7487723376.1 $x^{6} - x^{5} + 2 x^{4} + 8 x^{3} - 172 x^{2} + 128 x - 848$ $2^{4}\cdot 3^{3}\cdot 7\cdot 19^{5}$ $C_3^2:D_4$ (as 6T13) $[3]$ $2562.62144217$
6.0.7765046464.3 $x^{6} - 2 x^{5} + 27 x^{4} - 12 x^{3} + 117 x^{2} + 106 x + 334$ $-\,2^{6}\cdot 7^{2}\cdot 19^{5}$ $\PGL(2,5)$ (as 6T14) $[6]$ $251.742416555$
6.2.8240457472.1 $x^{6} - 19 x^{4} - 76 x^{3} - 133 x^{2} - 114 x - 38$ $2^{8}\cdot 13\cdot 19^{5}$ $S_4\times C_2$ (as 6T11) $[6]$ $113.649646409$
6.4.8913956400.1 $x^{6} - 3 x^{5} - 20 x^{4} + 45 x^{3} - 100 x^{2} - 75 x + 125$ $-\,2^{4}\cdot 3^{2}\cdot 5^{2}\cdot 19^{5}$ $S_4\times C_2$ (as 6T11) $[3]$ $972.144542593$
6.0.8913956400.2 $x^{6} - x^{5} + 2 x^{4} - 11 x^{3} + 208 x^{2} - 81 x + 729$ $-\,2^{4}\cdot 3^{2}\cdot 5^{2}\cdot 19^{5}$ $S_3^2$ (as 6T9) $[3, 3]$ $89.364999505$
6.0.9025380855.1 $x^{6} - 19 x^{3} + 171 x^{2} + 57 x + 95$ $-\,3^{6}\cdot 5\cdot 19^{5}$ $C_3^2:D_4$ (as 6T13) $[3]$ $145.956738157$
6.0.9213564379.1 $x^{6} - 2 x^{5} + 8 x^{4} + 26 x^{3} + 98 x^{2} + 68 x + 277$ $-\,19^{5}\cdot 61^{2}$ $S_3\times C_3$ (as 6T5) $[3]$ $190.951190149$
6.2.9594883625.1 $x^{6} - 2 x^{5} + 8 x^{4} + 26 x^{3} - 35 x^{2} + 125 x + 125$ $5^{3}\cdot 19^{5}\cdot 31$ $S_6$ (as 6T16) $[3]$ $445.812444761$
6.0.9706308080.1 $x^{6} - 2 x^{5} + 8 x^{4} + 26 x^{3} - 16 x^{2} + 106 x + 277$ $-\,2^{4}\cdot 5\cdot 7^{2}\cdot 19^{5}$ $C_3^2:D_4$ (as 6T13) $[3]$ $344.947400183$
6.0.11115208411.1 $x^{6} - x^{5} + 40 x^{4} - 11 x^{3} + 607 x^{2} - 100 x + 3028$ $-\,19^{5}\cdot 67^{2}$ $D_{6}$ (as 6T3) $[3]$ $436.357425607$
6.2.11885275200.1 $x^{6} - 2 x^{5} - 11 x^{4} - 12 x^{3} + 60 x^{2} - 160 x + 220$ $2^{6}\cdot 3\cdot 5^{2}\cdot 19^{5}$ $S_6$ (as 6T16) $[6]$ $832.113910247$
6.6.11885275200.1 $x^{6} - 19 x^{4} + 95 x^{2} - 57$ $2^{6}\cdot 3\cdot 5^{2}\cdot 19^{5}$ $S_4\times C_2$ (as 6T11) $[3]$ $974.213798824$
6.0.12234405159.1 $x^{6} - 19 x^{3} - 114 x^{2} + 285 x + 1900$ $-\,3^{4}\cdot 19^{5}\cdot 61$ $S_6$ (as 6T16) $[2, 6]$ $145.36042744$
6.2.13103515908.2 $x^{6} - 3 x^{5} - x^{4} - 50 x^{3} - 119 x^{2} - 113 x + 49$ $2^{2}\cdot 3^{3}\cdot 7^{2}\cdot 19^{5}$ $S_3^2$ (as 6T9) $[3]$ $1511.47519463$
6.2.13103515908.4 $x^{6} - 3 x^{5} - x^{4} - 12 x^{3} - 5 x^{2} - 75 x + 87$ $2^{2}\cdot 3^{3}\cdot 7^{2}\cdot 19^{5}$ $S_3^2$ (as 6T9) $[3]$ $926.560177511$
6.2.14440609368.2 $x^{6} - 19 x^{3} - 57 x^{2} + 285 x - 266$ $2^{3}\cdot 3^{6}\cdot 19^{5}$ $C_3^2:D_4$ (as 6T13) $[3]$ $1232.72007801$
6.2.14856594000.2 $x^{6} - 3 x^{5} + 18 x^{4} - 31 x^{3} + 52 x^{2} - 37 x - 103$ $2^{4}\cdot 3\cdot 5^{3}\cdot 19^{5}$ $S_4\times C_2$ (as 6T11) $[6]$ $257.844555041$
6.2.14856594000.3 $x^{6} - 2 x^{5} + 8 x^{4} + 64 x^{3} + 60 x^{2} + 296 x + 524$ $2^{4}\cdot 3\cdot 5^{3}\cdot 19^{5}$ $S_4\times C_2$ (as 6T11) $[6]$ $142.277248721$
6.0.16480914944.1 $x^{6} - 38 x^{3} + 152 x^{2} - 304 x + 665$ $-\,2^{9}\cdot 13\cdot 19^{5}$ $S_4\times C_2$ (as 6T11) $[2, 6]$ $122.946853133$
6.2.17114796288.3 $x^{6} - 2 x^{5} + 8 x^{4} - 12 x^{3} - 111 x^{2} - 46 x - 8$ $2^{8}\cdot 3^{3}\cdot 19^{5}$ $S_4\times C_2$ (as 6T11) $[12]$ $430.403173701$
6.2.17114796288.4 $x^{6} - 2 x^{5} + 8 x^{4} - 12 x^{3} + 60 x^{2} - 768 x + 1056$ $2^{8}\cdot 3^{3}\cdot 19^{5}$ $\PGL(2,5)$ (as 6T14) $[3]$ $2184.02214118$
6.0.17471354544.1 $x^{6} - x^{5} - 36 x^{4} + 141 x^{3} + 588 x^{2} - 2513 x + 2401$ $-\,2^{4}\cdot 3^{2}\cdot 7^{2}\cdot 19^{5}$ $D_{6}$ (as 6T3) $[3]$ $296.818695167$
6.0.17748677632.1 $x^{6} - 3 x^{5} - 20 x^{4} + 26 x^{3} + 223 x^{2} + 343 x + 182$ $-\,2^{10}\cdot 7\cdot 19^{5}$ $S_4\times C_2$ (as 6T11) $[6]$ $569.259414457$
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