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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
6.0.1778112.1	$x^{6} + 3 x^{4} - 2 x^{3} + 6 x^{2} + 1$	$6$	[0,3]	$-\,2^{6}\cdot 3^{4}\cdot 7^{3}$	$3$	$11.0067690039$	$29.3133549806909$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$7.66963675212$
6.0.2177712.1	$x^{6} - x^{5} - 4 x^{2} + 8$	$6$	[0,3]	$-\,2^{4}\cdot 3^{3}\cdot 71^{2}$	$3$	$11.3850097631$	$33.442143949031745$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$17.6663598699$
6.2.2299968.1	$x^{6} - 2 x^{5} - x^{4} + 4 x^{3} - 4 x^{2} + 4 x + 1$	$6$	[2,2]	$2^{6}\cdot 3^{3}\cdot 11^{3}$	$3$	$11.4891252931$	$38.94309359419253$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$3$	$8.94858785913$
6.0.2611467.1	$x^{6} - 3 x^{5} + 7 x^{4} - 6 x^{3} + 6 x^{2} - 7 x + 5$	$6$	[0,3]	$-\,3^{3}\cdot 311^{2}$	$2$	$11.7349368552$	$40.199544816599136$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$8.73416086387$
6.0.2725888.1	$x^{6} - x^{5} + 2 x^{4} - 4 x^{3} + 4 x^{2} + 4 x + 8$	$6$	[0,3]	$-\,2^{11}\cdot 11^{3}$	$2$	$11.8191070971$	$40.63282352308103$				$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$27.7367899009$
6.2.2725888.5	$x^{6} - x^{5} - x^{4} + 2 x^{3} - 5 x^{2} - x - 3$	$6$	[2,2]	$2^{11}\cdot 11^{3}$	$2$	$11.8191070971$	$40.63282352308103$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$3$	$18.6829042442$
6.2.3200000.1	$x^{6} - 2 x^{5} + 4 x + 2$	$6$	[2,2]	$2^{10}\cdot 5^{5}$	$2$	$12.1392446201$	$28.57900880593445$			✓	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$3$	$15.5733986742$
6.0.3421872.4	$x^{6} - 2 x^{5} + 6 x^{4} - 12 x^{3} + 14 x^{2} - 10 x + 4$	$6$	[0,3]	$-\,2^{4}\cdot 3^{3}\cdot 89^{2}$	$3$	$12.2756348091$	$28.44982682753188$			?	$\PGL(2,5)$ (as 6T14)	$[4]$	$2$	$2$	$5.3725526246$
6.0.3479787.1	$x^{6} - 3 x^{5} + 4 x^{4} - 3 x^{2} + 3 x + 3$	$6$	[0,3]	$-\,3^{3}\cdot 359^{2}$	$2$	$12.3100205204$	$43.190493395557326$			✓	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$9.57099207339$
6.0.3786752.3	$x^{6} - x^{5} + 3 x^{4} - 4 x^{3} + 2 x^{2} - 6 x + 10$	$6$	[0,3]	$-\,2^{11}\cdot 43^{2}$	$2$	$12.4846913645$	$44.11301238665728$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$14.013439558$
6.0.3895843.1	$x^{6} - x^{5} + x^{4} - 2 x^{3} + 2 x^{2} - x + 3$	$6$	[0,3]	$-\,7^{2}\cdot 43^{3}$	$2$	$12.5439286323$	$44.42734513579336$			✓	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$8.75310751929$
6.2.5000000.1	$x^{6} - 2 x^{5} - 8 x - 4$	$6$	[2,2]	$2^{6}\cdot 5^{7}$	$2$	$13.0766048601$	$27.202271339006447$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$3$	$22.9563447187$
6.2.5256144.1	$x^{6} - x^{5} - 2 x^{4} - 2 x^{3} + x^{2} + 5 x + 4$	$6$	[2,2]	$2^{4}\cdot 3^{3}\cdot 23^{3}$	$3$	$13.1859434583$	$41.68317719787903$			✓	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$3$	$38.3435411021$
6.0.5400000.3	$x^{6} - 2 x^{5} + 5 x^{2} + 2 x + 1$	$6$	[0,3]	$-\,2^{6}\cdot 3^{3}\cdot 5^{5}$	$3$	$13.2454167278$	$31.18323200079904$			✓	$\PGL(2,5)$ (as 6T14)	$[2]$	$2$	$2$	$4.93230060794$
6.0.5400000.4	$x^{6} - 2 x^{5} + 5 x^{4} + 6 x + 3$	$6$	[0,3]	$-\,2^{6}\cdot 3^{3}\cdot 5^{5}$	$3$	$13.2454167278$	$41.03944127612018$			✓	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$13.8203686028$
6.2.5778125.2	$x^{6} - 5 x^{2} - 6 x - 5$	$6$	[2,2]	$5^{5}\cdot 43^{2}$	$2$	$13.3956714983$	$41.739739355256155$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$3$	$21.401504859$
6.0.5787963.1	$x^{6} - x^{5} + 4 x^{4} - 12 x^{3} + 15 x^{2} - 9 x + 3$	$6$	[0,3]	$-\,3^{3}\cdot 463^{2}$	$2$	$13.3994701129$	$49.04914445444661$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$12.1291618824$
6.0.6154544.2	$x^{6} - 2 x^{5} + 5 x^{4} - 2 x^{3} + 6 x^{2} + 12 x + 4$	$6$	[0,3]	$-\,2^{4}\cdot 11^{3}\cdot 17^{2}$	$3$	$13.5373184967$	$49.80798473323167$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$34.7329016144$
6.0.6627103.2	$x^{6} - 2 x^{5} - 8 x^{3} + 21 x^{2} - 8 x + 1$	$6$	[0,3]	$-\,7^{3}\cdot 139^{2}$	$2$	$13.7052602488$	$50.73771797850044$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$10.0973990726$
6.0.6750000.1	$x^{6} - x^{5} + 5 x^{2} + 3 x + 2$	$6$	[0,3]	$-\,2^{4}\cdot 3^{3}\cdot 5^{6}$	$3$	$13.74729637$	$32.16073334649287$			✓	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$42.3233145267$
6.0.7129088.4	$x^{6} - 3 x^{5} + 7 x^{4} - 4 x^{3} + 8 x^{2} - 4 x + 4$	$6$	[0,3]	$-\,2^{11}\cdot 59^{2}$	$2$	$13.8730620665$	$51.6723833953922$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$20.5428136872$
6.0.8108208.2	$x^{6} - 3 x^{5} + 4 x^{4} - 2 x + 2$	$6$	[0,3]	$-\,2^{4}\cdot 3^{3}\cdot 137^{2}$	$3$	$14.1738385061$	$46.45422521927823$			✓	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$44.1031162279$
6.0.9148592.2	$x^{6} - x^{5} + 4 x^{4} + x^{2} + 3 x + 2$	$6$	[0,3]	$-\,2^{4}\cdot 83^{3}$	$2$	$14.4619118474$	$47.877621361804$			✓	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$46.6823817044$
6.2.9483264.1	$x^{6} - 2 x^{5} + x^{4} - 4 x^{3} + 7 x^{2} - 2 x - 5$	$6$	[2,2]	$2^{10}\cdot 3^{3}\cdot 7^{3}$	$3$	$14.5487709578$	$44.04495071120707$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$3$	$36.4613498789$
6.0.9590832.1	$x^{6} - x^{5} + 4 x^{4} + 4 x^{3} + x^{2} + 3 x + 10$	$6$	[0,3]	$-\,2^{4}\cdot 3^{3}\cdot 149^{2}$	$3$	$14.5761461422$	$36.811012081445085$			?	$\PGL(2,5)$ (as 6T14)	$[4]$	$2$	$2$	$9.58735606627$
6.2.9800000.2	$x^{6} - 10 x^{3} - 4 x + 5$	$6$	[2,2]	$2^{6}\cdot 5^{5}\cdot 7^{2}$	$3$	$14.628653257$	$47.63317368567695$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$3$	$34.6257839335$
6.0.9834496.1	$x^{6} - 2 x^{5} + 3 x^{4} - 4 x^{3} + 5 x^{2} - 6 x + 7$	$6$	[0,3]	$-\,2^{12}\cdot 7^{4}$	$2$	$14.6372228401$	$31.90883292885454$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$31.6560004442$
6.0.10209375.1	$x^{6} - 2 x^{5} + 5 x^{4} + 9 x + 12$	$6$	[0,3]	$-\,3^{3}\cdot 5^{5}\cdot 11^{2}$	$3$	$14.7287715469$	$48.12301053396556$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$30.6381933629$
6.2.10368000.1	$x^{6} - 2 x^{5} + 4 x^{4} - 4 x^{3} + 2 x^{2} - 4 x - 6$	$6$	[2,2]	$2^{10}\cdot 3^{4}\cdot 5^{3}$	$3$	$14.7666675706$	$24.1776264427508$			?	$\PGL(2,5)$ (as 6T14)	$[2]$	$2$	$3$	$21.9198018435$
6.0.10546875.1	$x^{6} - 5 x^{4} + 15 x^{2} - 11 x + 5$	$6$	[0,3]	$-\,3^{3}\cdot 5^{8}$	$2$	$14.8088260968$	$29.935943327131625$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$17.5548258232$
6.2.10731125.1	$x^{6} - x^{5} + 2 x^{4} + 4 x^{3} - 3 x^{2} - 3 x + 1$	$6$	[2,2]	$5^{3}\cdot 293^{2}$	$2$	$14.8516330053$	$38.27531841800928$			✓	$\PGL(2,5)$ (as 6T14)	$[2]$	$2$	$3$	$6.81902608276$
6.0.10784448.3	$x^{6} - 2 x^{5} + 4 x^{4} - 4 x^{3} + 4 x^{2} + 4 x + 4$	$6$	[0,3]	$-\,2^{6}\cdot 3^{3}\cdot 79^{2}$	$3$	$14.8639072536$	$45.48373790490821$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$34.1944381174$
6.0.10916416.1	$x^{6} - 2 x^{5} + 2 x^{4} + 7 x^{2} + 1$	$6$	[0,3]	$-\,2^{6}\cdot 7^{2}\cdot 59^{2}$	$3$	$14.8940684767$	$40.64480286580315$			?	$\PGL(2,5)$ (as 6T14)	$[4]$	$2$	$2$	$5.4020629411$
6.2.11366912.2	$x^{6} - 2 x^{5} + 7 x^{4} - 10 x^{3} + 12 x^{2} - 8 x + 1$	$6$	[2,2]	$2^{9}\cdot 149^{2}$	$2$	$14.9947909805$	$34.52535300326414$			✓	$\PGL(2,5)$ (as 6T14)	$[2]$	$2$	$3$	$11.2091815101$
6.0.12800000.1	$x^{6} - 2 x^{5} + 5 x^{4} + 4 x + 2$	$6$	[0,3]	$-\,2^{12}\cdot 5^{5}$	$2$	$15.2944898266$	$42.82013114405259$			✓	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$61.8109645217$
6.2.12869712.1	$x^{6} - x^{5} - x^{3} + 4 x^{2} + 3 x - 9$	$6$	[2,2]	$2^{4}\cdot 3^{3}\cdot 31^{3}$	$3$	$15.3083413628$	$47.53887228405204$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$3$	$34.8170402258$
6.2.13203125.1	$x^{6} - x^{5} - 4 x - 1$	$6$	[2,2]	$5^{7}\cdot 13^{2}$	$2$	$15.3737373026$	$43.68930970521314$			✓	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$3$	$18.2488150839$
6.2.13530125.1	$x^{6} - 2 x^{5} + 3 x^{4} - x^{3} + 2 x^{2} + 3 x - 1$	$6$	[2,2]	$5^{3}\cdot 7^{2}\cdot 47^{2}$	$3$	$15.4365520444$	$60.64925245200599$			✓	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$3$	$20.0167357786$
6.2.13530125.2	$x^{6} - 3 x^{4} - 2 x^{3} + 11 x^{2} - 7 x + 1$	$6$	[2,2]	$5^{3}\cdot 7^{2}\cdot 47^{2}$	$3$	$15.4365520444$	$40.55859958134649$			✓	$\PGL(2,5)$ (as 6T14)	$[2]$	$2$	$3$	$8.49157891171$
6.0.13687488.1	$x^{6} - x^{5} + x^{4} + x^{3} + x^{2} - x + 4$	$6$	[0,3]	$-\,2^{6}\cdot 3^{3}\cdot 89^{2}$	$3$	$15.4663306968$	$60.82483477139187$			✓	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$55.9028130089$
6.0.13841712.3	$x^{6} - 2 x^{5} + 8 x^{4} - 12 x^{3} + 12 x^{2} - 10 x + 4$	$6$	[0,3]	$-\,2^{4}\cdot 3^{3}\cdot 179^{2}$	$3$	$15.4952397934$	$40.34698988068586$			?	$\PGL(2,5)$ (as 6T14)	$[4]$	$2$	$2$	$9.45065645161$
6.0.14625792.2	$x^{6} - 2 x^{5} + 5 x^{4} - 12 x^{3} + 15 x^{2} - 18 x + 15$	$6$	[0,3]	$-\,2^{10}\cdot 3^{3}\cdot 23^{2}$	$3$	$15.6381928835$	$49.08361221655921$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$39.4471392322$
6.0.14697207.1	$x^{6} - x^{5} + 3 x^{4} + 6 x^{2} + 3$	$6$	[0,3]	$-\,3^{4}\cdot 7^{3}\cdot 23^{2}$	$3$	$15.6508934626$	$49.70321159788357$			✓	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$38.4305857854$
6.2.14792000.2	$x^{6} - 3 x^{4} - 8 x^{3} - 9 x^{2} - 8 x - 4$	$6$	[2,2]	$2^{6}\cdot 5^{3}\cdot 43^{2}$	$3$	$15.6676724305$	$41.47288270665544$			?	$\PGL(2,5)$ (as 6T14)	$[2]$	$2$	$3$	$20.0397950081$
6.2.15000633.1	$x^{6} - 3 x^{5} - 3 x^{4} + 4 x^{3} - 12 x^{2} + 6 x - 5$	$6$	[2,2]	$3^{7}\cdot 19^{3}$	$2$	$15.7042884755$	$32.78737625893961$			✓	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$3$	$48.9955672887$
6.0.15106608.2	$x^{6} - 3 x^{5} + 4 x^{4} + 6 x^{2} + 2 x + 2$	$6$	[0,3]	$-\,2^{4}\cdot 3^{3}\cdot 11^{2}\cdot 17^{2}$	$4$	$15.7227252981$	$54.2732390008592$			✓	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$52.8636670977$
6.0.15268608.1	$x^{6} - 2 x^{5} + 2 x^{4} + 3 x^{2} - 18 x + 18$	$6$	[0,3]	$-\,2^{8}\cdot 3^{3}\cdot 47^{2}$	$3$	$15.7507017366$	$62.510052166634665$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$2$	$35.9635639851$
6.0.16133283.3	$x^{6} - x^{5} + 3 x^{4} + 9 x^{3} + 5 x^{2} - 2 x + 1$	$6$	[0,3]	$-\,3^{3}\cdot 773^{2}$	$2$	$15.8959733257$	$48.155996511338024$			?	$\PGL(2,5)$ (as 6T14)	$[4]$	$2$	$2$	$8.60637589824$
6.2.16200000.1	$x^{6} - 2 x^{5} - 6 x - 3$	$6$	[2,2]	$2^{6}\cdot 3^{4}\cdot 5^{5}$	$3$	$15.9069104351$	$43.356828069359494$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$3$	$77.61245252$
6.2.16200000.2	$x^{6} - 2 x^{5} + 5 x^{4} - 5 x^{2} + 8 x - 1$	$6$	[2,2]	$2^{6}\cdot 3^{4}\cdot 5^{5}$	$3$	$15.9069104351$	$34.41233724365281$			?	$\PGL(2,5)$ (as 6T14)	trivial	$2$	$3$	$66.4566196514$

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