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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
6.0.121328851.1	x^6 - 3x^5 - x^4 - 12x^3 + 71x^2 + 96x + 163	$6$	[0,3]	$-\,7^{2}\cdot 19^{5}$	$2$	$22.2498633197$			?	$S_3\times C_3$ (as 6T5)	$[3]$	$2$	$2$	$25.678740087$
6.0.158470336.1	x^6 - 3x^5 - x^4 - 12x^3 + 52x^2 + 20x + 68	$6$	[0,3]	$-\,2^{6}\cdot 19^{5}$	$2$	$23.2625862551$				$D_{6}$ (as 6T3)	$[3]$	$2$	$2$	$33.1099798427$
6.2.255038197.2	x^6 - 3x^5 - x^4 + 7x^3 - 5x^2 - 18x - 8	$6$	[2,2]	$19^{5}\cdot 103$	$2$	$25.1826176489$			?	$S_6$ (as 6T16)	$[3]$	$2$	$3$	$109.257774467$
6.0.398651939.1	x^6 - x^5 + 2x^4 + 8x^3 + 18x^2 + 14x + 7	$6$	[0,3]	$-\,7\cdot 19^{5}\cdot 23$	$3$	$27.1289080431$			✓	$C_3^2:D_4$ (as 6T13)	$[6]$	$2$	$2$	$17.441380723$
6.0.633881344.1	x^6 - 2x^5 + 8x^4 - 12x^3 + 41x^2 - 46x + 68	$6$	[0,3]	$-\,2^{8}\cdot 19^{5}$	$2$	$29.3090220978$			?	$S_4\times C_2$ (as 6T11)	$[6]$	$2$	$2$	$17.7437539865$
6.0.775018987.1	x^6 - 2x^5 + 8x^4 - 12x^3 + 22x^2 - 27x + 11	$6$	[0,3]	$-\,19^{5}\cdot 313$	$2$	$30.3076356089$			✓	$C_3^2:D_4$ (as 6T13)	$[3]$	$2$	$2$	$27.0762162451$
6.0.814636571.1	x^6 - x^5 + 2x^4 - 11x^3 - x^2 + 14x + 7	$6$	[0,3]	$-\,7\cdot 19^{5}\cdot 47$	$3$	$30.560513722$			✓	$C_3^2:D_4$ (as 6T13)	$[3]$	$2$	$2$	$33.1239091084$
6.0.990439600.1	x^6 - x^5 + 2x^4 - 49x^3 + 132x^2 - 195x + 425	$6$	[0,3]	$-\,2^{4}\cdot 5^{2}\cdot 19^{5}$	$3$	$31.5721869692$	✓		?	$D_{6}$ (as 6T3)	$[3, 3]$	$2$	$2$	$33.5100484823$
6.0.1198431916.1	x^6 - 2x^5 + 8x^4 + 7x^3 + 22x^2 + 11x + 11	$6$	[0,3]	$-\,2^{2}\cdot 11^{2}\cdot 19^{5}$	$3$	$32.5913408098$			✓	$S_6$ (as 6T16)	$[12]$	$2$	$2$	$18.1491876721$
6.0.1238049500.1	x^6 - 3x^5 + 18x^4 - 12x^3 + 52x^2 + 96x + 144	$6$	[0,3]	$-\,2^{2}\cdot 5^{3}\cdot 19^{5}$	$3$	$32.7684828824$			?	$S_3^2$ (as 6T9)	$[24]$	$2$	$2$	$43.5806451898$
6.2.1267762688.2	x^6 - 38x^3 - 38x^2 - 76x + 323	$6$	[2,2]	$2^{9}\cdot 19^{5}$	$2$	$32.8982649779$			?	$D_{6}$ (as 6T3)	$[3]$	$2$	$3$	$142.50146044$
6.2.1604512152.2	x^6 - 3x^5 + 18x^4 + 7x^3 - 24x^2 - 18x - 8	$6$	[2,2]	$2^{3}\cdot 3^{4}\cdot 19^{5}$	$3$	$34.2155743935$			?	$S_6$ (as 6T16)	$[3]$	$2$	$3$	$563.484847448$
6.0.1941261616.2	x^6 - 2x^5 - 11x^4 + 26x^3 + 41x^2 - 8x + 125	$6$	[0,3]	$-\,2^{4}\cdot 7^{2}\cdot 19^{5}$	$3$	$35.3194564398$			?	$S_3\times C_3$ (as 6T5)	$[3, 3]$	$2$	$2$	$47.6633763961$
6.0.1941261616.4	x^6 - 3x^5 - 20x^4 + 45x^3 + 280x^2 + 381x + 163	$6$	[0,3]	$-\,2^{4}\cdot 7^{2}\cdot 19^{5}$	$3$	$35.3194564398$			?	$S_3\times C_3$ (as 6T5)	$[3, 3]$	$2$	$2$	$14.3254424945$
6.0.2693995712.1	x^6 - x^5 + 2x^4 - 11x^3 + 37x^2 + 14x + 26	$6$	[0,3]	$-\,2^{6}\cdot 17\cdot 19^{5}$	$3$	$37.3020600324$			?	$S_4\times C_2$ (as 6T11)	$[6]$	$2$	$2$	$120.778731975$
6.0.2785611375.2	x^6 - 2x^5 + 8x^4 + 7x^3 + 41x^2 + 49x + 49	$6$	[0,3]	$-\,3^{2}\cdot 5^{3}\cdot 19^{5}$	$3$	$37.5105490623$			?	$C_3^2:D_4$ (as 6T13)	$[3]$	$2$	$2$	$201.155012087$
6.2.2971318800.1	x^6 - x^5 - 17x^4 - 11x^3 + 56x^2 - 24x - 12	$6$	[2,2]	$2^{4}\cdot 3\cdot 5^{2}\cdot 19^{5}$	$4$	$37.9162060871$			?	$S_4\times C_2$ (as 6T11)	$[3]$	$2$	$3$	$347.761220736$
6.4.3961758400.1	x^6 - 2x^5 - 11x^4 - 12x^3 + 79x^2 - 8x - 65	$6$	[4,1]	$-\,2^{6}\cdot 5^{2}\cdot 19^{5}$	$3$	$39.7784629537$			?	$S_4\times C_2$ (as 6T11)	$[3]$	$2$	$4$	$491.373929148$
6.2.4278699072.6	x^6 - 3x^5 - 20x^4 + 26x^3 + 109x^2 + 229x + 106	$6$	[2,2]	$2^{6}\cdot 3^{3}\cdot 19^{5}$	$3$	$40.2919813093$				$D_{6}$ (as 6T3)	$[3]$	$2$	$3$	$1264.61896163$
6.0.4578307051.1	x^6 - x^5 + 21x^4 + 8x^3 + 37x^2 + 128x + 83	$6$	[0,3]	$-\,19^{5}\cdot 43^{2}$	$2$	$40.7490497829$			?	$S_3\times C_3$ (as 6T5)	$[3]$	$2$	$2$	$50.3262544452$
6.4.4952198000.1	x^6 - 3x^5 - x^4 + 7x^3 - 24x^2 + 20x + 68	$6$	[4,1]	$-\,2^{4}\cdot 5^{3}\cdot 19^{5}$	$3$	$41.2857013566$			?	$S_4\times C_2$ (as 6T11)	$[3]$	$2$	$4$	$802.340667575$
6.0.4952198000.1	x^6 - 3x^5 + 37x^4 - 69x^3 + 394x^2 - 360x + 1170	$6$	[0,3]	$-\,2^{4}\cdot 5^{3}\cdot 19^{5}$	$3$	$41.2857013566$	✓		?	$D_{6}$ (as 6T3)	$[3, 24]$	$2$	$2$	$33.5100484823$
6.2.5071050752.1	x^6 - 38x^2 - 76x - 38	$6$	[2,2]	$2^{11}\cdot 19^{5}$	$2$	$41.4492165506$			?	$S_3^2$ (as 6T9)	$[3]$	$2$	$3$	$172.468305585$
6.2.5071050752.2	x^6 - 19x^2 - 38	$6$	[2,2]	$2^{11}\cdot 19^{5}$	$2$	$41.4492165506$			?	$S_4\times C_2$ (as 6T11)	$[6]$	$2$	$3$	$302.368128692$
6.0.5945113699.1	x^6 - x^5 + 2x^4 + 122x^3 + 474x^2 + 888x + 881	$6$	[0,3]	$-\,7^{4}\cdot 19^{5}$	$2$	$42.5624573566$	✓	✓	?	$C_6$ (as 6T1)	$[3, 3]$	$2$	$2$	$43.4693954291$
6.0.6440333499.1	x^6 - x^5 - 17x^4 + 8x^3 + 113x^2 + 33x + 7	$6$	[0,3]	$-\,3^{2}\cdot 17^{2}\cdot 19^{5}$	$3$	$43.1338336893$				$D_{6}$ (as 6T3)	$[3]$	$2$	$2$	$179.112758889$
6.0.7220304684.1	x^6 - 3x^5 + 18x^4 - 31x^3 + 90x^2 - 18x + 11	$6$	[0,3]	$-\,2^{2}\cdot 3^{6}\cdot 19^{5}$	$3$	$43.9635331467$			?	$S_6$ (as 6T16)	$[6]$	$2$	$2$	$115.586430031$
6.2.7487723376.1	x^6 - x^5 + 2x^4 + 8x^3 - 172x^2 + 128x - 848	$6$	[2,2]	$2^{4}\cdot 3^{3}\cdot 7\cdot 19^{5}$	$4$	$44.2308173916$				$C_3^2:D_4$ (as 6T13)	$[3]$	$2$	$3$	$2562.62144217$
6.0.7765046464.3	x^6 - 2x^5 + 27x^4 - 12x^3 + 117x^2 + 106x + 334	$6$	[0,3]	$-\,2^{6}\cdot 7^{2}\cdot 19^{5}$	$3$	$44.4997266393$			?	$\PGL(2,5)$ (as 6T14)	$[6]$	$2$	$2$	$251.742416555$
6.2.8240457472.1	x^6 - 19x^4 - 76x^3 - 133x^2 - 114x - 38	$6$	[2,2]	$2^{8}\cdot 13\cdot 19^{5}$	$3$	$44.9426372856$			?	$S_4\times C_2$ (as 6T11)	$[6]$	$2$	$3$	$113.649646409$
6.4.8913956400.1	x^6 - 3x^5 - 20x^4 + 45x^3 - 100x^2 - 75x + 125	$6$	[4,1]	$-\,2^{4}\cdot 3^{2}\cdot 5^{2}\cdot 19^{5}$	$4$	$45.53497309$			?	$S_4\times C_2$ (as 6T11)	$[3]$	$2$	$4$	$972.144542593$
6.0.8913956400.2	x^6 - x^5 + 2x^4 - 11x^3 + 208x^2 - 81x + 729	$6$	[0,3]	$-\,2^{4}\cdot 3^{2}\cdot 5^{2}\cdot 19^{5}$	$4$	$45.53497309$			?	$S_3^2$ (as 6T9)	$[3, 3]$	$2$	$2$	$89.364999505$
6.0.9025380855.1	x^6 - 19x^3 + 171x^2 + 57x + 95	$6$	[0,3]	$-\,3^{6}\cdot 5\cdot 19^{5}$	$3$	$45.6293472724$			?	$C_3^2:D_4$ (as 6T13)	$[3]$	$2$	$2$	$145.956738157$
6.0.9213564379.1	x^6 - 2x^5 + 8x^4 + 26x^3 + 98x^2 + 68x + 277	$6$	[0,3]	$-\,19^{5}\cdot 61^{2}$	$2$	$45.7865526325$				$S_3\times C_3$ (as 6T5)	$[3]$	$2$	$2$	$190.951190149$
6.2.9594883625.1	x^6 - 2x^5 + 8x^4 + 26x^3 - 35x^2 + 125x + 125	$6$	[2,2]	$5^{3}\cdot 19^{5}\cdot 31$	$3$	$46.0970661173$			?	$S_6$ (as 6T16)	$[3]$	$2$	$3$	$445.812444761$
6.0.9706308080.1	x^6 - 2x^5 + 8x^4 + 26x^3 - 16x^2 + 106x + 277	$6$	[0,3]	$-\,2^{4}\cdot 5\cdot 7^{2}\cdot 19^{5}$	$4$	$46.1858575737$				$C_3^2:D_4$ (as 6T13)	$[3]$	$2$	$2$	$344.947400183$
6.0.11115208411.1	x^6 - x^5 + 40x^4 - 11x^3 + 607x^2 - 100x + 3028	$6$	[0,3]	$-\,19^{5}\cdot 67^{2}$	$2$	$47.241056508$				$D_{6}$ (as 6T3)	$[3]$	$2$	$2$	$436.357425607$
6.2.11885275200.1	x^6 - 2x^5 - 11x^4 - 12x^3 + 60x^2 - 160x + 220	$6$	[2,2]	$2^{6}\cdot 3\cdot 5^{2}\cdot 19^{5}$	$4$	$47.7714261812$			?	$S_6$ (as 6T16)	$[6]$	$2$	$3$	$832.113910247$
6.6.11885275200.1	x^6 - 19x^4 + 95x^2 - 57	$6$	[6,0]	$2^{6}\cdot 3\cdot 5^{2}\cdot 19^{5}$	$4$	$47.7714261812$			?	$S_4\times C_2$ (as 6T11)	$[3]$	$2$	$5$	$974.213798824$
6.0.12234405159.1	x^6 - 19x^3 - 114x^2 + 285x + 1900	$6$	[0,3]	$-\,3^{4}\cdot 19^{5}\cdot 61$	$3$	$48.0024948587$			?	$S_6$ (as 6T16)	$[2, 6]$	$2$	$2$	$145.36042744$
6.2.13103515908.2	x^6 - 3x^5 - x^4 - 50x^3 - 119x^2 - 113x + 49	$6$	[2,2]	$2^{2}\cdot 3^{3}\cdot 7^{2}\cdot 19^{5}$	$4$	$48.5547035305$			?	$S_3^2$ (as 6T9)	$[3]$	$2$	$3$	$1511.47519463$
6.2.13103515908.4	x^6 - 3x^5 - x^4 - 12x^3 - 5x^2 - 75x + 87	$6$	[2,2]	$2^{2}\cdot 3^{3}\cdot 7^{2}\cdot 19^{5}$	$4$	$48.5547035305$			?	$S_3^2$ (as 6T9)	$[3]$	$2$	$3$	$926.560177511$
6.2.14440609368.2	x^6 - 19x^3 - 57x^2 + 285x - 266	$6$	[2,2]	$2^{3}\cdot 3^{6}\cdot 19^{5}$	$3$	$49.3473974668$			?	$C_3^2:D_4$ (as 6T13)	$[3]$	$2$	$3$	$1232.72007801$
6.2.14856594000.2	x^6 - 3x^5 + 18x^4 - 31x^3 + 52x^2 - 37x - 103	$6$	[2,2]	$2^{4}\cdot 3\cdot 5^{3}\cdot 19^{5}$	$4$	$49.5815244795$			?	$S_4\times C_2$ (as 6T11)	$[6]$	$2$	$3$	$257.844555041$
6.2.14856594000.3	x^6 - 2x^5 + 8x^4 + 64x^3 + 60x^2 + 296x + 524	$6$	[2,2]	$2^{4}\cdot 3\cdot 5^{3}\cdot 19^{5}$	$4$	$49.5815244795$			?	$S_4\times C_2$ (as 6T11)	$[6]$	$2$	$3$	$142.277248721$
6.0.16480914944.1	x^6 - 38x^3 + 152x^2 - 304x + 665	$6$	[0,3]	$-\,2^{9}\cdot 13\cdot 19^{5}$	$3$	$50.4464047041$			?	$S_4\times C_2$ (as 6T11)	$[2, 6]$	$2$	$2$	$122.946853133$
6.2.17114796288.3	x^6 - 2x^5 + 8x^4 - 12x^3 - 111x^2 - 46x - 8	$6$	[2,2]	$2^{8}\cdot 3^{3}\cdot 19^{5}$	$3$	$50.7647153936$				$S_4\times C_2$ (as 6T11)	$[12]$	$2$	$3$	$430.403173701$
6.2.17114796288.4	x^6 - 2x^5 + 8x^4 - 12x^3 + 60x^2 - 768x + 1056	$6$	[2,2]	$2^{8}\cdot 3^{3}\cdot 19^{5}$	$3$	$50.7647153936$				$\PGL(2,5)$ (as 6T14)	$[3]$	$2$	$3$	$2184.02214118$
6.0.17471354544.1	x^6 - x^5 - 36x^4 + 141x^3 + 588x^2 - 2513x + 2401	$6$	[0,3]	$-\,2^{4}\cdot 3^{2}\cdot 7^{2}\cdot 19^{5}$	$4$	$50.9394708738$				$D_{6}$ (as 6T3)	$[3]$	$2$	$2$	$296.818695167$
6.0.17748677632.1	x^6 - 3x^5 - 20x^4 + 26x^3 + 223x^2 + 343x + 182	$6$	[0,3]	$-\,2^{10}\cdot 7\cdot 19^{5}$	$3$	$51.073348655$				$S_4\times C_2$ (as 6T11)	$[6]$	$2$	$2$	$569.259414457$

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