LMFDB - Global number field search results

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Results (displaying matches 1-50 of at least 1000) Next

Label	Polynomial	Discriminant	Galois group	Class group
3.1.54893107083.1	x³ - 135269	$ -\,3\cdot 17^{2}\cdot 73^{2}\cdot 109^{2} $	$S_3$ (as 3T2)	$[3, 3, 1143]$
3.1.257262282732.1	x³ - 585676	$ -\,2^{2}\cdot 3\cdot 7^{2}\cdot 13^{2}\cdot 1609^{2} $	$S_3$ (as 3T2)	$[3, 3, 1287]$
3.1.392652134523.1	x³ - 2291267	$ -\,3^{3}\cdot 11^{2}\cdot 19^{2}\cdot 577^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 387]$
3.1.495241833996.13	x³ + 81396x - 81396	$ -\,2^{2}\cdot 3^{4}\cdot 7^{2}\cdot 13\cdot 17^{2}\cdot 19^{2}\cdot 23 $	$S_3$ (as 3T2)	$[3, 3, 3, 429]$
3.1.976650374700.12	x³ - 29289260	$ -\,2^{2}\cdot 3^{3}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 19^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 129]$
3.1.1168285253292.1	x³ - 1248084	$ -\,2^{2}\cdot 3^{5}\cdot 37^{2}\cdot 937^{2} $	$S_3$ (as 3T2)	$[3, 3, 1404]$
3.1.1212366355308.1	x³ - 1271412	$ -\,2^{2}\cdot 3^{5}\cdot 35317^{2} $	$S_3$ (as 3T2)	$[6, 2700]$
3.1.1341117996300.24	x³ - 63517950	$ -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 444]$
3.1.1537134688908.25	x³ - 63468132	$ -\,2^{2}\cdot 3^{5}\cdot 7^{2}\cdot 13^{2}\cdot 19^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 6, 186]$
3.1.1635247380627.1	x³ - 246099	$ -\,3^{5}\cdot 7^{2}\cdot 11719^{2} $	$S_3$ (as 3T2)	$[3, 3, 2646]$
3.1.1742439528963.1	x³ - 254037	$ -\,3^{5}\cdot 7^{2}\cdot 12097^{2} $	$S_3$ (as 3T2)	$[3, 3, 3186]$
3.1.2110227909075.8	x³ - 52278655	$ -\,3^{3}\cdot 5^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 570]$
3.1.2164879392588.1	x³ - 283162	$ -\,2^{2}\cdot 3^{3}\cdot 11^{2}\cdot 61^{2}\cdot 211^{2} $	$S_3$ (as 3T2)	$[3, 3, 6, 300]$
3.1.2300141660652.1	x³ - 291874	$ -\,2^{2}\cdot 3^{3}\cdot 11^{2}\cdot 13267^{2} $	$S_3$ (as 3T2)	$[3, 6, 912]$
3.1.2628591272748.5	x³ - 11856684	$ -\,2^{2}\cdot 3^{5}\cdot 7^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 546]$
3.1.2830346831907.1	x³ - 323771	$ -\,3^{3}\cdot 7^{2}\cdot 23^{2}\cdot 2011^{2} $	$S_3$ (as 3T2)	$[3, 6, 1740]$
3.1.2999274043923.1	x³ - 333293	$ -\,3^{3}\cdot 23^{2}\cdot 43^{2}\cdot 337^{2} $	$S_3$ (as 3T2)	$[3, 6, 1596]$
3.1.3057089042700.8	x³ - 2355430	$ -\,2^{2}\cdot 3^{3}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 19^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 6, 126]$
3.1.3418220414700.7	x³ - 211706950	$ -\,2^{2}\cdot 3^{3}\cdot 5^{2}\cdot 7^{2}\cdot 13^{2}\cdot 17^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 285]$
3.1.3709538592588.1	x³ - 370662	$ -\,2^{2}\cdot 3^{5}\cdot 163^{2}\cdot 379^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 609]$
3.1.3795781578732.3	x³ - 1124838	$ -\,2^{2}\cdot 3^{5}\cdot 11^{2}\cdot 13^{2}\cdot 19^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 684]$
3.1.3814025824332.1	x³ - 375846	$ -\,2^{2}\cdot 3^{5}\cdot 37^{2}\cdot 1693^{2} $	$S_3$ (as 3T2)	$[3, 18, 414]$
3.1.4136046701787.9	x³ - 86497411	$ -\,3^{3}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 6, 504]$ (GRH)
3.1.4269357352260.19	x³ + 513513x - 77483406	$ -\,2^{2}\cdot 3^{5}\cdot 5\cdot 7\cdot 11^{2}\cdot 13^{2}\cdot 17\cdot 19^{2} $	$S_3$ (as 3T2)	$[3, 3, 1956]$ (GRH)
3.1.5248486827675.31	x³ - 9258795	$ -\,3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 969]$ (GRH)
3.1.5506571052675.21	x³ - 38386425	$ -\,3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 17^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 546]$ (GRH)
3.1.5760244046700.12	x³ - 39260650	$ -\,2^{2}\cdot 3^{3}\cdot 5^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 228]$ (GRH)
3.1.5760244046700.18	x³ - 86373430	$ -\,2^{2}\cdot 3^{3}\cdot 5^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 243]$ (GRH)
3.1.6585083726760.1	x³ + 500973x - 43410554	$ -\,2^{3}\cdot 3^{4}\cdot 5\cdot 7\cdot 11^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23 $	$S_3$ (as 3T2)	$[3, 3, 1203]$ (GRH)
3.1.7036752422700.2	x³ - 10720710	$ -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 6, 90]$ (GRH)
3.1.7036752422700.41	x³ - 364504140	$ -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 315]$ (GRH)
3.1.7301642424300.17	x³ - 59803450	$ -\,2^{2}\cdot 3^{3}\cdot 5^{2}\cdot 7^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 300]$ (GRH)
3.1.7640727985800.4	x³ + 188370x - 9878960	$ -\,2^{3}\cdot 3^{3}\cdot 5^{2}\cdot 7^{2}\cdot 13^{2}\cdot 17\cdot 19\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 18, 90]$ (GRH)
3.1.8440911636300.14	x³ - 399777950	$ -\,2^{2}\cdot 3^{3}\cdot 5^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 6, 90]$ (GRH)
3.1.8789853372300.5	x³ - 1141140	$ -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 19^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 288]$ (GRH)
3.1.8789853372300.20	x³ - 188288100	$ -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 19^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 162]$ (GRH)
3.1.8789853372300.36	x³ - 32522490	$ -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 19^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 240]$ (GRH)
3.1.8789853372300.41	x³ - 37657620	$ -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 19^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 180]$ (GRH)
3.1.8789853372300.57	x³ - 7417410	$ -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 19^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 288]$ (GRH)
3.1.9065957654988.6	x³ - 15066012	$ -\,2^{2}\cdot 3^{5}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 822]$ (GRH)
3.1.9607091805675.6	x³ - 162845865	$ -\,3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 13^{2}\cdot 19^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 6, 558]$ (GRH)
3.1.10543837718700.14	x³ - 34370050	$ -\,2^{2}\cdot 3^{3}\cdot 5^{2}\cdot 11^{2}\cdot 13^{2}\cdot 19^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 126]$ (GRH)
3.1.10543837718700.20	x³ - 8123830	$ -\,2^{2}\cdot 3^{3}\cdot 5^{2}\cdot 11^{2}\cdot 13^{2}\cdot 19^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 138]$ (GRH)
3.1.11290078331532.5	x³ - 153901748	$ -\,2^{2}\cdot 3^{3}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 180]$ (GRH)
3.1.11489018616075.7	x³ - x² - 652318x + 214467772	$ -\,3\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 6, 792]$ (GRH)
3.1.12960549105075.28	x³ - 65819325	$ -\,3^{5}\cdot 5^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 1272]$ (GRH)
3.1.15031169376300.6	x³ - 126842100	$ -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 17^{2}\cdot 19^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 288]$ (GRH)
3.1.15031169376300.39	x³ - 418578930	$ -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 17^{2}\cdot 19^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 327]$ (GRH)
3.1.16428695454675.2	x³ - 11700675	$ -\,3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 6, 264]$ (GRH)
3.1.16544186807148.18	x³ - 612135524	$ -\,2^{2}\cdot 3^{3}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 243]$ (GRH)

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	Polynomial	Discriminant	Galois group	Class group
3.1.54893107083.1	x³ - 135269	\( -\,3\cdot 17^{2}\cdot 73^{2}\cdot 109^{2} \)	$S_3$ (as 3T2)	$[3, 3, 1143]$
3.1.257262282732.1	x³ - 585676	\( -\,2^{2}\cdot 3\cdot 7^{2}\cdot 13^{2}\cdot 1609^{2} \)	$S_3$ (as 3T2)	$[3, 3, 1287]$
3.1.392652134523.1	x³ - 2291267	\( -\,3^{3}\cdot 11^{2}\cdot 19^{2}\cdot 577^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 387]$
3.1.495241833996.13	x³ + 81396x - 81396	\( -\,2^{2}\cdot 3^{4}\cdot 7^{2}\cdot 13\cdot 17^{2}\cdot 19^{2}\cdot 23 \)	$S_3$ (as 3T2)	$[3, 3, 3, 429]$
3.1.976650374700.12	x³ - 29289260	\( -\,2^{2}\cdot 3^{3}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 19^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 129]$
3.1.1168285253292.1	x³ - 1248084	\( -\,2^{2}\cdot 3^{5}\cdot 37^{2}\cdot 937^{2} \)	$S_3$ (as 3T2)	$[3, 3, 1404]$
3.1.1212366355308.1	x³ - 1271412	\( -\,2^{2}\cdot 3^{5}\cdot 35317^{2} \)	$S_3$ (as 3T2)	$[6, 2700]$
3.1.1341117996300.24	x³ - 63517950	\( -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 444]$
3.1.1537134688908.25	x³ - 63468132	\( -\,2^{2}\cdot 3^{5}\cdot 7^{2}\cdot 13^{2}\cdot 19^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 6, 186]$
3.1.1635247380627.1	x³ - 246099	\( -\,3^{5}\cdot 7^{2}\cdot 11719^{2} \)	$S_3$ (as 3T2)	$[3, 3, 2646]$
3.1.1742439528963.1	x³ - 254037	\( -\,3^{5}\cdot 7^{2}\cdot 12097^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3186]$
3.1.2110227909075.8	x³ - 52278655	\( -\,3^{3}\cdot 5^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 570]$
3.1.2164879392588.1	x³ - 283162	\( -\,2^{2}\cdot 3^{3}\cdot 11^{2}\cdot 61^{2}\cdot 211^{2} \)	$S_3$ (as 3T2)	$[3, 3, 6, 300]$
3.1.2300141660652.1	x³ - 291874	\( -\,2^{2}\cdot 3^{3}\cdot 11^{2}\cdot 13267^{2} \)	$S_3$ (as 3T2)	$[3, 6, 912]$
3.1.2628591272748.5	x³ - 11856684	\( -\,2^{2}\cdot 3^{5}\cdot 7^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 546]$
3.1.2830346831907.1	x³ - 323771	\( -\,3^{3}\cdot 7^{2}\cdot 23^{2}\cdot 2011^{2} \)	$S_3$ (as 3T2)	$[3, 6, 1740]$
3.1.2999274043923.1	x³ - 333293	\( -\,3^{3}\cdot 23^{2}\cdot 43^{2}\cdot 337^{2} \)	$S_3$ (as 3T2)	$[3, 6, 1596]$
3.1.3057089042700.8	x³ - 2355430	\( -\,2^{2}\cdot 3^{3}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 19^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 6, 126]$
3.1.3418220414700.7	x³ - 211706950	\( -\,2^{2}\cdot 3^{3}\cdot 5^{2}\cdot 7^{2}\cdot 13^{2}\cdot 17^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 285]$
3.1.3709538592588.1	x³ - 370662	\( -\,2^{2}\cdot 3^{5}\cdot 163^{2}\cdot 379^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 609]$
3.1.3795781578732.3	x³ - 1124838	\( -\,2^{2}\cdot 3^{5}\cdot 11^{2}\cdot 13^{2}\cdot 19^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 684]$
3.1.3814025824332.1	x³ - 375846	\( -\,2^{2}\cdot 3^{5}\cdot 37^{2}\cdot 1693^{2} \)	$S_3$ (as 3T2)	$[3, 18, 414]$
3.1.4136046701787.9	x³ - 86497411	\( -\,3^{3}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 6, 504]$ (GRH)
3.1.4269357352260.19	x³ + 513513x - 77483406	\( -\,2^{2}\cdot 3^{5}\cdot 5\cdot 7\cdot 11^{2}\cdot 13^{2}\cdot 17\cdot 19^{2} \)	$S_3$ (as 3T2)	$[3, 3, 1956]$ (GRH)
3.1.5248486827675.31	x³ - 9258795	\( -\,3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 969]$ (GRH)
3.1.5506571052675.21	x³ - 38386425	\( -\,3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 17^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 546]$ (GRH)
3.1.5760244046700.12	x³ - 39260650	\( -\,2^{2}\cdot 3^{3}\cdot 5^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 228]$ (GRH)
3.1.5760244046700.18	x³ - 86373430	\( -\,2^{2}\cdot 3^{3}\cdot 5^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 243]$ (GRH)
3.1.6585083726760.1	x³ + 500973x - 43410554	\( -\,2^{3}\cdot 3^{4}\cdot 5\cdot 7\cdot 11^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23 \)	$S_3$ (as 3T2)	$[3, 3, 1203]$ (GRH)
3.1.7036752422700.2	x³ - 10720710	\( -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 6, 90]$ (GRH)
3.1.7036752422700.41	x³ - 364504140	\( -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 315]$ (GRH)
3.1.7301642424300.17	x³ - 59803450	\( -\,2^{2}\cdot 3^{3}\cdot 5^{2}\cdot 7^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 300]$ (GRH)
3.1.7640727985800.4	x³ + 188370x - 9878960	\( -\,2^{3}\cdot 3^{3}\cdot 5^{2}\cdot 7^{2}\cdot 13^{2}\cdot 17\cdot 19\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 18, 90]$ (GRH)
3.1.8440911636300.14	x³ - 399777950	\( -\,2^{2}\cdot 3^{3}\cdot 5^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 6, 90]$ (GRH)
3.1.8789853372300.5	x³ - 1141140	\( -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 19^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 288]$ (GRH)
3.1.8789853372300.20	x³ - 188288100	\( -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 19^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 162]$ (GRH)
3.1.8789853372300.36	x³ - 32522490	\( -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 19^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 240]$ (GRH)
3.1.8789853372300.41	x³ - 37657620	\( -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 19^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 180]$ (GRH)
3.1.8789853372300.57	x³ - 7417410	\( -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 19^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 288]$ (GRH)
3.1.9065957654988.6	x³ - 15066012	\( -\,2^{2}\cdot 3^{5}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 822]$ (GRH)
3.1.9607091805675.6	x³ - 162845865	\( -\,3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 13^{2}\cdot 19^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 6, 558]$ (GRH)
3.1.10543837718700.14	x³ - 34370050	\( -\,2^{2}\cdot 3^{3}\cdot 5^{2}\cdot 11^{2}\cdot 13^{2}\cdot 19^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 126]$ (GRH)
3.1.10543837718700.20	x³ - 8123830	\( -\,2^{2}\cdot 3^{3}\cdot 5^{2}\cdot 11^{2}\cdot 13^{2}\cdot 19^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 138]$ (GRH)
3.1.11290078331532.5	x³ - 153901748	\( -\,2^{2}\cdot 3^{3}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 180]$ (GRH)
3.1.11489018616075.7	x³ - x² - 652318x + 214467772	\( -\,3\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 6, 792]$ (GRH)
3.1.12960549105075.28	x³ - 65819325	\( -\,3^{5}\cdot 5^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 1272]$ (GRH)
3.1.15031169376300.6	x³ - 126842100	\( -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 17^{2}\cdot 19^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 288]$ (GRH)
3.1.15031169376300.39	x³ - 418578930	\( -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 17^{2}\cdot 19^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 327]$ (GRH)
3.1.16428695454675.2	x³ - 11700675	\( -\,3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 6, 264]$ (GRH)
3.1.16544186807148.18	x³ - 612135524	\( -\,2^{2}\cdot 3^{3}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 243]$ (GRH)