LMFDB - Global number field search results

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Results (displaying all 24 matches)

Label	Polynomial	Discriminant	Galois group	Class group
3.1.148897681264332.64	x³ - 98630532	$ -\,2^{2}\cdot 3^{5}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 6, 618]$ (GRH)
3.1.308494392426675.6	x³ - 2247829675	$ -\,3^{3}\cdot 5^{2}\cdot 7^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 1284]$ (GRH)
3.1.516648048216300.41	x³ - 9142433300	$ -\,2^{2}\cdot 3^{3}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 19^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 3, 873]$ (GRH)
3.1.2540267624594700.52	x³ - 21930999090	$ -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 6, 294]$ (GRH)
3.1.3047169100704300.21	x³ - 25825655570	$ -\,2^{2}\cdot 3^{3}\cdot 5^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 3, 651]$ (GRH)
3.1.3047169100704300.38	x³ - 584290850	$ -\,2^{2}\cdot 3^{3}\cdot 5^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 6, 666]$ (GRH)
3.1.5972451437380428.16	x³ - 26339831518	$ -\,2^{2}\cdot 3^{3}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 6, 234]$ (GRH)
3.1.5972451437380428.31	x³ - 4446984542	$ -\,2^{2}\cdot 3^{3}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 3, 2322]$ (GRH)
3.1.11105798127360300.54	x³ - 30320349150	$ -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 6, 264]$ (GRH)
3.1.11105798127360300.73	x³ - 42448488810	$ -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 3, 2565]$ (GRH)
3.1.11105798127360300.87	x³ - 5171698350	$ -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 3, 525]$ (GRH)
3.1.13438015734105963.62	x³ - 95952243387	$ -\,3^{5}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 6, 6, 396]$ (GRH)
3.1.37327821483627675.33	x³ - 57520778315	$ -\,3^{3}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 3, 444]$ (GRH)
3.1.37327821483627675.43	x³ - 9183989815	$ -\,3^{3}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 3, 918]$ (GRH)
3.1.53752062936423852.8	x³ - 11288499222	$ -\,2^{2}\cdot 3^{5}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 3, 2124]$ (GRH)
3.1.53752062936423852.64	x³ - 253478118894	$ -\,2^{2}\cdot 3^{5}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 3, 450]$ (GRH)
3.1.149311285934510700.42	x³ - 9667357700	$ -\,2^{2}\cdot 3^{3}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 3, 6, 84]$ (GRH)
3.1.335950393352649075.93	x³ - 557732175	$ -\,3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 3, 522]$ (GRH)
3.1.335950393352649075.110	x³ - 73955286405	$ -\,3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 6, 600]$ (GRH)
3.1.1343801573410596300.6	x³ - 292028566830	$ -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 3, 3, 174]$ (GRH)
3.1.1343801573410596300.11	x³ - 261687936510	$ -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 3, 3, 666]$ (GRH)
3.1.1343801573410596300.77	x³ - 42387645300	$ -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 3, 3, 162]$ (GRH)
3.1.1343801573410596300.118	x³ - 4238764530	$ -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 3, 3, 168]$ (GRH)
3.1.1343801573410596300.122	x³ - 2900207310	$ -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} $	$S_3$ (as 3T2)	$[3, 3, 3, 3, 3, 3, 264]$ (GRH)

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Further refine search

Results (displaying all 24 matches)

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
3.1.148897681264332.64	x³ - 98630532	\( -\,2^{2}\cdot 3^{5}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 6, 618]$ (GRH)
3.1.308494392426675.6	x³ - 2247829675	\( -\,3^{3}\cdot 5^{2}\cdot 7^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 1284]$ (GRH)
3.1.516648048216300.41	x³ - 9142433300	\( -\,2^{2}\cdot 3^{3}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 19^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 3, 873]$ (GRH)
3.1.2540267624594700.52	x³ - 21930999090	\( -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 6, 294]$ (GRH)
3.1.3047169100704300.21	x³ - 25825655570	\( -\,2^{2}\cdot 3^{3}\cdot 5^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 3, 651]$ (GRH)
3.1.3047169100704300.38	x³ - 584290850	\( -\,2^{2}\cdot 3^{3}\cdot 5^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 6, 666]$ (GRH)
3.1.5972451437380428.16	x³ - 26339831518	\( -\,2^{2}\cdot 3^{3}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 6, 234]$ (GRH)
3.1.5972451437380428.31	x³ - 4446984542	\( -\,2^{2}\cdot 3^{3}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 3, 2322]$ (GRH)
3.1.11105798127360300.54	x³ - 30320349150	\( -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 6, 264]$ (GRH)
3.1.11105798127360300.73	x³ - 42448488810	\( -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 3, 2565]$ (GRH)
3.1.11105798127360300.87	x³ - 5171698350	\( -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 3, 525]$ (GRH)
3.1.13438015734105963.62	x³ - 95952243387	\( -\,3^{5}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 6, 6, 396]$ (GRH)
3.1.37327821483627675.33	x³ - 57520778315	\( -\,3^{3}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 3, 444]$ (GRH)
3.1.37327821483627675.43	x³ - 9183989815	\( -\,3^{3}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 3, 918]$ (GRH)
3.1.53752062936423852.8	x³ - 11288499222	\( -\,2^{2}\cdot 3^{5}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 3, 2124]$ (GRH)
3.1.53752062936423852.64	x³ - 253478118894	\( -\,2^{2}\cdot 3^{5}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 3, 450]$ (GRH)
3.1.149311285934510700.42	x³ - 9667357700	\( -\,2^{2}\cdot 3^{3}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 3, 6, 84]$ (GRH)
3.1.335950393352649075.93	x³ - 557732175	\( -\,3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 3, 522]$ (GRH)
3.1.335950393352649075.110	x³ - 73955286405	\( -\,3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 6, 600]$ (GRH)
3.1.1343801573410596300.6	x³ - 292028566830	\( -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 3, 3, 174]$ (GRH)
3.1.1343801573410596300.11	x³ - 261687936510	\( -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 3, 3, 666]$ (GRH)
3.1.1343801573410596300.77	x³ - 42387645300	\( -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 3, 3, 162]$ (GRH)
3.1.1343801573410596300.118	x³ - 4238764530	\( -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 3, 3, 168]$ (GRH)
3.1.1343801573410596300.122	x³ - 2900207310	\( -\,2^{2}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}\cdot 19^{2}\cdot 23^{2} \)	$S_3$ (as 3T2)	$[3, 3, 3, 3, 3, 3, 264]$ (GRH)