LMFDB - Global number field search results

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Results (displaying all 33 matches)

Label	Polynomial	Discriminant	Galois group	Class group
1.1.1.1	x	$ 1 $	Trivial (as 1T1)	Trivial
2.2.5.1	x² - x - 1	$ 5 $	$C_2$ (as 2T1)	Trivial
2.2.8.1	x² - 2	$ 2^{3} $	$C_2$ (as 2T1)	Trivial
2.2.12.1	x² - 3	$ 2^{2}\cdot 3 $	$C_2$ (as 2T1)	Trivial
2.2.13.1	x² - x - 3	$ 13 $	$C_2$ (as 2T1)	Trivial
2.2.17.1	x² - x - 4	$ 17 $	$C_2$ (as 2T1)	Trivial
2.2.21.1	x² - x - 5	$ 3\cdot 7 $	$C_2$ (as 2T1)	Trivial
2.2.24.1	x² - 6	$ 2^{3}\cdot 3 $	$C_2$ (as 2T1)	Trivial
2.2.28.1	x² - 7	$ 2^{2}\cdot 7 $	$C_2$ (as 2T1)	Trivial
2.2.29.1	x² - x - 7	$ 29 $	$C_2$ (as 2T1)	Trivial
2.2.33.1	x² - x - 8	$ 3\cdot 11 $	$C_2$ (as 2T1)	Trivial
2.2.37.1	x² - x - 9	$ 37 $	$C_2$ (as 2T1)	Trivial
2.2.40.1	x² - 10	$ 2^{3}\cdot 5 $	$C_2$ (as 2T1)	$[2]$
2.2.41.1	x² - x - 10	$ 41 $	$C_2$ (as 2T1)	Trivial
2.2.44.1	x² - 11	$ 2^{2}\cdot 11 $	$C_2$ (as 2T1)	Trivial
2.2.53.1	x² - x - 13	$ 53 $	$C_2$ (as 2T1)	Trivial
2.2.56.1	x² - 14	$ 2^{3}\cdot 7 $	$C_2$ (as 2T1)	Trivial
2.2.57.1	x² - x - 14	$ 3\cdot 19 $	$C_2$ (as 2T1)	Trivial
2.2.60.1	x² - 15	$ 2^{2}\cdot 3\cdot 5 $	$C_2$ (as 2T1)	$[2]$
2.2.61.1	x² - x - 15	$ 61 $	$C_2$ (as 2T1)	Trivial
2.2.65.1	x² - x - 16	$ 5\cdot 13 $	$C_2$ (as 2T1)	$[2]$
2.2.69.1	x² - x - 17	$ 3\cdot 23 $	$C_2$ (as 2T1)	Trivial
2.2.73.1	x² - x - 18	$ 73 $	$C_2$ (as 2T1)	Trivial
2.2.76.1	x² - 19	$ 2^{2}\cdot 19 $	$C_2$ (as 2T1)	Trivial
2.2.77.1	x² - x - 19	$ 7\cdot 11 $	$C_2$ (as 2T1)	Trivial
2.2.85.1	x² - x - 21	$ 5\cdot 17 $	$C_2$ (as 2T1)	$[2]$
2.2.88.1	x² - 22	$ 2^{3}\cdot 11 $	$C_2$ (as 2T1)	Trivial
2.2.89.1	x² - x - 22	$ 89 $	$C_2$ (as 2T1)	Trivial
2.2.92.1	x² - 23	$ 2^{2}\cdot 23 $	$C_2$ (as 2T1)	Trivial
2.2.93.1	x² - x - 23	$ 3\cdot 31 $	$C_2$ (as 2T1)	Trivial
2.2.97.1	x² - x - 24	$ 97 $	$C_2$ (as 2T1)	Trivial
3.3.49.1	x³ - x² - 2x + 1	$ 7^{2} $	$C_3$ (as 3T1)	Trivial
3.3.81.1	x³ - 3x - 1	$ 3^{4} $	$C_3$ (as 3T1)	Trivial

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Further refine search

Results (displaying all 33 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
1.1.1.1	x	\( 1 \)	Trivial (as 1T1)	Trivial
2.2.5.1	x² - x - 1	\( 5 \)	$C_2$ (as 2T1)	Trivial
2.2.8.1	x² - 2	\( 2^{3} \)	$C_2$ (as 2T1)	Trivial
2.2.12.1	x² - 3	\( 2^{2}\cdot 3 \)	$C_2$ (as 2T1)	Trivial
2.2.13.1	x² - x - 3	\( 13 \)	$C_2$ (as 2T1)	Trivial
2.2.17.1	x² - x - 4	\( 17 \)	$C_2$ (as 2T1)	Trivial
2.2.21.1	x² - x - 5	\( 3\cdot 7 \)	$C_2$ (as 2T1)	Trivial
2.2.24.1	x² - 6	\( 2^{3}\cdot 3 \)	$C_2$ (as 2T1)	Trivial
2.2.28.1	x² - 7	\( 2^{2}\cdot 7 \)	$C_2$ (as 2T1)	Trivial
2.2.29.1	x² - x - 7	\( 29 \)	$C_2$ (as 2T1)	Trivial
2.2.33.1	x² - x - 8	\( 3\cdot 11 \)	$C_2$ (as 2T1)	Trivial
2.2.37.1	x² - x - 9	\( 37 \)	$C_2$ (as 2T1)	Trivial
2.2.40.1	x² - 10	\( 2^{3}\cdot 5 \)	$C_2$ (as 2T1)	$[2]$
2.2.41.1	x² - x - 10	\( 41 \)	$C_2$ (as 2T1)	Trivial
2.2.44.1	x² - 11	\( 2^{2}\cdot 11 \)	$C_2$ (as 2T1)	Trivial
2.2.53.1	x² - x - 13	\( 53 \)	$C_2$ (as 2T1)	Trivial
2.2.56.1	x² - 14	\( 2^{3}\cdot 7 \)	$C_2$ (as 2T1)	Trivial
2.2.57.1	x² - x - 14	\( 3\cdot 19 \)	$C_2$ (as 2T1)	Trivial
2.2.60.1	x² - 15	\( 2^{2}\cdot 3\cdot 5 \)	$C_2$ (as 2T1)	$[2]$
2.2.61.1	x² - x - 15	\( 61 \)	$C_2$ (as 2T1)	Trivial
2.2.65.1	x² - x - 16	\( 5\cdot 13 \)	$C_2$ (as 2T1)	$[2]$
2.2.69.1	x² - x - 17	\( 3\cdot 23 \)	$C_2$ (as 2T1)	Trivial
2.2.73.1	x² - x - 18	\( 73 \)	$C_2$ (as 2T1)	Trivial
2.2.76.1	x² - 19	\( 2^{2}\cdot 19 \)	$C_2$ (as 2T1)	Trivial
2.2.77.1	x² - x - 19	\( 7\cdot 11 \)	$C_2$ (as 2T1)	Trivial
2.2.85.1	x² - x - 21	\( 5\cdot 17 \)	$C_2$ (as 2T1)	$[2]$
2.2.88.1	x² - 22	\( 2^{3}\cdot 11 \)	$C_2$ (as 2T1)	Trivial
2.2.89.1	x² - x - 22	\( 89 \)	$C_2$ (as 2T1)	Trivial
2.2.92.1	x² - 23	\( 2^{2}\cdot 23 \)	$C_2$ (as 2T1)	Trivial
2.2.93.1	x² - x - 23	\( 3\cdot 31 \)	$C_2$ (as 2T1)	Trivial
2.2.97.1	x² - x - 24	\( 97 \)	$C_2$ (as 2T1)	Trivial
3.3.49.1	x³ - x² - 2x + 1	\( 7^{2} \)	$C_3$ (as 3T1)	Trivial
3.3.81.1	x³ - 3x - 1	\( 3^{4} \)	$C_3$ (as 3T1)	Trivial