Global number field search results

Further refine search

Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 12 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.0.22174929740517389369344.1	x^18 - x^16 - 4x^14 - 4x^12 + 30x^10 + 26x^8 - 72x^6 - 40x^4 + 61x^2 + 19	\( -\,2^{36}\cdot 19^{9} \)	18T185	$[2]$
18.0.91504216022104748589056.1	x^18 - 2x^17 - 4x^16 + 20x^15 + x^14 - 52x^13 + 61x^12 + 60x^11 - 61x^10 + 58x^9 + 40x^8 + 4x^7 - 6x^6 - 14x^5 + 33x^4 - 42x^3 + 33x^2 - 10x + 1	\( -\,2^{18}\cdot 11^{9}\cdot 23^{6} \)	18T185	Trivial
18.0.1672397478216599718592512.1	x^18 + 3x^16 + 18x^14 - 24x^12 - 108x^11 - 72x^10 + 28x^9 + 138x^8 + 72x^7 - 6x^6 + 48x^5 + 156x^4 + 180x^3 + 147x^2 + 84x + 31	\( -\,2^{24}\cdot 3^{25}\cdot 7^{6} \)	18T185	$[2]$
18.0.1675426071127220243892207.1	x^18 - 6x^17 + 24x^16 - 64x^15 + 117x^14 - 141x^13 + 130x^12 - 42x^11 + 15x^10 + 122x^9 - 27x^8 + 72x^7 + 83x^6 + 27x^5 + 120x^4 + 26x^3 + 48x^2 + 6x + 1	\( -\,3^{18}\cdot 7^{4}\cdot 23^{9} \)	18T185	$[4]$
18.6.45236503920434946585089589.1	x^18 - 6x^17 + 3x^16 + 49x^15 - 114x^14 + 27x^13 + 326x^12 - 720x^11 + 249x^10 + 1215x^9 - 1740x^8 + 351x^7 + 1389x^6 - 1467x^5 - 69x^4 + 869x^3 - 312x^2 - 99x + 49	\( 3^{21}\cdot 7^{4}\cdot 23^{9} \)	18T185	$[2]$ (GRH)
18.6.148074416822550528000000000.1	x^18 + 3x^16 - 24x^14 - 132x^12 - 18x^10 + 630x^8 + 316x^6 - 840x^4 + 525x^2 - 125	\( 2^{28}\cdot 3^{24}\cdot 5^{9} \)	18T185	$[2]$
18.10.472009233031319506561856000000.1	x^18 - 2x^17 - 27x^16 + 65x^15 + 283x^14 - 917x^13 - 1379x^12 + 7005x^11 + 1657x^10 - 31522x^9 + 14508x^8 + 84467x^7 - 77429x^6 - 129717x^5 + 164555x^4 + 102326x^3 - 162761x^2 - 31281x + 61141	\( 2^{12}\cdot 5^{6}\cdot 269^{9} \)	18T185	$[2]$ (GRH)
18.10.565071894936117706417730670592.1	x^18 - 9x^17 + 29x^16 - 28x^15 - 110x^14 + 546x^13 - 959x^12 + 34x^11 + 2778x^10 - 5145x^9 + 3489x^8 + 2234x^7 - 7296x^6 + 7783x^5 - 4778x^4 + 1753x^3 - 334x^2 + 12x + 4	\( 2^{12}\cdot 37^{9}\cdot 101^{6} \)	18T185	Trivial (GRH)
18.6.1830442047151925289439232000000.1	x^18 + 33x^16 + 373x^14 + 1368x^12 - 2812x^10 - 23147x^8 - 7249x^6 + 50857x^4 + 20542x^2 - 23837	\( 2^{18}\cdot 5^{6}\cdot 197^{9} \)	18T185	$[2, 2]$ (GRH)
18.6.1830442047151925289439232000000.2	x^18 - 8x^17 + 34x^16 - 150x^15 + 647x^14 - 2382x^13 + 7331x^12 - 16924x^11 + 27937x^10 - 35946x^9 + 36868x^8 - 21088x^7 - 7948x^6 + 41496x^5 - 45499x^4 + 19692x^3 + 11029x^2 - 11660x + 2425	\( 2^{18}\cdot 5^{6}\cdot 197^{9} \)	18T185	$[2]$ (GRH)
18.18.418742218942989658791871808000000.1	x^18 - 9x^17 - 9x^16 + 260x^15 - 297x^14 - 2617x^13 + 5175x^12 + 10647x^11 - 29500x^10 - 12538x^9 + 67859x^8 - 13157x^7 - 58981x^6 + 26049x^5 + 15055x^4 - 9041x^3 - 299x^2 + 700x - 85	\( 2^{12}\cdot 5^{6}\cdot 11^{4}\cdot 197^{9} \)	18T185	$[2]$ (GRH)
18.18.2314534481658338125487024826744832.1	x^18 - 6x^17 - 55x^16 + 288x^15 + 1240x^14 - 4936x^13 - 14667x^12 + 37148x^11 + 96154x^10 - 116460x^9 - 323261x^8 + 80582x^7 + 444457x^6 + 127504x^5 - 172672x^4 - 113814x^3 - 20448x^2 - 532x + 74	\( 2^{24}\cdot 37^{9}\cdot 101^{6} \)	18T185	Trivial (GRH)