Global number field search results

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

Results (displaying all 20 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.12.6755077431611414576088768.1	x^18 - 15x^16 + 72x^14 - 93x^12 - 225x^10 + 675x^8 - 297x^6 - 378x^4 + 162x^2 + 27	\( -\,2^{6}\cdot 3^{27}\cdot 7^{12} \)	18T263	Trivial (GRH)
18.12.16012035393449278995173376.1	x^18 - 9x^16 + 18x^14 + 53x^12 - 273x^10 + 417x^8 - 239x^6 + 6x^4 + 24x^2 + 1	\( -\,2^{12}\cdot 3^{24}\cdot 7^{12} \)	18T263	Trivial (GRH)
18.4.16012035393449278995173376.1	x^18 + 12x^16 + 36x^14 - 19x^12 - 159x^10 - 117x^8 + 43x^6 + 60x^4 + 15x^2 + 1	\( -\,2^{12}\cdot 3^{24}\cdot 7^{12} \)	18T263	Trivial
18.4.16012035393449278995173376.2	x^18 + 3x^16 - 24x^14 - 97x^12 + 51x^10 + 669x^8 + 1077x^6 + 684x^4 + 156x^2 + 1	\( -\,2^{12}\cdot 3^{24}\cdot 7^{12} \)	18T263	Trivial
18.6.128096283147594231961387008.1	x^18 + 6x^16 - 46x^12 - 45x^10 + 78x^8 + 93x^6 - 30x^4 - 48x^2 - 8	\( 2^{15}\cdot 3^{24}\cdot 7^{12} \)	18T263	Trivial (GRH)
18.6.128096283147594231961387008.2	x^18 + 3x^16 - 21x^14 - 109x^12 - 159x^10 - 33x^8 + 93x^6 + 48x^4 - 12x^2 - 8	\( 2^{15}\cdot 3^{24}\cdot 7^{12} \)	18T263	Trivial (GRH)
18.10.268299605528119179177846592.1	x^18 - 4x^17 - 5x^16 + 34x^15 - 14x^14 - 53x^13 - 11x^12 + 41x^11 + 376x^10 - 880x^9 + 489x^8 + 1076x^7 - 2314x^6 + 1391x^5 + 511x^4 - 876x^3 + 267x^2 - 29x + 1	\( 2^{6}\cdot 7^{12}\cdot 13^{13} \)	18T263	Trivial (GRH)
18.14.268299605528119179177846592.1	x^18 - x^17 - 25x^16 + 17x^15 + 228x^14 - 173x^13 - 1064x^12 + 1010x^11 + 2757x^10 - 3247x^9 - 3776x^8 + 5614x^7 + 2042x^6 - 4766x^5 + 376x^4 + 1471x^3 - 428x^2 - 29x + 1	\( 2^{6}\cdot 7^{12}\cdot 13^{13} \)	18T263	Trivial (GRH)
18.14.432324955623130532869681152.1	x^18 - 6x^16 - 18x^14 + 195x^12 - 369x^10 - 297x^8 + 1611x^6 - 1566x^4 + 405x^2 - 27	\( 2^{12}\cdot 3^{27}\cdot 7^{12} \)	18T263	Trivial (GRH)
18.12.532067895824267826219741867.1	x^18 - 6x^17 - 3x^16 + 80x^15 - 63x^14 - 558x^13 + 1007x^12 + 1614x^11 - 5415x^10 + 93x^9 + 12687x^8 - 9180x^7 - 12972x^6 + 17313x^5 + 4263x^4 - 13241x^3 + 648x^2 + 4173x + 127	\( -\,3^{27}\cdot 7^{12}\cdot 71^{2} \)	18T263	Trivial (GRH)
18.12.1399141503834185765244506391.1	x^18 - 18x^16 - 10x^15 + 84x^14 + 147x^13 - 308x^12 - 216x^11 + 1626x^10 - 1979x^9 - 3810x^8 + 6918x^7 + 2232x^6 - 6987x^5 + 198x^4 + 2619x^3 - 264x^2 - 303x - 1	\( -\,3^{24}\cdot 7^{12}\cdot 71^{3} \)	18T263	Trivial (GRH)
18.8.1399141503834185765244506391.1	x^18 - 8x^15 - 39x^14 - 30x^13 - 59x^12 + 369x^11 - 75x^10 + 2212x^9 - 3813x^8 - 1536x^7 + 3116x^6 - 1506x^5 + 7647x^4 - 9349x^3 + 2397x^2 + 1203x - 503	\( -\,3^{24}\cdot 7^{12}\cdot 71^{3} \)	18T263	Trivial (GRH)
18.8.1399141503834185765244506391.2	x^18 - 6x^17 + 3x^16 + 47x^15 - 138x^14 + 174x^13 + 36x^12 - 723x^11 + 1551x^10 - 2113x^9 + 1890x^8 - 459x^7 - 732x^6 + 2064x^5 - 1920x^4 + 1399x^3 - 690x^2 + 129x - 1	\( -\,3^{24}\cdot 7^{12}\cdot 71^{3} \)	18T263	Trivial (GRH)
18.10.17171174753799627467382181888.1	x^18 - 3x^16 - 148x^14 + 41x^12 + 1023x^10 + 113x^8 - 1175x^6 + 442x^4 + 26x^2 - 13	\( 2^{12}\cdot 7^{12}\cdot 13^{13} \)	18T263	Trivial (GRH)
18.6.29887202898467161742960366013.1	x^18 - 6x^17 + 18x^16 - 12x^15 - 120x^14 + 531x^13 - 1152x^12 + 1857x^11 - 477x^10 - 1626x^9 + 6816x^8 - 5754x^7 - 7941x^6 + 7392x^5 - 7617x^4 - 12980x^3 + 7359x^2 + 6405x - 631	\( 3^{24}\cdot 7^{12}\cdot 197^{3} \)	18T263	Trivial (GRH)
18.6.29887202898467161742960366013.2	x^18 - 6x^17 + 12x^16 + 24x^15 - 201x^14 + 681x^13 - 2006x^12 + 4443x^11 - 4875x^10 - 2843x^9 + 8115x^8 + 2994x^7 - 3033x^6 + 4443x^5 + 2862x^4 + 1442x^3 - 2457x^2 + 162x + 71	\( 3^{24}\cdot 7^{12}\cdot 197^{3} \)	18T263	Trivial (GRH)
18.0.5165866906776180186538815258624.1	x^18 + 36x^16 + 525x^14 + 4014x^12 + 17550x^10 + 45426x^8 + 69728x^6 + 61395x^4 + 28116x^2 + 5041	\( -\,2^{18}\cdot 3^{24}\cdot 7^{12}\cdot 71^{2} \)	18T263	$[2, 2, 2, 160]$ (GRH)
18.0.16528519607100378938441688416256.1	x^18 + 57x^16 + 1314x^14 + 15789x^12 + 106527x^10 + 406209x^8 + 836429x^6 + 820710x^4 + 272034x^2 + 16129	\( -\,2^{18}\cdot 3^{24}\cdot 7^{12}\cdot 127^{2} \)	18T263	$[2, 2, 2, 252]$ (GRH)
18.18.139478406482956865036548011982848.1	x^18 - 60x^16 + 1503x^14 - 20397x^12 + 162603x^10 - 770526x^8 + 2085012x^6 - 2889297x^4 + 1593027x^2 - 136107	\( 2^{18}\cdot 3^{27}\cdot 7^{12}\cdot 71^{2} \)	18T263	Trivial (GRH)
18.18.139478406482956865036548011982848.2	x^18 - 63x^16 + 1269x^14 - 12825x^12 + 75375x^10 - 271809x^8 + 602928x^6 - 786564x^4 + 534843x^2 - 136107	\( 2^{18}\cdot 3^{27}\cdot 7^{12}\cdot 71^{2} \)	18T263	Trivial (GRH)