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 8 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.0.44245913779931177475091.1	x^18 - x^17 - 2x^16 + 5x^15 - 4x^14 - 8x^13 + 31x^12 + 30x^11 + 6x^10 - 53x^9 - 100x^8 + 55x^7 + 124x^6 - 66x^5 + 5x^4 + 11x^3 - 6x^2 + 1	\( -\,7^{12}\cdot 14731^{3} \)	18T362	Trivial
18.6.340271260224306722157133.1	x^18 - x^17 + 3x^16 - 8x^14 + 27x^13 - 16x^12 + 10x^11 - 42x^10 - 11x^9 - 101x^8 + 105x^7 + 81x^6 - 45x^5 + 29x^4 - 6x^3 - 2x^2 + 4x - 1	\( 7^{12}\cdot 29077^{3} \)	18T362	Trivial (GRH)
18.12.11054154796697849551765939.1	x^18 - x^17 - 12x^16 + 15x^15 + 40x^14 - 82x^13 - 61x^12 + 200x^11 + 174x^10 - 275x^9 - 352x^8 + 317x^7 + 198x^6 - 178x^5 - 15x^4 + 43x^3 - 10x^2 - 4x + 1	\( -\,7^{12}\cdot 92779^{3} \)	18T362	Trivial (GRH)
18.18.2881346768906705526417803981.1	x^18 - x^17 - 27x^16 + 22x^15 + 256x^14 - 167x^13 - 1098x^12 + 558x^11 + 2290x^10 - 951x^9 - 2405x^8 + 807x^7 + 1283x^6 - 333x^5 - 327x^4 + 62x^3 + 34x^2 - 4x - 1	\( 7^{12}\cdot 592661^{3} \)	18T362	Trivial (GRH)
18.18.58793479288873825670640491661.1	x^18 - 33x^16 - 4x^15 + 387x^14 + 84x^13 - 2000x^12 - 603x^11 + 4698x^10 + 1567x^9 - 5094x^8 - 1761x^7 + 2474x^6 + 792x^5 - 531x^4 - 134x^3 + 45x^2 + 6x - 1	\( 3^{24}\cdot 592661^{3} \)	18T362	Trivial (GRH)
18.0.24684604940694766798215200273653100123.1	x^18 - 3x^17 - 212x^16 + 529x^15 + 18943x^14 - 36741x^13 - 912645x^12 + 1241272x^11 + 24954124x^10 - 19669300x^9 - 364735736x^8 + 95910807x^7 + 2159872996x^6 + 270111793x^5 + 1281634724x^4 + 3880241552x^3 + 3052031404x^2 + 1641530792x + 2131673741	\( -\,109^{12}\cdot 20627^{3} \)	18T362	$[3]$ (GRH)
18.6.17430833533433961760936249428002260688796269.1	x^18 - 616x^16 - 1089x^15 + 157899x^14 + 558714x^13 - 21067880x^12 - 114438093x^11 + 1452518286x^10 + 11579275791x^9 - 36749458486x^8 - 560572362906x^7 - 927056448710x^6 + 8490300074811x^5 + 49877012665008x^4 + 121979392650997x^3 + 159845988807863x^2 + 109980874355720x + 31988346309151	\( 17^{6}\cdot 101^{3}\cdot 307^{12} \)	18T362	Trivial (GRH)
18.12.452133353535905818128970950058166588468589916171.1	x^18 - 3x^17 - 233x^16 + 857x^15 + 22264x^14 - 95339x^13 - 1123935x^12 + 5480324x^11 + 32117323x^10 - 178749505x^9 - 514147324x^8 + 3380634011x^7 + 4197277102x^6 - 36042457633x^5 - 13016923698x^4 + 198118012009x^3 + 5836768917x^2 - 436493676409x - 141347172337	\( -\,7^{12}\cdot 14731^{9} \)	18T362	Trivial (GRH)