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
18.6.131792047867311076441.1	x^18 - 7x^16 - 4x^15 + 21x^14 + 21x^13 - 29x^12 - 49x^11 + 14x^10 + 63x^9 + 14x^8 - 49x^7 - 29x^6 + 21x^5 + 21x^4 - 4x^3 - 7x^2 + 1	\( 7^{12}\cdot 97579^{2} \)	18T703	Trivial (GRH)
18.6.212093107812829398169.1	x^18 - 2x^17 + x^16 - 5x^15 + 4x^14 + 2x^13 + 4x^12 + 5x^11 - 10x^10 + x^9 - 10x^8 + 5x^7 + 4x^6 + 2x^5 + 4x^4 - 5x^3 + x^2 - 2x + 1	\( 7^{12}\cdot 123787^{2} \)	18T703	Trivial (GRH)
18.6.263750124729014300881.1	x^18 - 4x^16 - x^15 + 6x^14 + 5x^13 - 6x^12 - 10x^11 + 3x^10 + 11x^9 + 3x^8 - 10x^7 - 6x^6 + 5x^5 + 6x^4 - x^3 - 4x^2 + 1	\( 7^{12}\cdot 138041^{2} \)	18T703	Trivial (GRH)
18.6.347202338514706980361.1	x^18 - x^17 - 5x^16 + 10x^15 + 14x^14 - 30x^13 - 30x^12 + 35x^11 + 29x^10 - 28x^9 - 3x^8 + 28x^7 - 16x^6 - 22x^5 + 14x^4 + 10x^3 - 6x^2 - 2x + 1	\( 7^{12}\cdot 251^{2}\cdot 631^{2} \)	18T703	Trivial
18.6.397461902755541307649.1	x^18 - 2x^17 - 3x^16 + 11x^15 - 9x^14 - 7x^13 + 22x^12 - 14x^11 - 11x^10 + 25x^9 - 11x^8 - 14x^7 + 22x^6 - 7x^5 - 9x^4 + 11x^3 - 3x^2 - 2x + 1	\( 7^{12}\cdot 169457^{2} \)	18T703	Trivial (GRH)
18.6.811666663658785884481.1	x^18 - x^17 - 5x^16 + 5x^15 + 8x^14 - 16x^13 + 3x^12 + 40x^11 - 32x^10 - 63x^9 + 62x^8 + 76x^7 - 63x^6 - 64x^5 + 15x^4 - x^3 - 11x^2 + 2x + 1	\( 7^{12}\cdot 113^{2}\cdot 2143^{2} \)	18T703	Trivial (GRH)
18.6.1689720307611555768409.1	x^18 - x^17 - 5x^16 + 3x^15 + 13x^14 - 8x^13 - 26x^12 + 35x^11 + 14x^10 - 67x^9 + 42x^8 + 42x^7 - 68x^6 + 5x^5 + 38x^4 - 11x^3 - 10x^2 + 3x + 1	\( 7^{12}\cdot 349397^{2} \)	18T703	Trivial
18.6.6588165551501521267641.1	x^18 - 3x^17 - 6x^16 + 30x^15 - 3x^14 - 108x^13 + 88x^12 + 180x^11 - 234x^10 - 152x^9 + 291x^8 + 72x^7 - 218x^6 - 15x^5 + 102x^4 - 6x^3 - 18x^2 - 3x + 1	\( 3^{24}\cdot 163^{2}\cdot 937^{2} \)	18T703	Trivial
18.10.57388858189268996325376.1	x^18 - 8x^16 + 19x^14 - 4x^12 - 27x^10 + x^8 + 27x^6 - 9x^4 - 1	\( 2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2} \)	18T703	Trivial (GRH)
18.10.57388858189268996325376.2	x^18 - 7x^16 + 21x^14 - 41x^12 + 49x^10 - 28x^8 + 12x^6 - 14x^4 + 7x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2} \)	18T703	Trivial (GRH)
18.10.66983486784702356675569.1	x^18 - 4x^17 + 8x^15 - 3x^14 + 6x^13 + 14x^12 - 18x^11 - 59x^10 - 26x^9 + 69x^8 + 92x^7 + 23x^6 - 67x^5 - 69x^4 - x^3 + 23x^2 + 9x + 1	\( 7^{12}\cdot 97^{2}\cdot 22679^{2} \)	18T703	Trivial (GRH)
18.10.173460040503181804605289.1	x^18 - 4x^17 + x^16 + x^15 + 23x^14 + 6x^13 - 75x^12 - 10x^11 + 39x^10 + 124x^9 - 36x^8 - 145x^7 + 75x^6 + 12x^5 - 43x^4 + 15x^3 + 12x^2 - 2x - 1	\( 7^{12}\cdot 3540067^{2} \)	18T703	Trivial (GRH)
18.10.2481624923575295556989329.1	x^18 - 5x^17 + 2x^16 + 35x^15 - 100x^14 + 110x^13 + 36x^12 - 251x^11 + 134x^10 + 541x^9 - 1211x^8 + 1012x^7 - 39x^6 - 569x^5 + 336x^4 + 14x^3 - 62x^2 + 16x - 1	\( 7^{12}\cdot 97^{2}\cdot 138041^{2} \)	18T703	Trivial (GRH)
18.10.2670257724509390156868609.1	x^18 - 3x^17 - 9x^16 + 28x^15 + 30x^14 - 90x^13 - 32x^12 + 108x^11 - 57x^10 - 58x^9 + 102x^8 + 33x^7 - 24x^6 - 48x^5 + 9x^4 + 48x^3 - 9x^2 - 9x - 1	\( 3^{24}\cdot 73^{4}\cdot 577^{2} \)	18T703	Trivial (GRH)
18.14.4627653845488381463962761.1	x^18 - 15x^16 - 15x^15 + 54x^14 + 114x^13 - 32x^12 - 327x^11 - 102x^10 + 457x^9 + 102x^8 - 327x^7 + 32x^6 + 114x^5 - 54x^4 - 15x^3 + 15x^2 - 1	\( 3^{24}\cdot 199^{2}\cdot 20341^{2} \)	18T703	Trivial (GRH)
18.14.10145719923049728269615104.1	x^18 - 12x^16 + 54x^14 - 117x^12 + 134x^10 - 99x^8 + 73x^6 - 44x^4 + 12x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 52879^{2} \)	18T703	Trivial (GRH)
18.14.65162373998603777427181329.1	x^18 - 3x^17 - 9x^16 + 42x^15 - 9x^14 - 174x^13 + 244x^12 + 207x^11 - 702x^10 + 152x^9 + 813x^8 - 489x^7 - 397x^6 + 342x^5 + 54x^4 - 84x^3 + 6x^2 + 6x - 1	\( 3^{24}\cdot 15189497^{2} \)	18T703	Trivial (GRH)
18.14.104192253035948620552339456.1	x^18 - 7x^16 + x^14 + 85x^12 - 226x^10 + 220x^8 - 66x^6 - 17x^4 + 11x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 169457^{2} \)	18T703	Trivial (GRH)
18.18.104192253035948620552339456.1	x^18 - 17x^16 + 114x^14 - 389x^12 + 728x^10 - 758x^8 + 433x^6 - 131x^4 + 19x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 169457^{2} \)	18T703	Trivial (GRH)
18.18.1373804974140802360768493281.1	x^18 - 9x^17 + 16x^16 + 76x^15 - 296x^14 + 28x^13 + 1181x^12 - 1340x^11 - 1305x^10 + 3126x^9 - 756x^8 - 2054x^7 + 1651x^6 - 80x^5 - 370x^4 + 141x^3 - 3x^2 - 7x + 1	\( 7^{12}\cdot 71^{2}\cdot 281^{2}\cdot 15791^{2} \)	18T703	Trivial (GRH)