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 30 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.2.228289854753724432384.1	x^18 - 3x^16 + 6x^14 - 8x^12 + 8x^10 - 5x^8 + 3x^6 - x^4 + x^2 - 1	\( 2^{18}\cdot 101^{2}\cdot 292181^{2} \)	18T964	Trivial
18.2.228289854753724432384.2	x^18 + 2x^16 + 2x^14 - 3x^10 - 7x^8 - 8x^6 - 6x^4 - 3x^2 - 1	\( 2^{18}\cdot 101^{2}\cdot 292181^{2} \)	18T964	Trivial
18.6.431338652085594133521.1	x^18 - 4x^17 + 7x^16 - 13x^15 + 16x^14 + x^13 - 15x^12 + 21x^11 - 65x^10 + 69x^9 - 10x^8 - 12x^7 + 29x^6 - 61x^5 + 42x^4 + 3x^3 - 16x^2 + 7x - 1	\( 3^{4}\cdot 2307632671^{2} \)	18T964	Trivial
18.6.1937392724457335897761.1	x^18 - 2x^17 + 4x^16 - 11x^15 + 12x^14 - 27x^13 + 15x^12 - 29x^11 - 9x^10 + 3x^9 - 53x^8 + 16x^7 - 20x^6 - 32x^5 + 8x^4 - 15x^3 - 14x^2 + x + 1	\( 97^{2}\cdot 453771377^{2} \)	18T964	Trivial
18.2.3165035193944739414016.1	x^18 + 4x^16 + 4x^14 - 9x^12 - 29x^10 - 31x^8 - 12x^6 + x^4 - x^2 - 1	\( 2^{18}\cdot 367^{2}\cdot 299401^{2} \)	18T964	Trivial
18.6.3165035193944739414016.1	x^18 - 2x^16 - 4x^14 + 6x^12 + 4x^10 - 14x^8 + 22x^6 - 18x^4 + 7x^2 - 1	\( 2^{18}\cdot 367^{2}\cdot 299401^{2} \)	18T964	Trivial
18.2.3165035193944739414016.2	x^18 - 3x^16 - 3x^14 + 19x^12 - 23x^10 - x^8 + 19x^6 - 14x^4 + 5x^2 - 1	\( 2^{18}\cdot 367^{2}\cdot 299401^{2} \)	18T964	Trivial
18.6.3165035193944739414016.2	x^18 - 4x^16 + 14x^14 - 30x^12 + 50x^10 - 59x^8 + 48x^6 - 26x^4 + 8x^2 - 1	\( 2^{18}\cdot 367^{2}\cdot 299401^{2} \)	18T964	Trivial
18.10.11352034160315922565129.1	x^18 - 5x^17 + 7x^16 + 12x^15 - 49x^14 + 22x^13 + 97x^12 - 132x^11 - 48x^10 + 256x^9 - 151x^8 - 165x^7 + 222x^6 - 41x^5 - 73x^4 + 59x^3 - 7x^2 - 5x + 1	\( 11^{2}\cdot 9685993193^{2} \)	18T964	Trivial
18.10.15855320438788354657081.1	x^18 - 5x^17 + 37x^15 - 50x^14 - 54x^13 + 130x^12 - 18x^11 - 35x^10 - 49x^9 - 4x^8 + 97x^7 - 76x^6 + 43x^5 - 15x^4 + 2x^3 + 2x^2 - 4x - 1	\( 13^{2}\cdot 9685993193^{2} \)	18T964	Trivial
18.10.53977668015744910360576.1	x^18 + 3x^16 - 4x^14 - 11x^12 + 4x^10 - 4x^8 + 33x^6 - 32x^4 + 10x^2 - 1	\( 2^{18}\cdot 453771377^{2} \)	18T964	Trivial (GRH)
18.2.53977668015744910360576.1	x^18 + 6x^16 + 16x^14 + 32x^12 + 53x^10 + 61x^8 + 54x^6 + 38x^4 + 11x^2 - 1	\( 2^{18}\cdot 453771377^{2} \)	18T964	Trivial
18.6.53977668015744910360576.1	x^18 - 4x^16 + 2x^14 + 8x^12 - 12x^10 + 4x^8 - 2x^6 + 14x^4 - 11x^2 - 1	\( 2^{18}\cdot 453771377^{2} \)	18T964	Trivial
18.2.53977668015744910360576.2	x^18 + 4x^16 + 5x^14 + 6x^12 + 12x^10 + x^8 - 23x^6 - 22x^4 - 8x^2 - 1	\( 2^{18}\cdot 453771377^{2} \)	18T964	Trivial
18.10.54463704731702620585984.1	x^18 - 8x^16 + 22x^14 - 26x^12 + 20x^10 - 20x^8 + 6x^6 + 2x^4 + 5x^2 - 1	\( 2^{18}\cdot 109^{2}\cdot 4181741^{2} \)	18T964	Trivial (GRH)
18.6.119566353449087128338769.1	x^18 - 9x^17 + 44x^16 - 148x^15 + 368x^14 - 700x^13 + 1018x^12 - 1090x^11 + 745x^10 - 73x^9 - 560x^8 + 802x^7 - 612x^6 + 256x^5 - 12x^4 - 54x^3 + 33x^2 - 9x + 1	\( 7^{2}\cdot 179^{2}\cdot 2551^{2}\cdot 108179^{2} \)	18T964	Trivial
18.10.1821632477226108224536576.1	x^18 + x^16 - 14x^14 + 44x^10 - 27x^8 + 9x^6 - 21x^4 + 9x^2 - 1	\( 2^{18}\cdot 2791^{2}\cdot 944497^{2} \)	18T964	Trivial (GRH)
18.14.1821632477226108224536576.1	x^18 - 11x^16 + 40x^14 - 50x^12 - x^10 + 25x^8 + 23x^6 - 38x^4 + 13x^2 - 1	\( 2^{18}\cdot 2791^{2}\cdot 944497^{2} \)	18T964	Trivial (GRH)
18.2.1821632477226108224536576.1	x^18 + 5x^16 + 2x^14 - 21x^12 - 20x^10 + 30x^8 + 33x^6 - 14x^4 - 16x^2 - 1	\( 2^{18}\cdot 2791^{2}\cdot 944497^{2} \)	18T964	Trivial
18.6.1821632477226108224536576.1	x^18 - 8x^14 + x^12 + 23x^10 - 4x^8 - 27x^6 + 4x^4 + 10x^2 - 1	\( 2^{18}\cdot 2791^{2}\cdot 944497^{2} \)	18T964	Trivial (GRH)
18.10.1821632477226108224536576.2	x^18 - x^16 - 11x^14 + 16x^12 + 29x^10 - 61x^8 + 14x^6 + 17x^4 - 2x^2 - 1	\( 2^{18}\cdot 2791^{2}\cdot 944497^{2} \)	18T964	Trivial (GRH)
18.2.1821632477226108224536576.2	x^18 + 9x^16 + 28x^14 + 29x^12 - 13x^10 - 28x^8 + 11x^6 + 12x^4 - 5x^2 - 1	\( 2^{18}\cdot 2791^{2}\cdot 944497^{2} \)	18T964	Trivial
18.14.2047104877383620556488704.1	x^18 - 9x^16 + 32x^14 - 74x^12 + 152x^10 - 221x^8 + 180x^6 - 76x^4 + 15x^2 - 1	\( 2^{18}\cdot 23^{2}\cdot 5569^{2}\cdot 21817^{2} \)	18T964	Trivial (GRH)
18.14.24593947462164109131513856.1	x^18 - 11x^16 + 45x^14 - 80x^12 + 40x^10 + 54x^8 - 69x^6 + 17x^4 + 3x^2 - 1	\( 2^{18}\cdot 9685993193^{2} \)	18T964	Trivial (GRH)
18.14.36374607805480156224815104.1	x^18 - 9x^16 + 27x^14 - 23x^12 - 29x^10 + 54x^8 - 8x^6 - 20x^4 + 9x^2 - 1	\( 2^{18}\cdot 11779563529^{2} \)	18T964	Trivial (GRH)
18.2.36374607805480156224815104.1	x^18 + 11x^16 + 39x^14 + 29x^12 - 110x^10 - 246x^8 - 204x^6 - 81x^4 - 15x^2 - 1	\( 2^{18}\cdot 11779563529^{2} \)	18T964	Trivial
18.6.36374607805480156224815104.1	x^18 + x^16 - 20x^14 - 24x^12 + 95x^10 + 152x^8 + 22x^6 - 50x^4 - 19x^2 - 1	\( 2^{18}\cdot 11779563529^{2} \)	18T964	Trivial
18.2.36374607805480156224815104.2	x^18 + 8x^16 + 11x^14 - 70x^12 - 291x^10 - 444x^8 - 318x^6 - 108x^4 - 17x^2 - 1	\( 2^{18}\cdot 11779563529^{2} \)	18T964	Trivial
18.18.3668149136240353301118582784.1	x^18 - 20x^16 + 167x^14 - 761x^12 + 2070x^10 - 3445x^8 + 3446x^6 - 1942x^4 + 532x^2 - 49	\( 2^{18}\cdot 7^{2}\cdot 17^{2}\cdot 994046201^{2} \)	18T964	Trivial (GRH)
18.18.522206502690334026627487091405357056.1	x^18 - 204x^16 + 16830x^14 - 725390x^12 + 17608192x^10 - 242461463x^8 + 1830195673x^6 - 7048170148x^4 + 11899821517x^2 - 6975757441	\( 2^{18}\cdot 17^{10}\cdot 994046201^{2} \)	18T964	$[2]$ (GRH)